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1 Chris McLernon CS-370 : Current / Emerging Trends in CS Timothy Alexander, M.S., CIS

CS-340 : Client / Server Development 2 Solving Cartpole Problem with REINFORCE Algorithm: The REINFORCE algorithm is a policy gradient method that aims to directly optimize the policy parameters to maximize the expected cumulative reward. In the context of the Cartpole problem, the algorithm generates episodes using the current policy, computes the returns for each time step, and updates the policy parameters using the policy gradient. Initialize θ # Set learning rate α = 0.01 # Repeat until convergence for episode in range(num_episodes): # Generate an episode using the current policy states, actions, rewards = generate_episode(θ) # Compute the return for each time step returns = calculate_returns(rewards) # Update the policy parameters using the policy gradient for t in range(len(states)): # Compute the gradient of the log-probability of the action

CS-340 : Client / Server Development 3 gradient = compute_gradient(states[t], actions[t], θ) # Update the policy parameters θ += α * gradient * returns[t] Solving Cartpole Problem with A2C Algorithm: The A2C (Advantage Actor-Critic) algorithm combines policy learning and value estimation by maintaining an actor network for policy updates and a critic network for estimating the value function. This integration aims to improve the stability and efficiency of the learning process. # Initialize actor and critic networks Initialize θ_actor, θ_critic # Set learning rates α_actor = 0.01 α_critic = 0.05 # Repeat until convergence for episode in range(num_episodes): # Generate an episode using the current policy states, actions, rewards = generate_episode(θ_actor)

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CS-340 : Client / Server Development 4 # Compute the advantages using the critic advantages = calculate_advantages(states, rewards, θ_critic) # Update the actor parameters using the policy gradient for t in range(len(states)): gradient_actor = compute_actor_gradient(states[t], actions[t], θ_actor) θ_actor += α_actor * gradient_actor * advantages[t] # Update the critic parameters using the value function gradient value_estimate = critic_network(states[t], θ_critic) gradient_critic = compute_critic_gradient(states[t], value_estimate, θ_critic) θ_critic += α_critic * gradient_critic Policy Gradient vs. Value-Based (Q-Learning): The primary distinction between policy gradient methods, exemplified by algorithms like REINFORCE, and value-based approaches such as Q-learning, lies in the fundamental nature of their optimization targets. These two classes of reinforcement learning algorithms adopt divergent strategies for updating their parameters based on the experienced rewards within the environment. In the realm of policy gradient methods like REINFORCE, the primary objective is to directly optimize the policy of the agent. The policy, denoted by a set of parameters, represents the strategy or behavior that the agent employs to select actions in different states. During training, the parameters of this policy are adjusted to maximize the expected cumulative

CS-340 : Client / Server Development 5 reward. Crucially, policy gradient methods learn a probability distribution over actions for each state. This probabilistic nature allows for a more flexible and expressive representation of the agent's decision-making process, making policy gradient methods particularly well-suited for environments with continuous action spaces. On the other hand, value-based approaches such as Q-learning take a different route in the pursuit of optimal decision-making. Instead of directly optimizing the policy, these methods focus on learning a value function. The value function estimates the expected cumulative reward associated with taking a particular action in a specific state and following a certain policy thereafter. In the case of Q- learning, the Q-value represents the expected cumulative reward for a state-action pair. The agent then derives its policy by selecting the action with the highest Q-value in a given state. The key advantage of value-based approaches is their ability to separate the evaluation of actions (through the value function) from the policy itself. By learning a value function, the algorithm gains insights into the desirability of different state-action pairs, which can be leveraged to derive an optimal policy. This separation of concerns contributes to the stability of learning, especially in situations with sparse rewards or noisy environments. Actor-Critic vs. Value- and Policy-Based: Actor-Critic methods provide a sophisticated framework for reinforcement learning by incorporating elements from both value-based and policy-based approaches. In the A2C (Advantage Actor-Critic) algorithm, this integration is realized through the presence of two distinct neural networks: the actor network and the critic network. The actor network is responsible for policy learning, determining the mapping from states to actions. It directly influences the agent's decision-making process by outputting a probability distribution over the

CS-340 : Client / Server Development 6 available actions in a given state. The parameters of this network are updated using policy gradient methods, such as the advantage-weighted gradient in A2C, which takes into account the advantage of each action in a given state. On the other hand, the critic network is tasked with estimating the value function. It evaluates the expected cumulative reward associated with being in a particular state and following the current policy. By providing a measure of the long-term desirability of states, the critic helps to guide the actor in making better decisions. The parameters of the critic network are updated to minimize the difference between predicted and actual returns, typically using a mean squared error loss. The integration of these two components in the actor-critic architecture brings several advantages. One notable benefit is faster convergence. The critic's estimation of the value function provides a form of guidance to the actor, enabling it to focus on actions that lead to higher long-term rewards. This reduces the variance in the learning process and accelerates convergence compared to training an actor in isolation. The actor-critic architecture often results in improved stability during training. The critic's role in assessing state values helps to smooth out the learning process by providing a more stable baseline for updating the policy. This stability is crucial, especially in scenarios where the environment might be stochastic or contain sparse rewards. The actor-critic approach is particularly advantageous in environments with complex and continuous action spaces. While value-based methods like Q-learning can struggle in such domains due to the need for discretization, and pure policy-based methods face challenges in high-dimensional action spaces, actor-critic methods effectively bridge this gap. The actor provides the flexibility to handle continuous actions, and the critic enhances learning efficiency by estimating the value function.

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CS-340 : Client / Server Development 7 Bibliography

CS-340 : Client / Server Development 8 Maciej Balawejder (Apr 20, 2021). Solving OpenAI's Cartpole Using Reinforcement Learning: Part 2. https://medium.com/analytics-vidhya/solving-open-ais-cartpole-using-reinforcement- learning-part-2-73848cbda4f1

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