Author: saqibkhan

Gradient Boosting
Gradient Boosting Machines (GBM) is a powerful machine learning technique that is widely used for building predictive models. It is a type of ensemble method that combines the predictions of multiple weaker models to create a stronger and more accurate model.

GBM is a popular choice for a wide range of applications, including regression, classification, and ranking problems. Let’s understand the workings of GBM and how it can be used in machine learning.

What is a Gradient Boosting Machine (GBM)?

GBM is an iterative machine learning algorithm that combines the predictions of multiple decision trees to make a final prediction.

The algorithm works by training a sequence of decision trees, each of which is designed to correct the errors of the previous tree.

In each iteration, the algorithm identifies the samples in the dataset that are most difficult to predict and focuses on improving the model’s performance on these samples.

This is achieved by fitting a new decision tree that is optimized to reduce the errors on the difficult samples. The process continues until a specified stopping criteria is met, such as reaching a certain level of accuracy or the maximum number of iterations.

How Does a Gradient Boosting Machine Work?

The basic steps involved in training a GBM model are as follows −
- Initialize the model − The algorithm starts by creating a simple model, such as a single decision tree, to serve as the initial model.
- Calculate residuals − The initial model is used to make predictions on the training data, and the residuals are calculated as the differences between the predicted values and the actual values.
- Train a new model − A new decision tree is trained on the residuals, with the goal of minimizing the errors on the difficult samples.
- Update the model − The predictions of the new model are added to the predictions of the previous model, and the residuals are recalculated based on the updated predictions.
- Repeat − Steps 3-4 are repeated until a specified stopping criteria is met.
GBM can be further improved by introducing regularization techniques, such as L1 and L2 regularization, to prevent overfitting. Additionally, GBM can be extended to handle categorical variables, missing data, and multi-class classification problems.

Example

Here is an example of implementing GBM using the Sklearn breast cancer dataset −
```
from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.metrics import accuracy_score

# Load the breast cancer dataset
data = load_breast_cancer()
X = data.data
y = data.target

# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)# Train the model using GradientBoostingClassifier
model = GradientBoostingClassifier(n_estimators=100, max_depth=3, learning_rate=0.1)
model.fit(X_train, y_train)# Make predictions on the testing set
y_pred = model.predict(X_test)# Evaluate the model's accuracy
accuracy = accuracy_score(y_test, y_pred)print("Accuracy:", accuracy)
```
Output

In this example, we load the breast cancer dataset using Sklearn’s load_breast_cancer function and split it into training and testing sets. We then define the parameters for the GBM model using GradientBoostingClassifier, including the number of estimators (i.e., the number of decision trees), the maximum depth of each decision tree, and the learning rate.

We train the GBM model using the fit method and make predictions on the testing set using the predict method. Finally, we evaluate the model’s accuracy using the accuracy_score function from Sklearn’s metrics module.

When you execute this code, it will produce the following output −
```
Accuracy: 0.956140350877193
```
Advantages of Using Gradient Boosting Machines

There are several advantages of using GBM in machine learning −
- High accuracy − GBM is known for its high accuracy, as it combines the predictions of multiple weaker models to create a stronger and more accurate model.
- Robustness − GBM is robust to outliers and noisy data, as it focuses on improving the model’s performance on the most difficult samples.
- Flexibility − GBM can be used for a wide range of applications, including regression, classification, and ranking problems.
- Interpretability − GBM provides insights into the importance of different features in making predictions, which can be useful for understanding the underlying factors driving the predictions.
- Scalability − GBM can handle large datasets and can be parallelized to accelerate the training process.
Limitations of Gradient Boosting Machines

There are also some limitations to using GBM in machine learning −
- Training time − GBM can be computationally expensive and may require a significant amount of training time, especially when working with large datasets.
- Hyperparameter tuning − GBM requires careful tuning of hyperparameters, such as the learning rate, number of trees, and maximum depth, to achieve optimal performance.
- Black box model − GBM can be difficult to interpret, as the final model is a combination of multiple decision trees and may not provide clear insights into the underlying factors driving the predictions.
October 4, 2025
Boost Model Performance
Boosting is a popular ensemble learning technique that combines several weak learners to create a strong learner. It works by iteratively training weak learners on subsets of the data and assigning higher weights to the misclassified samples to increase their importance in the subsequent iterations. This process is repeated until the desired level of performance is achieved.

Here are some techniques to boost model performance in machine learning −
- Feature Engineering − Feature engineering involves creating new features from the existing features or transforming the existing features to make them more informative for the model. This can include techniques such as one-hot encoding, scaling, normalization, and feature selection.
- Hyperparameter Tuning − Hyperparameters are parameters that are not learned during training but are set by the data scientist. They control the behavior of the model, and tuning them can significantly impact model performance. Grid search and randomized search are common techniques for hyperparameter tuning.
- Ensemble Learning − Ensemble learning involves combining multiple models to improve performance. Techniques such as bagging, boosting, and stacking can be used to create ensembles. Random forests are an example of a bagging ensemble, while gradient boosting machines (GBMs) are an example of a boosting ensemble.
- Regularization − Regularization is a technique that prevents overfitting by adding a penalty term to the loss function. L1 regularization (Lasso) and L2 regularization (Ridge) are common techniques used in linear models, while dropout is a technique used in neural networks.
- Data Augmentation − Data augmentation involves generating new data from the existing data by applying transformations such as rotation, scaling, and flipping. This can help to reduce overfitting and improve model performance.
- Model Architecture − The architecture of the model can significantly impact its performance. Techniques such as deep learning and convolutional neural networks (CNNs) can be used to create more complex models that are better able to learn complex patterns in the data.
- Early Stopping − Early stopping is a technique used to prevent overfitting by stopping the training process once the model performance stops improving on a validation set. This prevents the model from continuing to learn the noise in the data and can help to improve generalization.
- Cross-Validation − Cross-validation is a technique used to evaluate the performance of a model on multiple subsets of the data. This can help to identify overfitting and can be used to select the best hyperparameters for the model.
These techniques can be implemented in Python using various machine learning libraries such as scikit-learn, TensorFlow, and Keras. By using these techniques, data scientists can improve the performance of their models and create more accurate predictions.

The following example below in which implement cross-validation using Scikit-learn −

Example
```
from sklearn.datasets import load_iris
from sklearn.model_selection import cross_val_score
from sklearn.ensemble import GradientBoostingClassifier

# Load the iris dataset
iris = load_iris()
X = iris.data
y = iris.target

# Create a Gradient Boosting Classifier
gb_clf = GradientBoostingClassifier()# Perform 5-fold cross-validation on the classifier
scores = cross_val_score(gb_clf, X, y, cv=5)# Print the average accuracy and standard deviation of the cross-validation scoresprint("Accuracy: %0.2f (+/- %0.2f)"%(scores.mean(), scores.std()*2))
```
Output

When you execute this code, it will produce the following output −
```
Accuracy: 0.96 (+/- 0.07)
```
Performance Improvement with Ensembles

Ensembles can give us boost in the machine learning result by combining several models. Basically, ensemble models consist of several individually trained supervised learning models and their results are merged in various ways to achieve better predictive performance compared to a single model. Ensemble methods can be divided into following two groups −

Sequential ensemble methods

As the name implies, in these kind of ensemble methods, the base learners are generated sequentially. The motivation of such methods is to exploit the dependency among base learners.

Parallel ensemble methods

As the name implies, in these kind of ensemble methods, the base learners are generated in parallel. The motivation of such methods is to exploit the independence among base learners.

Ensemble Learning Methods

The following are the most popular ensemble learning methods i.e. the methods for combining the predictions from different models −

Bagging

The term bagging is also known as bootstrap aggregation. In bagging methods, ensemble model tries to improve prediction accuracy and decrease model variance by combining predictions of individual models trained over randomly generated training samples. The final prediction of ensemble model will be given by calculating the average of all predictions from the individual estimators. One of the best examples of bagging methods are random forests.

Boosting

In boosting method, the main principle of building ensemble model is to build it incrementally by training each base model estimator sequentially. As the name suggests, it basically combine several week base learners, trained sequentially over multiple iterations of training data, to build powerful ensemble. During the training of week base learners, higher weights are assigned to those learners which were misclassified earlier. The example of boosting method is AdaBoost.

Voting

In this ensemble learning model, multiple models of different types are built and some simple statistics, like calculating mean or median etc., are used to combine the predictions. This prediction will serve as the additional input for training to make the final prediction.

Bagging Ensemble Algorithms

The following are three bagging ensemble algorithms −

Bagged Decision Tree

As we know that bagging ensemble methods work well with the algorithms that have high variance and, in this concern, the best one is decision tree algorithm. In the following Python recipe, we are going to build bagged decision tree ensemble model by using BaggingClassifier function of sklearn with DecisionTreeClasifier (a classification & regression trees algorithm) on Pima Indians diabetes dataset.

First, import the required packages as follows −
```
from pandas import read_csv
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
from sklearn.ensemble import BaggingClassifier
from sklearn.tree import DecisionTreeClassifier
```
Now, we need to load the Pima diabetes dataset as we did in the previous examples −
```
path =r"C:\pima-indians-diabetes.csv"
headernames =['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
array = data.values
X = array[:,0:8]
Y = array[:,8]
```
Next, give the input for 10-fold cross validation as follows −
```
seed =7
kfold = KFold(n_splits=10, random_state=seed)
cart = DecisionTreeClassifier()
```
We need to provide the number of trees we are going to build. Here we are building 150 trees −
```
num_trees =150
```
Next, build the model with the help of following script −
```
model = BaggingClassifier(base_estimator=cart, n_estimators=num_trees, random_state=seed)
```
Calculate and print the result as follows −
```
results = cross_val_score(model, X, Y, cv=kfold)print(results.mean())
```
Output
```
0.7733766233766234
```
The output above shows that we got around 77% accuracy of our bagged decision tree classifier model.

Random Forest

It is an extension of bagged decision trees. For individual classifiers, the samples of training dataset are taken with replacement, but the trees are constructed in such a way that reduces the correlation between them. Also, a random subset of features is considered to choose each split point rather than greedily choosing the best split point in construction of each tree.

In the following Python recipe, we are going to build bagged random forest ensemble model by using RandomForestClassifier class of sklearn on Pima Indians diabetes dataset.

First, import the required packages as follows −
```
from pandas import read_csv
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
from sklearn.ensemble import RandomForestClassifier
```
Now, we need to load the Pima diabetes dataset as did in previous examples −
```
path =r"C:\pima-indians-diabetes.csv"
headernames =['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
array = data.values
X = array[:,0:8]
Y = array[:,8]
```
Next, give the input for 10-fold cross validation as follows −
```
seed =7
kfold = KFold(n_splits=10, random_state=seed)
```
We need to provide the number of trees we are going to build. Here we are building 150 trees with split points chosen from 5 features −
```
num_trees =150
max_features =5
```
Next, build the model with the help of following script −
```
model = RandomForestClassifier(n_estimators=num_trees, max_features=max_features)
```
Calculate and print the result as follows −
```
results = cross_val_score(model, X, Y, cv=kfold)print(results.mean())
```
Output
```
0.7629357484620642
```
The output above shows that we got around 76% accuracy of our bagged random forest classifier model.

Extra Trees

It is another extension of bagged decision tree ensemble method. In this method, the random trees are constructed from the samples of the training dataset.

In the following Python recipe, we are going to build extra tree ensemble model by using ExtraTreesClassifier class of sklearn on Pima Indians diabetes dataset.

First, import the required packages as follows −
```
from pandas import read_csv
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
from sklearn.ensemble import ExtraTreesClassifier
```
Now, we need to load the Pima diabetes dataset as did in previous examples −
```
path =r"C:\pima-indians-diabetes.csv"
headernames =['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
array = data.values
X = array[:,0:8]
Y = array[:,8]
```
Next, give the input for 10-fold cross validation as follows −
```
seed =7
kfold = KFold(n_splits=10, random_state=seed)
```
We need to provide the number of trees we are going to build. Here we are building 150 trees with split points chosen from 5 features −
```
num_trees =150
max_features =5
```
Next, build the model with the help of following script −
```
model = ExtraTreesClassifier(n_estimators=num_trees, max_features=max_features)
```
Calculate and print the result as follows −
```
results = cross_val_score(model, X, Y, cv=kfold)print(results.mean())
```
Output
```
0.7551435406698566
```
The output above shows that we got around 75.5% accuracy of our bagged extra trees classifier model.

Boosting Ensemble Algorithms

The followings are the two most common boosting ensemble algorithms −

AdaBoost

It is one the most successful boosting ensemble algorithm. The main key of this algorithm is in the way they give weights to the instances in dataset. Due to this the algorithm needs to pay less attention to the instances while constructing subsequent models.

In the following Python recipe, we are going to build Ada Boost ensemble model for classification by using AdaBoostClassifier class of sklearn on Pima Indians diabetes dataset.

First, import the required packages as follows −
```
from pandas import read_csv
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
from sklearn.ensemble import AdaBoostClassifier
```
Now, we need to load the Pima diabetes dataset as did in previous examples −
```
path =r"C:\pima-indians-diabetes.csv"
headernames =['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
array = data.values
X = array[:,0:8]
Y = array[:,8]
```
Next, give the input for 10-fold cross validation as follows −
```
seed =5
kfold = KFold(n_splits=10, random_state=seed)
```
We need to provide the number of trees we are going to build. Here we are building 150 trees with split points chosen from 5 features −
```
num_trees =50
```
Next, build the model with the help of following script −
```
model = AdaBoostClassifier(n_estimators=num_trees, random_state=seed)
```
Calculate and print the result as follows −
```
results = cross_val_score(model, X, Y, cv=kfold)print(results.mean())
```
Output
```
0.7539473684210527
```
The output above shows that we got around 75% accuracy of our AdaBoost classifier ensemble model.

Stochastic Gradient Boosting

It is also called Gradient Boosting Machines. In the following Python recipe, we are going to build Stochastic Gradient Boostingensemble model for classification by using GradientBoostingClassifier class of sklearn on Pima Indians diabetes dataset.

First, import the required packages as follows −
```
from pandas import read_csv
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
from sklearn.ensemble import GradientBoostingClassifier
```
Now, we need to load the Pima diabetes dataset as did in previous examples −
```
path =r"C:\pima-indians-diabetes.csv"
headernames =['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
array = data.values
X = array[:,0:8]
Y = array[:,8]
```
Next, give the input for 10-fold cross validation as follows −
```
seed =5
kfold = KFold(n_splits=10, random_state=seed)
```
We need to provide the number of trees we are going to build. Here we are building 150 trees with split points chosen from 5 features −
```
num_trees =50
```
Next, build the model with the help of following script −
```
model = GradientBoostingClassifier(n_estimators=num_trees, random_state=seed)
```
Calculate and print the result as follows −
```
results = cross_val_score(model, X, Y, cv=kfold)print(results.mean())
```
Output
```
0.7746582365003418
```
The output above shows that we got around 77.5% accuracy of our Gradient Boosting classifier ensemble model.

Voting Ensemble Algorithms

As discussed, voting first creates two or more standalone models from training dataset and then a voting classifier will wrap the model along with taking the average of the predictions of sub-model whenever needed new data.

In the following Python recipe, we are going to build Voting ensemble model for classification by using VotingClassifier class of sklearn on Pima Indians diabetes dataset. We are combining the predictions of logistic regression, Decision Tree classifier and SVM together for a classification problem as follows −

First, import the required packages as follows −
```
from pandas import read_csv
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
from sklearn.linear_model import LogisticRegression
from sklearn.tree import DecisionTreeClassifier
from sklearn.svm import SVC
from sklearn.ensemble import VotingClassifier
```
Now, we need to load the Pima diabetes dataset as did in previous examples −
```
path =r"C:\pima-indians-diabetes.csv"
headernames =['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
array = data.values
X = array[:,0:8]
Y = array[:,8]
```
Next, give the input for 10-fold cross validation as follows −
```
kfold = KFold(n_splits=10, random_state=7)
```
Next, we need to create sub-models as follows −
```
estimators =[]
model1 = LogisticRegression()
estimators.append(('logistic', model1))
model2 = DecisionTreeClassifier()
estimators.append(('cart', model2))
model3 = SVC()
estimators.append(('svm', model3))
```
Now, create the voting ensemble model by combining the predictions of above created sub models.
```
ensemble = VotingClassifier(estimators)
results = cross_val_score(ensemble, X, Y, cv=kfold)print(results.mean())
```
Output
```
0.7382262474367738
```
The output above shows that we got around 74% accuracy of our voting classifier ensemble model.
October 4, 2025
Automatic Workflows
Introduction

In order to execute and produce results successfully, a machine learning model must automate some standard workflows. The process of automate these standard workflows can be done with the help of Scikit-learn Pipelines. From a data scientists perspective, pipeline is a generalized, but very important concept. It basically allows data flow from its raw format to some useful information. The working of pipelines can be understood with the help of following diagram −

The blocks of ML pipelines are as follows −

Data ingestion − As the name suggests, it is the process of importing the data for use in ML project. The data can be extracted in real time or batches from single or multiple systems. It is one of the most challenging steps because the quality of data can affect the whole ML model.

Data Preparation − After importing the data, we need to prepare data to be used for our ML model. Data preprocessing is one of the most important technique of data preparation.

ML Model Training − Next step is to train our ML model. We have various ML algorithms like supervised, unsupervised, reinforcement to extract the features from data, and make predictions.

Model Evaluation − Next, we need to evaluate the ML model. In case of AutoML pipeline, ML model can be evaluated with the help of various statistical methods and business rules.

ML Model retraining − In case of AutoML pipeline, it is not necessary that the first model is best one. The first model is considered as a baseline model and we can train it repeatably to increase models accuracy.

Deployment − At last, we need to deploy the model. This step involves applying and migrating the model to business operations for their use.

Challenges Accompanying ML Pipelines

In order to create ML pipelines, data scientists face many challenges. These challenges fall into the following three categories −

Quality of Data

The success of any ML model depends heavily on the quality of data. If the data we are providing to ML model is not accurate, reliable and robust, then we are going to end with wrong or misleading output.

Data Reliability

Another challenge associated with ML pipelines is the reliability of data we are providing to the ML model. As we know, there can be various sources from which data scientist can acquire data but to get the best results, it must be assured that the data sources are reliable and trusted.

Data Accessibility

To get the best results out of ML pipelines, the data itself must be accessible which requires consolidation, cleansing and curation of data. As a result of data accessibility property, metadata will be updated with new tags.

Modelling ML Pipeline and Data Preparation

Data leakage, happening from training dataset to testing dataset, is an important issue for data scientist to deal with while preparing data for ML model. Generally, at the time of data preparation, data scientist uses techniques like standardization or normalization on entire dataset before learning. But these techniques cannot help us from the leakage of data because the training dataset would have been influenced by the scale of the data in the testing dataset.

By using ML pipelines, we can prevent this data leakage because pipelines ensure that data preparation like standardization is constrained to each fold of our cross-validation procedure.

Example

The following is an example in Python that demonstrate data preparation and model evaluation workflow. For this purpose, we are using Pima Indian Diabetes dataset from Sklearn. First, we will be creating pipeline that standardized the data. Then a Linear Discriminative analysis model will be created and at last the pipeline will be evaluated using 10-fold cross validation.

First, import the required packages as follows −
```
from pandas import read_csv
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
```
Now, we need to load the Pima diabetes dataset as did in previous examples −
```
path =r"C:\pima-indians-diabetes.csv"
headernames =['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
array = data.values
```
Next, we will create a pipeline with the help of the following code −
```
estimators =[]
estimators.append(('standardize', StandardScaler()))
estimators.append(('lda', LinearDiscriminantAnalysis()))
model = Pipeline(estimators)
```
At last, we are going to evaluate this pipeline and output its accuracy as follows −
```
kfold = KFold(n_splits=20, random_state=7)
results = cross_val_score(model, X, Y, cv=kfold)print(results.mean())
```
Output
```
0.7790148448043184
```
The above output is the summary of accuracy of the setup on the dataset.

Modelling ML Pipeline and Feature Extraction

Data leakage can also happen at feature extraction step of ML model. That is why feature extraction procedures should also be restricted to stop data leakage in our training dataset. As in the case of data preparation, by using ML pipelines, we can prevent this data leakage also. FeatureUnion, a tool provided by ML pipelines can be used for this purpose.

Example

The following is an example in Python that demonstrates feature extraction and model evaluation workflow. For this purpose, we are using Pima Indian Diabetes dataset from Sklearn.

First, 3 features will be extracted with PCA (Principal Component Analysis). Then, 6 features will be extracted with Statistical Analysis. After feature extraction, result of multiple feature selection and extraction procedures will be combined by using

FeatureUnion tool. At last, a Logistic Regression model will be created, and the pipeline will be evaluated using 10-fold cross validation.

First, import the required packages as follows −
```
from pandas import read_csv
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
from sklearn.pipeline import Pipeline
from sklearn.pipeline import FeatureUnion
from sklearn.linear_model import LogisticRegression
from sklearn.decomposition import PCA
from sklearn.feature_selection import SelectKBest
```
Now, we need to load the Pima diabetes dataset as did in previous examples −
```
path =r"C:\pima-indians-diabetes.csv"
headernames =['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
array = data.values
```
Next, feature union will be created as follows −
```
features =[]
features.append(('pca', PCA(n_components=3)))
features.append(('select_best', SelectKBest(k=6)))
feature_union = FeatureUnion(features)
```
Next, pipeline will be creating with the help of following script lines −
```
estimators =[]
estimators.append(('feature_union', feature_union))
estimators.append(('logistic', LogisticRegression()))
model = Pipeline(estimators)
```
At last, we are going to evaluate this pipeline and output its accuracy as follows −
```
kfold = KFold(n_splits=20, random_state=7)
results = cross_val_score(model, X, Y, cv=kfold)print(results.mean())
```
Output
```
0.7789811066126855
```
The above output is the summary of accuracy of the setup on the dataset.
October 4, 2025
Performance Metrics in Machine Learning
Performance Metrics in Machine Learning

Performance metrics in machine learning are used to evaluate the performance of a machine learning model. These metrics provide quantitative measures to assess how well a model is performing and to compare the performance of different models. Performance metrics are important because they help us understand how well our model is performing and whether it is meeting our requirements. In this way, we can make informed decisions about whether to use a particular model or not.

We must carefully choose the metrics for evaluating ML performance because −
- How the performance of ML algorithms is measured and compared will be dependent entirely on the metric you choose.
- How you weight the importance of various characteristics in the result will be influenced completely by the metric you choose.
There are various metrics which we can use to evaluate the performance of ML algorithms, classification as well as regression algorithms. Let’s discuss these metrics for Classification and Regression problems separately.

Performance Metrics for Classification Problems

We have discussed classification and its algorithms in the previous chapters. Here, we are going to discuss various performance metrics that can be used to evaluate predictions for classification problems.
- Confusion Matrix
- Classification Accuracy
- Classification Report
- Precision
- Recall or Sensitivity
- Specificity
- Support
- F1 Score
- ROC AUC Score
- LOGLOSS (Logarithmic Loss)
Confusion Matrix

The consfusion matrix is the easiest way to measure the performance of a classification problem where the output can be of two or more type of classes. A confusion matrix is nothing but a table with two dimensions viz. “Actual” and “Predicted” and furthermore, both the dimensions have “True Positives (TP)”, “True Negatives (TN)”, “False Positives (FP)”, “False Negatives (FN)” as shown below −

Explanation of the terms associated with confusion matrix are as follows −
- True Positives (TP) − It is the case when both actual class & predicted class of data point is 1.
- True Negatives (TN) − It is the case when both actual class & predicted class of data point is 0.
- False Positives (FP) − It is the case when actual class of data point is 0 & predicted class of data point is 1.
- False Negatives (FN) − It is the case when actual class of data point is 1 & predicted class of data point is 0.
We can use confusion_matrix function of sklearn.metrics to compute Confusion Matrix of our classification model.

Classification Accuracy

Accuracy is most common performance metric for classification algorithms. It may be defined as the number of correct predictions made as a ratio of all predictions made. We can easily calculate it by confusion matrix with the help of following formula −

Accuracy=TP+TNðð+ð¹ð+ð¹ð+ððAccuracy=TP+TNð‘‡ð‘ƒ+ð¹ð‘ƒ+ð¹ð‘+ð‘‡ð‘

We can use accuracy_score function of sklearn.metrics to compute accuracy of our classification model.

Classification Report

This report consists of the scores of Precisions, Recall, F1 and Support. They are explained as follows −

Precision

Precision measures the proportion of true positive instances out of all predicted positive instances. It is calculated as the number of true positive instances divided by the sum of true positive and false positive instances.

We can easily calculate it by confusion matrix with the help of following formula −

Precision=TPTP+FPPrecision=TPTP+FP

Precision, used in document retrievals, may be defined as the number of correct documents returned by our ML model.

Recall or Sensitivity

Recall measures the proportion of true positive instances out of all actual positive instances. It is calculated as the number of true positive instances divided by the sum of true positive and false negative instances.

We can easily calculate it by confusion matrix with the help of following formula −

Recall=TPTP+FNRecall=TPTP+FN

Specificity

Specificity, in contrast to recall, may be defined as the number of negatives returned by our ML model. We can easily calculate it by confusion matrix with the help of following formula −

Specificity=TNTN+FPSpecificity=TNTN+FP

Support

Support may be defined as the number of samples of the true response that lies in each class of target values.

F1 Score

F1 score is the harmonic mean of precision and recall. It is a balanced measure that takes into account both precision and recall. Mathematically, F1 score is the weighted average of the precision and recall. The best value of F1 would be 1 and worst would be 0. We can calculate F1 score with the help of following formula −

F1=2∗(precision∗recall)/(precision+recall))F1=2∗(precision∗recall)/(precision+recall))

F1 score is having equal relative contribution of precision and recall.

We can use classification_report function of sklearn.metrics to get the classification report of our classification model.

ROC AUC Score

The ROC (Receiver Operating Characteristic) Area Under the Curve(AUC) score is a measure of the ability of a classifier to distinguish between positive and negative instances. It is calculated by plotting the true positive rate against the false positive rate at different classification thresholds and calculating the area under the curve.

As name suggests, ROC is a probability curve and AUC measure the separability. In simple words, ROC-AUC score will tell us about the capability of model in distinguishing the classes. Higher the score, better the model.

We can use roc_auc_score function of sklearn.metrics to compute AUC-ROC.

LOGLOSS (Logarithmic Loss)

It is also called Logistic regression loss or cross-entropy loss. It basically defined on probability estimates and measures the performance of a classification model where the input is a probability value between 0 and 1. It can be understood more clearly by differentiating it with accuracy. As we know that accuracy is the count of predictions (predicted value = actual value) in our model whereas Log Loss is the amount of uncertainty of our prediction based on how much it varies from the actual label. With the help of Log Loss value, we can have more accurate view of the performance of our model. We can use log_loss function of sklearn.metrics to compute Log Loss.

Example

The following is a simple recipe in Python which will give us an insight about how we can use the above explained performance metrics on binary classification model −
```
from sklearn.metrics import confusion_matrix
from sklearn.metrics import accuracy_score
from sklearn.metrics import classification_report
from sklearn.metrics import roc_auc_score
from sklearn.metrics import log_loss
X_actual =[1,1,0,1,0,0,1,0,0,0]
Y_predic =[1,0,1,1,1,0,1,1,0,0]
results = confusion_matrix(X_actual, Y_predic)print('Confusion Matrix :')print(results)print('Accuracy Score is',accuracy_score(X_actual, Y_predic))print('Classification Report : ')print(classification_report(X_actual, Y_predic))print('AUC-ROC:',roc_auc_score(X_actual, Y_predic))print('LOGLOSS Value is',log_loss(X_actual, Y_predic))
```
Output
```
Confusion Matrix :
[
   [3 3]
   [1 3]
]
Accuracy Score is 0.6
Classification Report :
        precision      recall      f1-score       support
  0       0.75          0.50      0.60           6
  1       0.50          0.75      0.60           4micro avg     0.60          0.60      0.60           10
macro avg     0.62          0.62      0.60           10
weighted avg  0.65          0.60      0.60           10
AUC-ROC:  0.625
LOGLOSS Value is 13.815750437193334
```
Performance Metrics for Regression Problems

We have discussed regression and its algorithms in previous chapters. Here, we are going to discuss various performance metrics that can be used to evaluate predictions for regression problems.
Mean Absolute Error (MAE)

It is the simplest error metric used in regression problems. It is basically the sum of average of the absolute difference between the predicted and actual values. In simple words, with MAE, we can get an idea of how wrong the predictions were. MAE does not indicate the direction of the model i.e. no indication about underperformance or overperformance of the model. The following is the formula to calculate MAE −

MAE=1n∑|Y−Ŷ |MAE=1n∑|Y−Y^|

Here, ð=Actual Output Values

And Ŷ Y^= Predicted Output Values.

We can use mean_absolute_error function of sklearn.metrics to compute MAE.

Mean Square Error (MSE)

MSE is like the MAE, but the only difference is that the it squares the difference of actual and predicted output values before summing them all instead of using the absolute value. The difference can be noticed in the following equation −

MSE=1n∑(Y−Ŷ )MSE=1n∑(Y−Y^)

Here, ð=Actual Output Values

And Ŷ Y^ = Predicted Output Values.

We can use mean_squared_error function of sklearn.metrics to compute MSE.

R Squared (R²) Score

R Squared metric is generally used for explanatory purpose and provides an indication of the goodness or fit of a set of predicted output values to the actual output values. The following formula will help us understanding it −

R2=1−1n∑ni=1(Yi−Yi^)21n∑ni=1(Yi−Yi)2¯R2=1−1n∑i=1n(Yi−Yi^)21n∑i=1n(Yi−Yi)2¯

In the above equation, numerator is MSE and the denominator is the variance in ð values.

We can use r2_score function of sklearn.metrics to compute R squared value.

Example

The following is a simple recipe in Python which will give us an insight about how we can use the above explained performance metrics on regression model −
```
from sklearn.metrics import r2_score
from sklearn.metrics import mean_absolute_error
from sklearn.metrics import mean_squared_error
X_actual =[5,-1,2,10]
Y_predic =[3.5,-0.9,2,9.9]print('R Squared =',r2_score(X_actual, Y_predic))print('MAE =',mean_absolute_error(X_actual, Y_predic))print('MSE =',mean_squared_error(X_actual, Y_predic))
```
Output
```
R Squared = 0.9656060606060606
MAE = 0.42499999999999993
MSE = 0.5674999999999999
```
October 4, 2025

Quantum Machine Learning With Python

Quantum Machine Learning (QML) can be effectively implemented using the Python programming language. The unique capabilities of python make it suitable for quantum machine learning. Researchers can combine the quantum mechanics principles with flexibility of Python libraries such as Qiskit and Cirq to develop and implement ML algorithms.

Researchers can explore novel approaches to solve complex problems in fields like drug discovery, financial modeling, etc., where traditional ML may fall short.

What is Quantum Machine Learning?

Quantum Machine Learning is an interdisciplinary research area that combines fields such as quantum computing, machine learning, optimization, etc. to improve the performance of machine learning models.

It applies unique capabilities of quantum computers to enhance the performance of machine learning algorithms. QML is capable of performing computations beyond the capabilities of conventional computers.

Why Python for Quantum Machine Learning?

There are many programming languages such as Python, Julia, C++, Q#, etc., that are being used for Quantum Machine Learning. But Python is the most popular among these programming languages.

Python is easy to learn and easy to implement machine learning algorithms for beginners as well as experienced.

Python provides many popular libraries and frameworks for quantum machine learning. Some popular ones include PennyLane, Qiskit, Cirq, etc.

Python also provides many scientific computing libraries such as SciPy, Pandas, Scikit-learn, etc. Python integrates these libraries with QML libraries.

Python Libraries/ Frameworks for Quantum Machine Learning

Python offers many libraries and frameworks that are currently being used for Quantum Machine Learning. The following are a few of important libraries –

PennyLane − a popular and user-friendly library for building and training quantum machine learning models.
Qiskit − it is a comprehensive quantum computing framework developed by IBM. It includes a dedicated module on QML. It provides various algorithms, simulators, etc., through the IBM cloud platform.
Cirq − developed by Google, it is another powerful quantum computing framework that supports Quantum Machine Learning.
TensorFlow Quantum (TFQ) minus; It is a quantum machine learning library for rapid prototyping of hybrid quantum-classical ML models.
sQUlearn − it is a user-friendly library that integrates quantum machine learning with classical machine learning libraries or tools such as scikit-learn.
PyQuil − It is developed by Rigetti Computing. It is a Python library for quantum programming and quantum machine learning. It provides tools for building and executing quantum circuits on Rigetti’s quantum processors.

Quantum Machine Learning Program with Python

Python is a very versatile programming language that provides many libraries for Quantum Machine Learning. The main part of the QML is to design and execute quantum circuits.

With the help of Python libraries, the designing and execution of quantum circuits are easy.

We need a specific quantum machine learning library to implement a QML program in Python. In this section, we will use the PennyLane Python library for this purpose.

Prerequisites

The following are the prerequisites for implementation of quantum machine learning in Python –

Programming Language: Python
QML library: PennyLane
Visualization Library: Matplotlib

Get started with PennyLane

We use the PennyLane Python library to implement the program below. It provides mechanisms to create and execute the quantum circuits. You can explore other Python libraries as well.

Before starting, you need to install the PennyLane library.

pip install pennylane

Steps

The following are the steps to perform a quantum machine learning program using Python –

Install and import required libraries
Prepare training and test data
Define a quantum device. Specify the device type and the number of wires.
Define the quantum circuit.
Define pre-/post processing. Here we define the loss function to find total loss.
Define a cost function which takes in your quantum circuit and loss function.
Perform optimization
- Choose an optimizer.
- Define the step size.
- Initialize the parameters (make an initial guess for the value of parameters).
- Iterate over a number of defined steps.
Test and Visualize the result.

Program Example

In the below example, we train a quantum circuit to model a sine function. We use the PennyLane Python library to define a quantum device and to create a quantum circuit. We use Gradient Descent optimizer as an optimization technique.

# Program to train a quantum circuit to model a sine function# Step 1- Import the necessary librariesimport pennylane as qml
from pennylane import numpy as np
import matplotlib.pyplot as plt

# Step 2 - Prepare the training data and test data# Training data preparation
X = np.linspace(0,2*np.pi,5)# 5 input datapoints from 0 to 2pi
X.requires_grad =False# Prevent optimization of input data
Y = np.sin(X)# Corresponding outputs# Test data preparation
X_test = np.linspace(0.2,2*np.pi+0.2,5)# 5 test datapoints
Y_test = np.sin(X_test)# Corresponding outputs# Step 3 - Quantum device setup# Using 'default.qubit' simulator with 1 qubit
dev = qml.device('default.qubit', wires=1)# Step 4 - Create the quantum [email protected](dev)defquantum_circuit(input_data, params):"""
Quantum circuit to model the sine function.
Args:
    input_data (float): Input data point.
    params (array): Parameters for the quantum gates.
Returns:
    float: Expectation value of PauliZ measurement.
"""# Encode the input data as an RX rotation
qml.RX(input_data, wires=0)# Create a rotation based on the angles in "params"
qml.Rot(params[0], params[1], params[2], wires=0)# We return the expected value of a measurement along the Z axisreturn qml.expval(qml.PauliZ(wires=0))# Step 5 -Loss function definitiondefloss_func(predictions):
total_losses =0for i inrange(len(Y)):
    output = Y[i]
    prediction = predictions[i]
    loss =(prediction - output)**2
    total_losses += loss
return total_losses
# Step 6 - Cost function definitiondefcost_fn(params):# Cost function to be minimized during optimization.
predictions =[quantum_circuit(x, params)for x in X]
cost = loss_func(predictions)return cost
# Steps 7 - Optimization Step# Choose Gradient Descent Optimizer and step size as 0.3
opt = qml.GradientDescentOptimizer(stepsize=0.3)# initialize the parameters
params = np.array([0.1,0.1,0.1],requires_grad=True)# iterate over a number of defined stepsfor i inrange(100):
params, prev_cost = opt.step_and_cost(cost_fn,params)if i%10==0:# print the result after every 10 stepsprint(f'Step {i} =&gt; Cost = {cost_fn(params)}')# Step 8 - # Testing and visualizationtest_predictions =[]for x_test in X_test:
prediction = quantum_circuit(x_test,params)
test_predictions.append(prediction)
fig = plt.figure()
ax1 = fig.add_subplot(111)

ax1.scatter(X, Y, s=30, c='b', marker="s", label='Training Data')
ax1.scatter(X_test,Y_test, s=60, c='r', marker="o", label='Test Data')
ax1.scatter(X_test,test_predictions, s=30, c='k', marker="x", label='Test Predictions')
plt.xlabel("Input")
plt.ylabel("Output")
plt.title("Quantum Machine Learning Results")
plt.legend(loc='upper right');
plt.show()

Output

Step 0 => Cost = 4.912499465469817
Step 10 => Cost = 0.01771261626471407
Step 20 => Cost = 0.0010549650559467845
Step 30 => Cost = 0.00033478390918249124
Step 40 => Cost = 0.00019081038150774426
Step 50 => Cost = 0.00012461609775915093
Step 60 => Cost = 8.781349557162982e-05
Step 70 => Cost = 6.52239822689053e-05
Step 80 => Cost = 5.0362401887345095e-05
Step 90 => Cost = 4.006386705383739e-05

Implementing Quantum Machine Learning with Python

October 4, 2025

Quantum Machine Learning

Quantum Machine Learning (QML) is an interdisciplinary field that combines quantum commuting with machine learning to improve the performance of machine learning models. The quantum computers are capable of performing computations beyond the capabilities of conventional computers. It applies the principles of quantum mechanics to perform computations beyond the capabilities of conventional computers.

Quantum machine learning is a rapidly evolving field with applications in areas such as drug discovery, healthcare, optimization, natural language processing, etc. It has the potential to revolutionize areas like data processing, optimization, and neural networks.

What is Quantum Machine Learning?

Quantum machine learning (QML) refers to the use of quantum computing principles to develop machine learning algorithms. It uses the unique properties of quantum machines to process and analyze large amounts of data more efficiently than the traditional machine learning systems.

Why Quantum Machine Learning?

While the traditional machine learning algorithms have achieved remarkable success, they are constrained by the limitations of computing hardware. With larger data and complex algorithms, the traditional computer systems face challenges to process data in a reasonable time frame. On the other hand, quantum computers can exponentially speed-up for certain types of problems in machine learning.

Quantum Machine Learning Concepts

Let’s understand the key concepts of quantum machine learning –

1. Qubits

In quantum computing, the basic unit of information is a quantum bit (qubit). A classical bit can exist in either 0 or 1 position. However, qubits can also exist in a state of superposition, meaning they can represent 0 and 1 simultaneously. So a qubit can represent 0, 1, or a linear combination of 0 and 1 simultaneously.

2. Superposition

Superposition allows quantum systems to exist in multiple states simultaneously. For example, a qubit can exist in multiple states at the same time. Because of the superposition property, a qubit can exist in a linear combination of both 0 and 1.

3. Entanglement

Superposition is a phenomenon in which the states of two or more qubits become interdependent such that the state of one qubit can influence the state of another qubit. This enables faster data transfer and computation across qubits.

4. Quantum interference

It refers to the ability to control the probabilities of qubit states by manipulating their wavefunctions. While constructing quantum circuits, we can amplify the correct solution and suppress the incorrect one.

5. Quantum Gates and Circuits

Similar to binary logic gates, quantum computers use the quantum gates to manipulate qubits. Quantum gates allow operations like superposition and entanglement to be performed on qubits. These gates are combined into quantum circuits, which are analogous to algorithms in classical computing.

How Quantum Machine Learning Works?

Quantum machine learning applies quantum algorithms to solve problems usually handled by machine learning techniques, such as classification, clustering, regression, etc. These quantum algorithms use quantum properties like superposition and entanglement to accelerate certain aspects of the machine learning process.

Quantum Machine Learning Algorithms

There are several quantum algorithms that have been developed to enhance machine learning models. The following are some of them –

1. Quantum Support Vector Machine (QSVM)

Support vector machines are used for classification and regression tasks. A Quantum SVM uses quantum kernels to map data into higher-dimensional spaces more efficiently. This enables faster and more accurate classification for large datasets.

2. Quantum Principal Component Analysis (QPCA)

Principal Component Analysis (PCA) is used to reduce the dimensionality of datasets. QPCA uses quantum algorithms to perform this task exponentially faster than classical methods, making it suitable for processing high-dimensional data.

3. Quantum k-Means Clustering

Quantum algorithms can be used to speed up k-means clustering. k-means clustering involves partitioning data into clusters based on similarity.

4. Variational Quantum Algorithms

Variational Quantum Algorithms (VQAs) use quantum circuits to optimize a given cost function. They can be applied to tasks like classification, regression, and optimization in machine learning.

5. Quantum Boltzmann Machines (QBM)

Boltzmann machines are a type of probabilistic graphical model used for unsupervised learning. Quantum Boltzmann Machines (QBMs) use quantum mechanics to represent and learn probability distributions more efficiently than their classical counterparts.

Applications of Quantum Machine Learning

Quantum machine learning has many applications across different domains –

1. Drug Discovery and Healthcare

In drug discovery, researchers need to explore vast chemical spaces and simulate molecular interactions. Quantum machine learning can accelerate these processes by quickly identifying compounds and predicting their effects on biological systems.

In healthcare, QML can enhance diagnostic tools by analyzing complex medical datasets, such as genomics and imaging data, more efficiently.

2. Financial Modeling and Risk Management

In finance, QML can optimize portfolio management, pricing models, and fraud detection. Quantum algorithms can process large financial datasets more efficiently. Quantum-based risk management tools can also provide more accurate forecasts in volatile markets.

3. Optimization in Supply Chains and Logistics

Supply chain management involves optimizing logistics, inventory, and distribution networks. Quantum machine learning can improve optimization algorithms used to streamline supply chains, reduce costs, and increase efficiency in industries like retail and manufacturing.

4. Artificial Intelligence and Natural Language Processing

Quantum machine learning may advance AI by speeding up training for complex models such as deep learning architectures. In natural language processing (NLP), QML can enable more efficient parsing and understanding of human language, leading to improved AI assistants, translation systems, and chatbots.

5. Climate Modeling and Energy Systems

Accurately modeling climate systems requires processing massive amounts of environmental data. Quantum machine learning could help simulate these systems more effectively and provide better predictions for climate change impacts.

Challenges in Quantum Machine Learning

Quantum machine learning has some challenges and limitations despite its potentials –

1. Hardware Limitations

Current quantum computers are known as Noisy Intermediate-Scale Quantum (NISQ) devices. They are prone to errors and have limited qubit counts. These hardware limitations restrict the complexity of QML algorithms that can be implemented today. Scalable, error-corrected quantum computers are still in development.

2. Algorithm Development

While quantum algorithms like QAOA and QSVM show promise, the field is still in its early stage. Developing more efficient, scalable, and robust quantum algorithms that outperform classical counterparts remains an ongoing challenge.

3. Hybrid Systems Complexity

Hybrid quantum-classical systems require efficient communication between classical and quantum processors. Ensuring that the quantum and classical components of hybrid systems work together efficiently can be challenging. Engineers and researchers need to carefully design algorithms to balance the workload between classical and quantum resources.

5. Data Representation and Quantum Encoding

It must be encoded into qubits to process classical data. It can introduce bottlenecks. It’s a key challenge to finding efficient methods to represent large datasets in quantum form, as well as to read results back into classical formats.

The Future of Quantum Machine Learning

Quantum machine learning is still in its early stages, but the field is advancing rapidly. As quantum hardware improves and new algorithms are developed, the potential applications of QML will expand significantly. The following are some of the anticipated advancements in the coming years –

1. Fault-Tolerant Quantum Computing

Today’s quantum computers suffer from noise and errors that limit their scalability. In the future, fault-tolerant quantum computers could enhance the capabilities of QML algorithms. These systems would be able to run more complex and accurate machine learning models.

2. Quantum Machine Learning Frameworks

Similar to TensorFlow and PyTorch for classical machine learning, quantum machine learning frameworks are beginning to emerge. Many tools like Google’s Cirq, IBM’s Qiskit, and PennyLane by Xanadu allow researchers to experiment with quantum algorithms more easily. As these frameworks mature, they will likely lower the barrier to entry for QML development.

3. Improved Hybrid Models

As hardware improves, hybrid quantum-classical models will become more powerful. We can expect to see breakthroughs in combining classical deep learning with quantum-enhanced optimization.

4. Commercial Applications

Many companies, including IBM, Google, and Microsoft, are actively investing in quantum computing research and QML applications. As quantum computers become more accessible, industries like pharmaceuticals, finance, and logistics will likely adopt QML.

October 4, 2025
Trust Region Methods
In reinforcement learning, especially in policy optimization techniques, the main goal is to modify the agent’s policy to improve the performance without affecting it’s behavior. This is important when working with deep neural networks, especially if updates are large or not properly limited there might be a case of instability. Trust regions help maintain stability by guaranteeing that parameter updates are smooth and effective during training.

What is Trust Region?

A trust region is a concept used in optimization that restricts updates to the policy or value function in training, maintaining stability and reliability in the learning process. Trust regions assist in limiting the extent to which the model’s parameters, like policy networks, are allowed to vary during updates. This will help in avoiding large or unpredictable changes that may disrupt the learning process.

Role of Trust Regions in Policy Optimization

The idea of trust regions is used to regulate the extent to which the policy can be altered during updates. This guarantees that every update improves the policy without implementing drastic changes that could cause instability or affect performance. Some of the aspects where trust regions play an important role are −
- Policy Gradient − Trust regions are often used in these methods to modify the policy to optimize expected rewards. However, in the absence of a trust region, important updates can result in unpredictable behavior, particularly when employing function approximators such as deep neural networks.
- KL Divergence − This is in Trust Region Policy Optimization (TRPO) which serves as the criteria for evaluating the extent of policy changes by calculating the divergence between the old and new policies. The main concept is that the minor policy changes tend to enhance the agent’s performance consistently, whereas major changes may lead to instability.
- Surrogate Objective in PPO − It is used to estimate the trust region through a surrogate objective function incorporating a clipping mechanism. The primary goal is to prevent major changes in the policy by implementing penalties on big deviations from the previous policy. Additionally, this will improve the performance of the policy.
Trust Region Methods for Deep Reinforcement Learning

Following is a list of algorithms that use trust regions in deep reinforcement learning to ensure that updates are effective and reliable, improving the overall performance −

1. Trust Region Policy Optimization

Trust Region Policy Optimization (TRPO) is a reinforcement learning algorithm that aims to enhance policies in a more efficient and steady way. It deals with the issue of large, unstable updates that usually occur in policy gradient methods by introducing trust region constraint.

The constraint used in TRPO is Kullback-Leibler(KL) divergence, as a restriction to guarantee minimal variation between the old and new policies through the assessment of their disparity. This process helps TRPO in maintaining stability of the learning process and improves the efficiency of the policy.

The TRPO algorithm works by consistently modifying the policy parameters to improve a surrogate objective function with the boundaries of the trust region constraint. For this it is necessary to find a solution for the dilemma of enhancing the policy while maintaining stability.

2. Proximal Policy Optimization

Proximal Policy Optimization is a reinforcement learning algorithm whose aim is to enhance the consistency and dependability of policy updates. This process uses an alternative objective function along with the clipping mechanism to avoid extreme adjustments to policies. This approach ensures that there isn’t much difference between the new policy and old , additionally maintaining a balance between exploration and exploitation.

PPO is an easier and effective among all the trust region techniques. It is widely used in many applications like robotics, autonomous cars because of its reliability and simplicity. The algorithm includes collecting a set of experiences, calculating the advantage estimates, and carrying out several rounds of stochastic gradient descent to modify the policy.

3. Natural Gradient Descent

This technique modifies the step size according to the curvature of the objective function to form a trust region surrounding the current policy. It is particularly effective in high-dimensional environments.

Challenges in Trust Regions

There are certain challenges while implementing trust region techniques in deep reinforcement learning −
- Most trust region techniques like TRPO and PPO require approximations, which can violate constraints or fail to find the optimal solution within the trust region.
- The techniques can be computationally intensive, especially with high-dimensional spaces.
- These techniques often require a wide range of samples for effective learning.
- The efficiency of trust region techniques highly depends on the choice of hyperparameters. Tuning these parameters is quite challenging and often requires expertise.
October 4, 2025
Deep Deterministic Policy Gradient (DDPG)
Deep Deterministic Policy Gradient (DDPG) is an algorithm that simultaneously learns from both Q-function and a policy. It learns the Q-function using off-policy data and the Bellman equation, which is then used to learn the policy.

What is Deep Deterministic Policy Gradient?

Deep Deterministic Policy Gradient (DDPG) is a reinforcement learning algorithm created to address problems with continuous action spaces. This algorithm, which is based on the actor-critic architecture, is off-policy and also a combination of Q-learning and policy gradient methods. DDPG is an off-policy algorithm that is model-free and uses deep learning to estimate value functions and policies, making it suitable for tasks involving continuous actions like robotic control and autonomous driving.

In simple, it expands Deep Q-Networks (DQN) to continuous action spaces with a deterministic policy instead of the usual stochastic policies in DQN or REINFORCE.

Key Concepts in DDPG

The key concepts involved in Deep Deterministic Policy Gradient (DDPG) are −
- Policy Gradient Theorem − The deterministic policy gradient theorem is employed by DDPG, which allows the calculation of the gradient of the expected return in relation to the policy parameters. Additionally, this gradient is used for updating the actor network.
- Off-Policy − DDPG is an off-policy algorithm, indicating it learns from experiences created by a policy that is not the one being optimized. This is done by storing previous experiences in the replay buffer and using them for learning.
What is Deterministic in DDPG?

A deterministic strategy maps states with actions. When you provide a state to the function, it gives back an action to perform. In comparison with the value function, where we obtain probability function for every state. Deterministic policies are used in deterministic environments where the actions taken determine the outcome.

Core Components in DDPG

Following the core components used in Deep Deterministic Policy Gradient (DDPG) −
- Actor-Critic Architecture − While the actor is the policy network, it takes the state as input and outputs a deterministic action. The critic is the Q-function approximator that calculates the action-value function Q(s,a). It considers both the state and the action as input and predicts the expected return.
- Deterministic Policy − DDPG uses deterministic policy instead of stochastic policies, which are mostly used by algorithms like REINFORCE or other policy gradient methods. The actor produces one action for a given state rather than a range of actions.
- Experience Relay − DDPG uses an experience replay buffer for storing previous experiences in tuples consisting of state, action, reward, and next state. The buffer is used for selecting mini-batches in order to break the temporal dependencies among successive experiences, ultimately helping to improve the training stability.
- Target Networks − In order to ensure stability in learning, DDPG employs target networks for both the actor and the critic. These updated versions of the original networks are gradually improved to decrease the variability of updates when training.
- Exploration Noise − Since DDPG is a deterministic policy gradient method, the policy is inherently greedy and would not explore the environment sufficiently.
How does DDPG Work?

Deep Deterministic Policy Gradient (DDPG) is a reinforcement learning algorithm used particularly for continuous action spaces. It is an actor-critic method i.e., it uses two models actor, which decides the action to be taken in the current state and critic, which assesses the effectiveness of the action taken. The working of DDPG is described below −

Continuous Action Spaces

DDPG is effective with environments that have continuous action spaces like controlling the speed and direction of car’s, in contrast to discrete action spaces found in games.

Experience Replay

DDPG uses experience replay by storing the agent’s experiences in a buffer and sampling random batches of experiences for updating the networks. The tuple is represented as (st,at,rt,st+1)(st,at,rt,st+1), where −
- stst represents the state at time tt.
- atat represents the action taken.
- rtrt represents the reward received.
- st+1st+1 represents the new state after the action.
Randomly selecting experiences from the replay buffer reduces the correlation between consecutive events, leading to more stable training.

Actor-Critic Training
- Critic Update − This critic update is based on Temporal Difference (TD) Learning, particularly the TD(0)TD(0) variation. The main task of the critic is to assess the actor’s decisions by calculating the Q-value, which predicts the future rewards for specific state-action combinations. Additionally, the critic update in DDPG consists of reducing the TD error (which is the difference between the predicted Q-value and the target Q-value).
- Actor Update − The actor update involves modifying the actor’s neural network to enhance the policy, or decision-making process. In the process of updating the actor, the Q-value gradient is calculated in relation to the action, and the actor’s network is adjusted using gradient ascent to boost the likelihood of choosing actions that result in higher Q-values, enhancing the policy in the end.
Target Networks and Soft Updates

Instead of directly copying learned networks to target networks, DDPG employs a soft update approach, which updates target networks with a portion of the learned networks.

θ′←τ+(1−τ)θ′θ′←τ+(1−τ)θ′ where, ττ is a small value that ensures slow updates and improves stability.

Exploration-exploitation

DDPG uses Ornstein-Uhlenbeck noise in addition to the actions to promote exploration, as deterministic policies could become trapped in less than ideal solutions with continuous action spaces. The agent is motivated by the noise to explore the environment.

Challenges in DDPG

The two main challenges in DDPG that have to be addressed are −
- Instability − DDPG may experience stability issues in training, especially when employed with function approximators such as neural networks. This is dealt using target networks and experience replay, however, it still needs precise adjustment of hyper parameters.
- Exploration − Even with the use of Ornstein-Uhlenbeck noise for exploration, DDPG could face difficulties in extremely complicated environments if exploration strategies are not effective.
October 4, 2025
Deep Q-Networks (DQN)
What are Deep Q-Networks?

A Deep Q-Network (DQN) is an algorithm in the field of reinforcement learning. It is a combination of deep neural networks and Q-learning, enabling agents to learn optimal policies in complex environments. While the traditional Q-learning works effectively for environments with a small and finite number of states, but it struggles with large or continuous state spaces due to the size of the Q-table. This limitation is overruled by Deep Q-Networks by replacing the Q-table with neural network that can approximate the Q-values for every state-action pair.

Key Components of Deep Q-Networks

Following is a list of components that are a part of the architecture of Deep Q-Networks −
- Input Layer − This layer receives state information from the environment in the form of a vector of numerical values.
- Hidden Layers − The DQN’s hidden layer consist of multiple fully connected neuron that transform the input data into more complex features that ate more suitable for predictions.
- Output Layer − Each possible action in the current state is represented by a single neuron in the DQN’s output layer. The output values of these neurons represent the estimated value of each action within that state.
- Memory − DQN utilizes a memory replay to store the training events of the agent. All the information including the current state, action taken, the reward received, and the next state are stored as tuples in the memory.
- Loss Function − the DQN computes the difference between the actual Q-values form replay memory and predicted Q-values to determine loss.
- Optimization − It involves adjusting the network’s weights in order to minimize the loss function. Usually, stochastic gradient descent (SGD) is employed for this purpose.
The following image depicts the components in the deep q-network architecture –

How Deep Q-Networks Work?

The working of DQN involves the following steps −

Neural Network Architecture −

The DQN uses a sequence of frames (such as images from a game) for input and generates a set of Q-values for every potential action at that particular state. the typical configuration includes convolutional layers for spatial relationships and fully connected layers for Q-values output.

Experience Replay

While training, the agent stores its interactions (state, action, reward, next state) in a replay buffer. Sampling random batches from this buffer trains the network, reducing correlation between consecutive experiences and improve training stability.

Target Network

In order to stabilize the training process, Deep Q-Networks employ a distinct target network for producing Q-value targets. the target network receives regular updates of weighs from the main network to minimize divergence risk while training.

Epsilon-Greedy Policy

The agent uses an epsilon-greedy strategy, where it selects a random action with probability ϵϵ and the action with highest Q-value with probability 1−ϵ1−ϵ. This balance between exploration and exploitation helps the agent learn effectively.

Training Process

The neural network is trained using gradient descent to minimize the loss between the predicted Q-values and the target Q-values. The target Q-values are calculated using the Bellman equation, which incorporates the reward received and the maximum Q-value of the nect state.

Limitations of Deep Q-Networks

Deep Q-Networks (DQNs) have several limitations that impacts it’s efficiency and performance −
- DQN’s suffer from instability due to the non-stationarity problem caused from frequent neural network updates.
- DQN’s at times over estimate Q-values, which might have an negative impact on the learning process.
- DQN’s require many samples to learn well, which can be expensive and time-consuming in terms of computation.
- DQN performance is greatly influence by the selection of hyper parameters, such as learning rate, discount factor, and exploration rate.
- DQNs are mainly intended for discrete action spaces and might face difficulties in environments with continuous action spaces.
Double Deep Q-Networks

Double DQN is an extended version of Deep Q-Network created to address an issues in the basic DQN method − Overestimation bias in Q-value updates. The overestimation bias is caused by the fact that the Q-learning update rule utilizes the same Q-network for choosing and assessing actions, resulting in inflated estimates of the Q-values. This problem can cause instability in training and hinder the learning process. The two different networks used in Double DQN to solve this issue −
- Q-Networks, responsible for choosing the action
- Target Network, assess the worth of the chosen action.
The major modification in Double DQN lies in how the target is calculated. Rather than using only Q-network for choosing and assessing the next action, Double DQN involves using the Q-network for selecting the action in the subsequent state and the target network for evaluating the Q-value of the chosen action. This separation decreases the tendency to overestimate and results in more precise value calculations. Due to this, Double DQN offers a more consistent and dependable training process, especially in scenarios such as Atari games, where the regular DQN approach may face challenges with overestimation.

Dueling Deep Q-Networks

Dueling Deep Q-Networks (Dueling DQN), improves the learning process of the traditional Deep Q-Network (DQN) by separating the estimation of state values from action advantages. In the traditional DQN, an individual Q-value is calculated for every state-action combination, representing the expected cumulative reward. However, this can be inefficient, particularly when numerous actions result in similar consequences. Dueling DQN handles this issue by breaking down the Q-value into two primary parts: the state value V(s)V(s) and the advantage function A(s,a)A(s,a). The Q-value is then given by Q(s,a)=V(s)+A(s,a)Q(s,a)=V(s)+A(s,a), where V(s) captures the value of being in a given state, and A(s,a)A(s,a) measures how much better an action is over others in the same state.

Dueling DQN helps the agent to enhance its understanding of the environment and prevent the learning of unnecessary action-value estimates by separately estimating state values and action advantages. This results in improved performance, particularly in situations with delayed rewards, allowing the agent to gain a better understanding of the importance of various states when choosing the optimal action.
October 4, 2025
Deep Reinforcement Learning Algorithms
Deep reinforcement learning algorithms are a type of algorithms in machine learning that combines deep learning and reinforcement learning.

Deep reinforcement learning addresses the challenge of enabling computational agents to learn decision-making by incorporating deep learning from unstructured input data without manual engineering of the state space.

Deep reinforcement learning algorithms are capable of deciding what actions to perform for the optimization of an objective even with large inputs.

Reinforcement Learning

Reinforcement Learning consists of an agent that learns from the feedback given in response to its actions while exploring an environment. The main goal of the agent is to maximize cumulative rewards by developing a strategy that guides decision-making in all possible scenarios.

Role of Deep Learning in Reinforcement Learning

In traditional reinforcement learning algorithms, tables or basic function approximates are commonly used to represent value functions, policies, or models. Well, these strategies are not efficient enough to be applied in challenging settings like video games, robotics or natural language processing. Neural networks allow for the approximation of complex, multi-dimensional functions through deep learning. This forms the basis of Deep Reinforcement Learning.

Some of the benefits of the combination of deep learning networks and reinforcement learning are −
- Dealing with inputs with high dimensions (such as raw images and continuous sensor data).
- Understanding complex relationships between states and actions through learning.
- Learning a common representation by generalizing among different states and actions.
Deep Reinforcement Learning Algorithms

The following are some of the common deep reinforcement learning algorithms are −

1. Deep Q-Networks

A Deep Q-Network (DQN) is an extension of conventional Q-learning that employs deep neural networks to estimate the action-value function Q(s,a)Q(s,a). Instead of storing Q-values within a table, DQN uses a neural network to deal with complicated input domains like game pixel data. This makes reinforcement learning appropriately address complex tasks, like playing Atari, where the agent learns from visual inputs.

DQN improves training stability through two primary methods: experience replay, which stores and selects past experiences, and target networks to maintain consistent Q-value targets by refreshing a different network periodically. These advancements assist DQN in effectively acquiring knowledge in large-scale settings.

2. Double Deep Q-Networks

Double Deep Q-Network (DDQN) enhances Deep Q-Network (DQN) by mitigating the problem of overestimation bias in Q-value updates. In typical DQN, a single Q-network is utilized for both action selection and value estimation, potentially resulting in overly optimistic value approximations.

DDQN uses two distinct networks to manage action selection and evaluation − a current Q-network for choosing the action and a target Q-network for evaluating the action. This decrease in bias in the Q-value estimates leads to improved learning accuracy. DDQN incorporates the experience replay and target network methods used in DQN to improve the robustness and dependability.

3. Dueling Deep Q-Networks

Dueling Deep Q-Networks (Dueling DQN) is an extension to the standard Deep Q-Network (DQN) used in reinforcement learning. It separates the Q-value into two components − the state value function V(s)V(s) and the advantage function A(s,a)A(s,a), which estimates the ratio of the value for each action to the average value.

The final Q-value is estimated by combining all these elements. This form of representation reduces the strength and effectiveness of Q-learning, where the model can estimate the state value more accurately and the need for accurate action values in certain situations is minimized.

4. Policy Gradient Methods

Policy Gradient Methods are algorithms based on a policy iteration approach where policy is directly manipulated to reach the optimal policy that maximizes the expected reward. Rather than focusing on learning a value function, these strategies have been developed in order to maximize rewards by optimizing the policy with respect to the gradient of the defined objective with respect to policy parameters.

The main objective is computing the average reward gradient and strategy modification. The following are the algorithms: REINFORCE, Actor-Critic, and Proximal Policy Optimization (PPO). These approaches can be applied effectively in high or continuous dimensional spaces.

5. Proximal Policy Optimization

A Proximal Policy Optimization (PPO) algorithm in reinforcement learning with an approach to achieve more stable and efficient policy optimization. This approach updates policies by maximizing an objective function associated with the policy, but puts a cap on the amount of allowance for a policy update in order to avoid drastic changes in a policy.

A new policy cannot be too far from an old policy, hence PPO adopts a clipped objective to ensure no policy ever changes drastically from the last policy. By using a clipped objective, PPO will prevent large changes in policy between the old and new one. This balance between the means of exploration and exploitation avoids performance degradation and promotes smoother convergence. PPO is applied in deep reinforcement learning for both continuous and discrete action spaces due to its simplicity and effectiveness.
October 4, 2025

Author: saqibkhan

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