Uncertainty in Reinforcement Learning: Exploration and Exploitation

This blog reviews the concepts and challenges of uncertainty in reinforcement learning, and the strategies for balancing exploration and exploitation to achieve optimal performance.

Table of Contents

1. Introduction

Reinforcement learning is a branch of machine learning that deals with learning from trial and error. In reinforcement learning, an agent interacts with an environment and learns to perform actions that maximize a reward signal. However, the agent often faces uncertainty about the environment, the reward, and the optimal action. How can the agent cope with uncertainty and learn effectively?

One of the key challenges in reinforcement learning is the trade-off between exploration and exploitation. Exploration is the process of trying out new actions and discovering new information about the environment. Exploitation is the process of using the current knowledge and choosing the best action according to the estimated reward. Both exploration and exploitation are essential for the agent to learn and improve its performance, but they are often in conflict. If the agent explores too much, it may waste time and resources on suboptimal actions. If the agent exploits too much, it may miss out on better actions and get stuck in a local optimum.

In this blog, we will review the concepts and challenges of uncertainty in reinforcement learning, and the strategies for balancing exploration and exploitation to achieve optimal performance. We will cover the following topics:

Sources and types of uncertainty in reinforcement learning
Measures and models of uncertainty in reinforcement learning
Exploration and exploitation trade-off
Exploration strategies
Exploitation strategies
Balancing exploration and exploitation

By the end of this blog, you will have a better understanding of how uncertainty affects reinforcement learning, and how to design and implement effective exploration and exploitation strategies. You will also learn some practical tips and examples of applying these strategies to real-world problems.

Are you ready to dive into the fascinating world of uncertainty in reinforcement learning? Let’s get started!

2. Uncertainty in Reinforcement Learning

Uncertainty is a fundamental aspect of reinforcement learning, as the agent has to deal with incomplete and noisy information about the environment, the reward, and the optimal action. Uncertainty can arise from various sources and have different types, which affect the agent’s learning process and performance.

Some of the main sources of uncertainty in reinforcement learning are:

Partial observability: The agent cannot observe the full state of the environment, but only a partial or noisy observation. For example, a robot navigating a maze may only see a limited area around it, or a self-driving car may have sensors that are affected by weather conditions.
Stochasticity: The environment is not deterministic, but stochastic, meaning that the same action in the same state may lead to different outcomes. For example, a slot machine may pay out different amounts of money for the same lever pull, or a stock market may fluctuate unpredictably.
Non-stationarity: The environment is not static, but dynamic, meaning that it changes over time. For example, a video game may have different levels of difficulty, or a customer’s preferences may change over time.
Limited data: The agent has a limited amount of data to learn from, either because the environment is large and complex, or because the agent has a limited lifespan or budget. For example, a chess player may not be able to explore all the possible moves, or a medical trial may have a limited number of patients.

Some of the main types of uncertainty in reinforcement learning are:

Aleatoric uncertainty: This is the uncertainty that is inherent to the environment and cannot be reduced by more data. For example, the outcome of a dice roll is always uncertain, no matter how many times you roll it.
Epistemic uncertainty: This is the uncertainty that is due to the agent’s lack of knowledge and can be reduced by more data. For example, the optimal action in a state is uncertain if the agent has not visited that state before, but it can become more certain if the agent explores it more.
Parametric uncertainty: This is the uncertainty that is related to the agent’s model parameters and can be reduced by more data. For example, the agent may have a neural network that approximates the value function, but the network weights are uncertain until they are trained with more data.
Model uncertainty: This is the uncertainty that is related to the agent’s model structure and cannot be reduced by more data. For example, the agent may have a linear model that approximates the value function, but the model may be too simple or too complex to capture the true function.

Understanding the sources and types of uncertainty in reinforcement learning is important for designing and evaluating exploration and exploitation strategies, as different strategies may be more or less effective depending on the nature and level of uncertainty. In the next section, we will discuss the exploration and exploitation trade-off and some of the common strategies for balancing them.

2.1. Sources and Types of Uncertainty

Some of the main sources of uncertainty in reinforcement learning are:

Partial observability: The agent cannot observe the full state of the environment, but only a partial or noisy observation. For example, a robot navigating a maze may only see a limited area around it, or a self-driving car may have sensors that are affected by weather conditions.
Stochasticity: The environment is not deterministic, but stochastic, meaning that the same action in the same state may lead to different outcomes. For example, a slot machine may pay out different amounts of money for the same lever pull, or a stock market may fluctuate unpredictably.
Non-stationarity: The environment is not static, but dynamic, meaning that it changes over time. For example, a video game may have different levels of difficulty, or a customer’s preferences may change over time.
Limited data: The agent has a limited amount of data to learn from, either because the environment is large and complex, or because the agent has a limited lifespan or budget. For example, a chess player may not be able to explore all the possible moves, or a medical trial may have a limited number of patients.

Some of the main types of uncertainty in reinforcement learning are:

Aleatoric uncertainty: This is the uncertainty that is inherent to the environment and cannot be reduced by more data. For example, the outcome of a dice roll is always uncertain, no matter how many times you roll it.
Epistemic uncertainty: This is the uncertainty that is due to the agent’s lack of knowledge and can be reduced by more data. For example, the optimal action in a state is uncertain if the agent has not visited that state before, but it can become more certain if the agent explores it more.
Parametric uncertainty: This is the uncertainty that is related to the agent’s model parameters and can be reduced by more data. For example, the agent may have a neural network that approximates the value function, but the network weights are uncertain until they are trained with more data.
Model uncertainty: This is the uncertainty that is related to the agent’s model structure and cannot be reduced by more data. For example, the agent may have a linear model that approximates the value function, but the model may be too simple or too complex to capture the true function.

2.2. Measures and Models of Uncertainty

Once we have identified the sources and types of uncertainty in reinforcement learning, the next question is how to measure and model them. Measuring and modeling uncertainty is crucial for designing and evaluating exploration and exploitation strategies, as they provide the agent with a way to quantify and represent its uncertainty and use it to guide its actions.

Some of the common measures of uncertainty in reinforcement learning are:

Variance: This is the measure of how much the agent’s estimates vary around their mean. For example, the agent may have a value function that estimates the expected return for each state-action pair, and the variance of the value function measures how much the agent’s estimates differ from the average value. A high variance indicates a high uncertainty, as the agent is unsure about the true value of its actions.
Entropy: This is the measure of how much information is missing or uncertain in the agent’s distribution. For example, the agent may have a policy that specifies the probability of choosing each action in each state, and the entropy of the policy measures how much the agent’s actions are random or unpredictable. A high entropy indicates a high uncertainty, as the agent has a lot of possible actions to choose from.
Confidence interval: This is the measure of how likely the agent’s estimates are to be within a certain range of the true value. For example, the agent may have a value function that estimates the expected return for each state-action pair, and the confidence interval of the value function measures the range of values that the agent is confident that the true value lies within. A wide confidence interval indicates a high uncertainty, as the agent has a large margin of error in its estimates.

Some of the common models of uncertainty in reinforcement learning are:

Bayesian models: These are models that use Bayesian inference to update the agent’s beliefs about the environment, the reward, and the optimal action based on the observed data. For example, the agent may have a prior distribution over the value function, and update it with a posterior distribution after observing a state, an action, and a reward. Bayesian models can capture both aleatoric and epistemic uncertainty, as they represent the agent’s uncertainty as a probability distribution over the possible values.
Bootstrap models: These are models that use bootstrapping to generate multiple estimates of the environment, the reward, and the optimal action based on the observed data. For example, the agent may have a set of neural networks that approximate the value function, and train each network with a different subset of the data. Bootstrap models can capture epistemic uncertainty, as they represent the agent’s uncertainty as a set of diverse estimates.
Ensemble models: These are models that use ensemble learning to combine multiple estimates of the environment, the reward, and the optimal action based on the observed data. For example, the agent may have a set of neural networks that approximate the value function, and average their outputs to obtain a final estimate. Ensemble models can capture parametric uncertainty, as they represent the agent’s uncertainty as a weighted average of the estimates.

Measuring and modeling uncertainty in reinforcement learning is not a trivial task, as different sources and types of uncertainty may require different methods and assumptions. Moreover, the choice of the measure and the model may affect the performance and the complexity of the agent, as they determine how the agent updates its knowledge and chooses its actions. In the following section, we will discuss the exploration and exploitation trade-off and some of the common strategies for balancing them.

3. Exploration and Exploitation Trade-off

The exploration and exploitation trade-off can be formalized as a multi-armed bandit problem. A multi-armed bandit is a simplified version of reinforcement learning, where the agent has to choose one of several actions (arms) in each round, and receive a stochastic reward based on the chosen action. The agent’s goal is to maximize its cumulative reward over a finite number of rounds. The agent faces uncertainty about the expected reward of each action, and has to balance between exploring the actions with unknown or high variance rewards, and exploiting the actions with known or high mean rewards.

The exploration and exploitation trade-off can be measured by the regret, which is the difference between the optimal cumulative reward and the actual cumulative reward obtained by the agent. The optimal cumulative reward is the reward that the agent would have obtained if it always chose the best action in each round. The actual cumulative reward is the reward that the agent obtained by following its exploration and exploitation strategy. The regret quantifies how much the agent loses by not knowing the optimal action in advance. The agent’s goal is to minimize its regret over time.

The exploration and exploitation trade-off can be influenced by several factors, such as the level and type of uncertainty, the number and quality of actions, the time horizon and the discount factor, the reward function and the objective function, and the prior knowledge and the feedback mechanism. Different exploration and exploitation strategies may have different assumptions and performance guarantees depending on these factors. In the following sections, we will discuss some of the common exploration and exploitation strategies and how they balance the trade-off.

3.1. Exploration Strategies

Exploration strategies are methods that the agent uses to try out new actions and discover new information about the environment. Exploration strategies can be classified into two main categories: random exploration and directed exploration.

Random exploration is the simplest and most common form of exploration, where the agent chooses actions randomly or according to a fixed probability distribution. Random exploration does not depend on the agent’s knowledge or uncertainty, and can be easily implemented and analyzed. However, random exploration can also be inefficient and wasteful, as the agent may explore irrelevant or redundant actions, or miss out on important actions.

Some of the common random exploration strategies are:

Epsilon-greedy: This is a strategy where the agent chooses the best action according to its current estimate of the value function with probability 1 – epsilon, and chooses a random action with probability epsilon. Epsilon is a parameter that controls the trade-off between exploration and exploitation. A high epsilon means more exploration, and a low epsilon means more exploitation. Epsilon can be fixed or decay over time.
Boltzmann exploration: This is a strategy where the agent chooses an action according to a softmax function of its current estimate of the value function. The softmax function assigns a probability to each action that is proportional to the exponential of its value. The temperature is a parameter that controls the trade-off between exploration and exploitation. A high temperature means more exploration, and a low temperature means more exploitation. The temperature can be fixed or decay over time.
Epsilon-decreasing: This is a strategy where the agent chooses a random action with probability epsilon, and chooses the best action according to its current estimate of the value function with probability 1 – epsilon. Epsilon is a parameter that starts from a high value and decreases over time, according to a predefined schedule. This strategy allows the agent to explore more in the beginning and exploit more in the end.

Directed exploration is a more sophisticated form of exploration, where the agent chooses actions based on its uncertainty or curiosity. Directed exploration depends on the agent’s knowledge or uncertainty, and can be more efficient and effective, as the agent can explore relevant or novel actions, or avoid exploring actions that are already well-known.

Some of the common directed exploration strategies are:

Optimism in the face of uncertainty: This is a strategy where the agent chooses the action that has the highest upper bound of its value, according to its uncertainty measure or model. This strategy encourages the agent to explore actions that have a high potential reward or a high uncertainty, as they may lead to better outcomes than the current estimate. This strategy can be implemented using confidence intervals, Bayesian models, or bootstrap models.
Thompson sampling: This is a strategy where the agent samples an action from its posterior distribution over the value function, according to its uncertainty measure or model. This strategy encourages the agent to explore actions that have a high probability of being optimal, according to its beliefs. This strategy can be implemented using Bayesian models or bootstrap models.
Information gain: This is a strategy where the agent chooses the action that maximizes the expected reduction in its uncertainty, according to its uncertainty measure or model. This strategy encourages the agent to explore actions that provide the most information about the environment, the reward, or the optimal action. This strategy can be implemented using entropy, Bayesian models, or ensemble models.

Exploration strategies are essential for the agent to learn and improve its performance in reinforcement learning, but they also have some challenges and limitations. For example, exploration strategies may require additional computation or memory, may depend on the choice of the uncertainty measure or model, may have different convergence or regret guarantees, or may be sensitive to the environment dynamics or the reward function. In the next section, we will discuss the exploitation strategies and how they balance the trade-off with exploration.

3.2. Exploitation Strategies

Exploitation strategies are the opposite of exploration strategies. They aim to maximize the expected reward by choosing the best action according to the current knowledge. Exploitation strategies are useful when the agent has enough data and confidence to make good decisions, and when the environment is stable and predictable.

Some of the common exploitation strategies are:

Greedy strategy: This is the simplest and most straightforward exploitation strategy. It simply chooses the action that has the highest estimated value or reward. For example, if the agent has a value function $V(s)$ that estimates the value of each state $s$, then the greedy strategy chooses the action that maximizes $V(s)$. The greedy strategy is easy to implement and efficient, but it can be very myopic and prone to errors, especially when the value function is inaccurate or incomplete.
Epsilon-greedy strategy: This is a variation of the greedy strategy that introduces a small probability of exploration. With probability $\epsilon$, the agent chooses a random action, and with probability $1-\epsilon$, the agent chooses the greedy action. The parameter $\epsilon$ controls the trade-off between exploration and exploitation. A high $\epsilon$ means more exploration, and a low $\epsilon$ means more exploitation. The epsilon-greedy strategy is a simple and effective way to balance exploration and exploitation, but it can be hard to choose the optimal value of $\epsilon$.
Boltzmann exploration: This is another variation of the greedy strategy that uses a softmax function to choose the action. The softmax function assigns a probability to each action based on its estimated value or reward, and then samples an action from this probability distribution. The softmax function is controlled by a temperature parameter $T$, which affects the exploration-exploitation trade-off. A high $T$ means more exploration, and a low $T$ means more exploitation. The Boltzmann exploration strategy is more flexible and adaptive than the epsilon-greedy strategy, but it can be more computationally expensive and sensitive to the temperature parameter.

Exploitation strategies are essential for the agent to achieve high performance and efficiency, but they can also lead to suboptimal behavior and stagnation if the agent does not explore enough. In the next section, we will discuss how to balance exploration and exploitation using some advanced strategies.

4. Balancing Exploration and Exploitation

Balancing exploration and exploitation is one of the most important and challenging problems in reinforcement learning. As we have seen, exploration and exploitation are often in conflict, and finding the optimal balance between them depends on many factors, such as the level and type of uncertainty, the size and complexity of the environment, the reward function, and the agent’s goals and constraints.

There is no single or universal solution to the exploration-exploitation dilemma, but there are some general principles and strategies that can help the agent achieve a good balance. Some of these strategies are:

Optimism in the face of uncertainty: This is a principle that states that the agent should act as if the unknown states or actions are better than the known ones. This encourages the agent to explore more and discover potentially better options. For example, the agent can initialize the value function with high values, or add a bonus to the reward function based on the uncertainty of the state or action.
Thompson sampling: This is a strategy that uses Bayesian inference to model the uncertainty of the value function or the reward function. The agent maintains a posterior distribution over the parameters of the function, and samples from this distribution to choose the action. This allows the agent to balance exploration and exploitation based on the probability of each action being optimal.
Upper confidence bound: This is a strategy that uses a confidence interval to estimate the uncertainty of the value function or the reward function. The agent chooses the action that has the highest upper bound of the confidence interval, which is a combination of the mean and the standard deviation of the function. This ensures that the agent explores the actions that have high uncertainty or high potential value.
Information gain: This is a strategy that uses information theory to measure the value of exploration. The agent chooses the action that maximizes the expected reduction in entropy or uncertainty of the value function or the reward function. This means that the agent explores the actions that provide the most information or learning.

These are some of the most popular and effective strategies for balancing exploration and exploitation, but they are not the only ones. There are many other methods and variations that can be applied to different reinforcement learning problems and scenarios. The choice of the best strategy depends on the specific characteristics and objectives of the problem, as well as the available resources and computational power.

In the next and final section, we will summarize the main points of this blog and provide some references and resources for further learning.

4.1. Optimism in the Face of Uncertainty

Optimism in the face of uncertainty is a principle that states that the agent should act as if the unknown states or actions are better than the known ones. This encourages the agent to explore more and discover potentially better options. Optimism in the face of uncertainty can be implemented in different ways, depending on the agent’s model and algorithm.

One way to implement optimism in the face of uncertainty is to initialize the value function with high values. This means that the agent assumes that every state or action has a high potential reward, until proven otherwise by experience. This makes the agent prefer the unexplored states or actions over the explored ones, as they have higher estimated values. For example, if the agent uses a table to store the value of each state-action pair, it can initialize the table with a large positive number, such as $+1$. This is also known as the optimistic initialization method.

Another way to implement optimism in the face of uncertainty is to add a bonus to the reward function based on the uncertainty of the state or action. This means that the agent receives an extra reward for choosing a state or action that has high uncertainty, in addition to the actual reward from the environment. This makes the agent value the exploration more, as it increases the expected reward. For example, if the agent uses a Bayesian model to estimate the uncertainty of the reward function, it can add a bonus that is proportional to the standard deviation of the posterior distribution. This is also known as the upper confidence bound method, which we will discuss in more detail in section 4.3.

Optimism in the face of uncertainty is a simple and effective way to balance exploration and exploitation, but it also has some limitations and drawbacks. For example, it can be too optimistic and overestimate the value of some states or actions, leading to poor performance. It can also be too sensitive to the choice of the initial values or the bonus function, which may not be easy to tune. Moreover, it may not work well in non-stationary environments, where the reward function changes over time.

In the next section, we will discuss another strategy for balancing exploration and exploitation, called Thompson sampling, which uses Bayesian inference to model the uncertainty of the value function or the reward function.

4.2. Thompson Sampling

Thompson sampling is a strategy that uses Bayesian inference to model the uncertainty of the value function or the reward function. The agent maintains a posterior distribution over the parameters of the function, and samples from this distribution to choose the action. This allows the agent to balance exploration and exploitation based on the probability of each action being optimal.

Thompson sampling works as follows:

The agent starts with a prior distribution over the parameters of the value function or the reward function, which represents the initial beliefs about the function.
At each time step, the agent samples a set of parameters from the posterior distribution, which is updated based on the observed data.
The agent chooses the action that maximizes the value function or the reward function, given the sampled parameters.
The agent observes the outcome of the action and updates the posterior distribution accordingly.

Thompson sampling has several advantages over other exploration and exploitation strategies. For example, it is more efficient and robust than the epsilon-greedy or the Boltzmann exploration strategies, as it does not require tuning any parameters. It is also more flexible and adaptive than the optimistic initialization or the upper confidence bound strategies, as it can handle different types and levels of uncertainty. Moreover, it can be applied to different reinforcement learning problems and scenarios, such as bandits, Markov decision processes, or contextual bandits.

Thompson sampling is a powerful and elegant strategy for balancing exploration and exploitation, but it also has some limitations and challenges. For example, it can be computationally expensive and intractable to maintain and sample from the posterior distribution, especially when the value function or the reward function is complex or high-dimensional. It can also be sensitive to the choice of the prior distribution, which may not reflect the true function. Furthermore, it may not work well in non-stationary environments, where the value function or the reward function changes over time.

In the next section, we will discuss another strategy for balancing exploration and exploitation, called upper confidence bound, which uses a confidence interval to estimate the uncertainty of the value function or the reward function.

4.3. Upper Confidence Bound

Upper confidence bound (UCB) is a strategy that uses a confidence interval to estimate the uncertainty of the value function or the reward function. The agent chooses the action that has the highest upper bound of the confidence interval, which is a combination of the mean and the standard deviation of the function. This ensures that the agent explores the actions that have high uncertainty or high potential value.

UCB works as follows:

The agent starts with a value function or a reward function that has a mean and a standard deviation for each state or action, which can be initialized arbitrarily.
At each time step, the agent calculates the upper bound of the confidence interval for each state or action, using a formula that depends on the number of times the state or action has been visited and a parameter that controls the exploration-exploitation trade-off.
The agent chooses the state or action that has the highest upper bound of the confidence interval.
The agent observes the outcome of the state or action and updates the mean and the standard deviation of the value function or the reward function accordingly.

UCB has several advantages over other exploration and exploitation strategies. For example, it is more robust and reliable than the greedy or the epsilon-greedy strategies, as it does not depend on a fixed parameter or a random choice. It is also more efficient and simple than the Thompson sampling or the information gain strategies, as it does not require maintaining and sampling from a posterior distribution or calculating the entropy of the function. Moreover, it can be applied to different reinforcement learning problems and scenarios, such as bandits, Markov decision processes, or contextual bandits.

UCB is a popular and effective strategy for balancing exploration and exploitation, but it also has some limitations and challenges. For example, it can be too optimistic and overexplore some states or actions, leading to suboptimal performance. It can also be sensitive to the choice of the exploration-exploitation parameter, which may not be easy to tune. Furthermore, it may not work well in non-stationary environments, where the value function or the reward function changes over time.

In the next section, we will discuss another strategy for balancing exploration and exploitation, called information gain, which uses information theory to measure the value of exploration.

4.4. Information Gain

Information gain is a strategy that uses information theory to measure the value of exploration. The agent chooses the action that maximizes the expected reduction in entropy or uncertainty of the value function or the reward function. This means that the agent explores the actions that provide the most information or learning.

Information gain works as follows:

The agent starts with a value function or a reward function that has an entropy or uncertainty for each state or action, which can be calculated based on the distribution of the function.
At each time step, the agent calculates the expected information gain for each state or action, using a formula that depends on the probability and the entropy of the state or action before and after taking the action.
The agent chooses the state or action that has the highest expected information gain.
The agent observes the outcome of the state or action and updates the entropy or uncertainty of the value function or the reward function accordingly.

Information gain has several advantages over other exploration and exploitation strategies. For example, it is more principled and rational than the greedy or the epsilon-greedy strategies, as it does not rely on a heuristic or a random choice. It is also more informative and selective than the optimistic initialization or the upper confidence bound strategies, as it does not assume that all unknown states or actions are equally valuable. Moreover, it can be applied to different reinforcement learning problems and scenarios, such as bandits, Markov decision processes, or contextual bandits.

Information gain is a sophisticated and elegant strategy for balancing exploration and exploitation, but it also has some limitations and challenges. For example, it can be computationally expensive and difficult to calculate the entropy or the information gain of the value function or the reward function, especially when the function is complex or high-dimensional. It can also be sensitive to the choice of the distribution or the model of the function, which may not reflect the true function. Furthermore, it may not work well in non-stationary environments, where the value function or the reward function changes over time.

In the next and final section, we will summarize the main points of this blog and provide some references and resources for further learning.

5. Conclusion

In this blog, we have reviewed the concepts and challenges of uncertainty in reinforcement learning, and the strategies for balancing exploration and exploitation to achieve optimal performance. We have covered the following topics:

Sources and types of uncertainty in reinforcement learning
Measures and models of uncertainty in reinforcement learning
Exploration and exploitation trade-off
Exploration strategies
Exploitation strategies
Balancing exploration and exploitation

We have learned that uncertainty is a fundamental aspect of reinforcement learning, as the agent has to deal with incomplete and noisy information about the environment, the reward, and the optimal action. We have also learned that exploration and exploitation are essential for the agent to learn and improve its performance, but they are often in conflict. Therefore, the agent needs to balance exploration and exploitation using different strategies, depending on the nature and level of uncertainty.

Some of the common strategies for balancing exploration and exploitation are:

Optimism in the face of uncertainty, which assumes that the unknown states or actions are better than the known ones.
Thompson sampling, which uses Bayesian inference to model the uncertainty of the value function or the reward function.
Upper confidence bound, which uses a confidence interval to estimate the uncertainty of the value function or the reward function.
Information gain, which uses information theory to measure the value of exploration.

Each of these strategies has its own advantages and limitations, and there is no single best strategy for all reinforcement learning problems and scenarios. The agent needs to choose the appropriate strategy based on the characteristics of the environment, the reward, and the optimal action, as well as the computational and data resources available.

We hope that this blog has given you a better understanding of how uncertainty affects reinforcement learning, and how to design and implement effective exploration and exploitation strategies. If you want to learn more about this topic, here are some references and resources that you can check out:

Uncertainty in Reinforcement Learning: Survey and Future Directions, a comprehensive survey paper that covers the theoretical and practical aspects of uncertainty in reinforcement learning.
Reinforcement Learning Course by David Silver – Lecture 10: Exploration and Exploitation, a video lecture that explains the exploration and exploitation trade-off and some of the common strategies for balancing them.
Uncertainty in Reinforcement Learning: Code Examples, a GitHub repository that contains code examples of implementing different exploration and exploitation strategies in Python.

Thank you for reading this blog, and we hope you enjoyed it. If you have any questions or feedback, please feel free to leave a comment below. Happy learning!