Chapter4.pdf

Notes on Chapter 4: Policy-Based Reinforcement Learning 1 Core Concepts Policy-Based Reinforcement Learning: A method that directly optimizes the policy that the agent follows, without explicitly using a value function. This approach is particularly effective in continuo...

Notes on Chapter 4: Policy-Based Reinforcement Learning 1 Core Concepts Policy-Based Reinforcement Learning: A method that directly optimizes the policy that the agent follows, without explicitly using a value function. This approach is particularly effective in continuous action spaces where value-based methods may become unstable. 2 Core Problem Core Problem in Policy-Based RL: Finding the optimal policy in environments with continuous action spaces, such as robotics, self-driving cars, and real-time strategy games. The challenge lies in efficiently exploring and exploiting the action space to improve the policy. 3 Core Algorithms Policy Gradient Methods: Optimize the policy by following the gradient of expected reward with respect to the policy parameters. Examples include REINFORCE and Actor-Critic methods. 4 Jumping Robots Example: Jumping robots in continuous action spaces illustrate the need for policy-based methods to handle the infinite possibilities of action values. 5 Continuous Problems Continuous Problems: These are problems where the action space is continuous rather than discrete. Examples include robotic control and real-time strategy games where actions can take any value within a range. 5.1 Continuous Policies Definition: Policies that can take on any value within a range, suitable for environments where actions are not discrete but continuous. Equation: The policy π(a|s, θ) represents the probability of taking action a in state s parameter- ized by θ. Example: A robotic arm moving over arbitrary angles. 5.2 Stochastic Policies Definition: Policies that introduce randomness in action selection to encourage exploration and prevent premature convergence to suboptimal actions. Equation: The stochastic policy is often modeled by a probability distribution, e.g., π(a|s, θ) = N (µ(s, θ), σ(s, θ)) for a Gaussian distribution. Example: A self-driving car deciding between multiple safe paths. 1 5.3 Environments: Gym and MuJoCo Gym: A toolkit for developing and comparing reinforcement learning algorithms with a wide variety of environments. MuJoCo: A physics engine for simulating continuous control tasks, often used in reinforcement learning research for robotics. 5.3.1 Robotics Application: Using policy-based methods to control robotic arms, drones, and other mechanical systems with continuous actions. 5.3.2 Physics Models Application: Simulating realistic physical interactions in environments to train agents for tasks like walking, jumping, or manipulating objects. 5.3.3 Games Application: Training agents in complex games with continuous actions, such as strategy games and simulations. 6 Policy-Based Agents Policy-Based Agents: Agents that use policy gradient methods to optimize their actions. These agents directly learn the policy that maps states to actions. 6.1 Policy-Based Algorithm: REINFORCE Algorithm 1 REINFORCE Algorithm 1: Initialize policy parameters θ 2: for each episode do 3: Generate episode using policy π(a|s, θ) 4: for each step in episode do 5: Compute return R 6: Update policy parameters: θ ← θ + α∇θ log π(a|s, θ)R 7: end for 8: end for Equation: The policy gradient update rule is θ ← θ + α∇θ log π(a|s, θ)R where R is the return. Example: Training a policy to maximize the reward in a game by directly updating the policy parameters based on the observed returns. 6.2 Online and Batch Online: Updating the policy parameters after every episode. Batch: Accumulating gradients over multiple episodes and then updating the parameters. 6.3 Bias-Variance Trade-Off in Policy-Based Methods Explanation: Balancing the trade-off between bias (error due to approximations) and variance (error due to randomness) to ensure stable and efficient learning. 2 6.4 Actor Critic Bootstrapping Algorithm 2 Actor-Critic Algorithm 1: Initialize actor parameters θ and critic parameters ϕ 2: for each episode do 3: Generate episode using policy π(a|s, θ) 4: for each step in episode do 5: Compute TD error: δ = r + γV (s′ , ϕ) − V (s, ϕ) 6: Update critic parameters: ϕ ← ϕ + βδ∇ϕ V (s, ϕ) 7: Update actor parameters: θ ← θ + α∇θ log π(a|s, θ)δ 8: end for 9: end for Temporal Difference Bootstrapping: Using estimates of future rewards to update the value function incrementally. Example: Using Actor-Critic methods to train a robot to navigate through an environment by continuously updating both the policy and value functions based on observed rewards and states. 6.5 Temporal Difference Bootstrapping Definition: A method that updates value estimates based on estimates of future values. It combines the ideas of dynamic programming and Monte Carlo methods. Equation: The update rule for the state-value function V is: V (st ) ← V (st ) + α [rt+1 + γV (st+1 ) − V (st )] where rt+1 is the reward received after taking action at in state st , γ is the discount factor, and α is the learning rate. Example: Using TD learning to update the value estimates in a game of tic-tac-toe by bootstrap- ping the current estimate with the next state’s estimated value. 6.6 Baseline Subtraction with Advantage Function Advantage Function: Measures how much better an action is compared to the average action in a given state. Equation: A(s, a) = Q(s, a) − V (s) Example: Improving policy updates by subtracting a baseline value from the observed rewards to reduce variance and make learning more stable. 6.7 Generic Policy Gradient Formulation Equation: ∇θ J(θ) = E[∇θ log π(a|s, θ)A(s, a)] 6.8 Asynchronous Advantage Actor Critic Algorithm: A3C (Asynchronous Advantage Actor-Critic) runs multiple agents in parallel to up- date the policy and value functions asynchronously. Example: Speeding up learning by having multiple agents explore the environment simultaneously and asynchronously updating the global policy and value functions. 3 Algorithm 3 Trust Region Policy Optimization (TRPO) 1: Initialize policy parameters θ 2: for each iteration do 3: Sample trajectories using current policy πθk 4: Compute policy gradient ĝ 5: Compute step direction dˆ using conjugate gradient 6: Update policy parameters: θk+1 = θk + αdˆ within trust region 7: end for 6.9 Trust Region Optimization Explanation: TRPO ensures policy updates are within a trust region to maintain stability and prevent large, destabilizing updates. 6.10 Entropy and Exploration Entropy: Adding an entropy term to the objective function to encourage exploration by preventing premature convergence. Soft Actor Critic: An algorithm that incorporates entropy maximization into the policy update to balance exploration and exploitation. Example: Encouraging an agent to explore more by adding an entropy term to the objective function, preventing it from getting stuck in suboptimal policies. 6.11 Deterministic Policy Gradient Algorithm: DDPG (Deep Deterministic Policy Gradient) combines DQN and policy gradients for environments with continuous actions. Equation: The deterministic policy gradient is ∇θ J(θ) = E[∇a Q(s, a)∇θ µ(s, θ)] where µ is the policy. Example: Training a robotic arm to precisely control its movements using deterministic policy gradients. 6.12 Hands On: PPO and DDPG MuJoCo Examples PPO: Proximal Policy Optimization, a method that simplifies TRPO while retaining performance. DDPG: Applying DDPG to control tasks in MuJoCo to demonstrate policy learning in continuous action spaces. Example: Implementing PPO and DDPG in a MuJoCo environment to train agents for various control tasks. 7 Locomotion and Visuo-Motor Environments Locomotion and Visuo-Motor Environments: These environments focus on training agents to move and interact with their surroundings using visual inputs and motor actions. 7.1 Locomotion Application: Training agents to move and navigate in environments, such as walking, running, or flying. Example: Using policy-based methods to train a bipedal robot to walk or a drone to fly through an obstacle course. 4 7.2 Visuo-Motor Interaction Application: Combining visual perception with motor control to interact with objects and envi- ronments. Example: Training an agent to play table tennis by integrating visual input to track the ball and motor control to hit it accurately. 7.3 Benchmarking Explanation: Using standardized tasks and environments to evaluate and compare the perfor- mance of reinforcement learning algorithms. Example: Evaluating different policy-based methods on common benchmarks like MuJoCo loco- motion tasks or Atari games to compare their effectiveness. 8 Conclusion 9 Summary and Further Reading 9.1 Summary Policy-based reinforcement learning directly optimizes the policy, making it suitable for continuous action spaces. Various algorithms like REINFORCE, Actor-Critic, TRPO, and PPO are used to handle the challenges in these environments. 9.2 Further Reading Suggested literature and resources for a deeper understanding of policy-based reinforcement learn- ing and its applications in complex environments. Questions 1. Why are value-based methods difficult to use in continuous action spaces? Value-based methods are difficult to use in continuous action spaces because they require discretizing the action space or finding the maximum value action, which is computationally infeasible. 2. What is MuJoCo? Can you name a few example tasks? MuJoCo is a physics engine used for simulating continuous control tasks. Examples include humanoid locomotion, robotic arm manipulation, and bipedal walking. 3. What is an advantage of policy-based methods? Policy-based methods can directly optimize the policy for continuous action spaces without requiring discretization or explicit value function estimation. 4. What is a disadvantage of full-trajectory policy-based methods? Full-trajectory policy-based methods can have high variance in their gradient estimates, which can slow down learning and make it unstable. 5. What is the difference between actor critic and vanilla policy-based methods? Actor-Critic methods combine policy-based (actor) and value-based (critic) approaches to reduce variance and improve learning stability, whereas vanilla policy-based methods use only the policy gradient. 6. How many parameter sets are used by actor critic? How can they be represented in a neural network? 5  Actor-Critic methods use two parameter sets: one for the actor (policy) and one for the critic (value function). They can be represented in a neural network with separate layers or heads for the actor and critic. 7. Describe the relation between Monte Carlo REINFORCE, n-step methods, and tem- poral difference bootstrapping. Monte Carlo REINFORCE uses full episode returns for updates, n-step methods use returns over n steps, and temporal difference bootstrapping uses a single step with a bootstrapped estimate of future rewards. 8. What is the advantage function? The advantage function measures the relative value of an action compared to the average value of all actions in a given state, defined as A(s, a) = Q(s, a) − V (s). 9. Describe a MuJoCo task that methods such as PPO can learn to perform well. PPO can learn to control a bipedal robot to walk or run efficiently in a MuJoCo environment by optimizing the policy for continuous and complex movements. 10. Give two actor critic approaches to further improve upon bootstrapping and advantage functions, that are used in high-performing algorithms such as PPO and SAC. Two approaches are using clipped surrogate objectives in PPO and entropy regularization in SAC to encourage exploration and stabilize learning. 11. Why is learning robot actions from image input hard? Learning robot actions from image input is hard due to the high-dimensionality of images, requiring complex feature extraction and representation learning, and the challenge of associ- ating visual input with motor actions. In class Questions Policy-Based 1. When do you use value-based, when policy-based? Use value-based methods in environments with discrete actions where you can estimate the value of actions precisely. Use policy-based methods in continuous action spaces or when the policy needs to be directly optimized. 2. What is policy-based? Policy-based reinforcement learning directly optimizes the policy that the agent follows, with- out explicitly using a value function. 3. Name a famous policy-based algorithm. REINFORCE. 4. What is a modern hybrid approach? Actor-Critic methods, which combine value-based and policy-based approaches. 5. What is a modern AC algorithm? Asynchronous Advantage Actor-Critic (A3C). 6. What approaches are there for improving AC algorithms? Approaches include using experience replay, prioritized experience replay, entropy regular- ization, trust region optimization (TRPO), proximal policy optimization (PPO), and asyn- chronous updates (A3C). 6