Policy iteration and value iteration: key methods of reinforcement learning

Policy iteration and value iteration are two algorithms commonly used in reinforcement learning. Policy iteration improves the agent's performance by iteratively improving the policy. Value iteration updates the state value function iteratively to obtain the optimal state value. The core ideas of the two are different, but they can both play a role in optimizing strategies in reinforcement learning tasks.

Strategy iteration

Strategy iteration gradually improves the strategy through iteration until a stable strategy is reached. In policy iteration, a policy is first initialized and then gradually improved through multiple iterations. Each iteration consists of two steps: evaluating the current strategy and improving the current strategy. The purpose of evaluating the current strategy is to calculate the expected reward value of the current strategy, which can be achieved through the Monte Carlo method or the temporal difference method. The purpose of improving the current strategy is to find a better strategy to replace the current strategy, which can be achieved through the deterministic policy gradient method or the Monte Carlo policy gradient method.

Value iteration

Value iteration is to gradually update the state value function through iteration to achieve a stable state value function. In value iteration, a state value function needs to be initialized first, and then the function is gradually updated through multiple iterations. Each iteration consists of two steps: calculating the expected reward value of the current state value function and updating the current state value function. The purpose of calculating the expected reward value of the current state value function is to determine the expected reward value of each state, which can be achieved by the Monte Carlo method or the temporal difference method. The Monte Carlo method estimates the expected reward value by simulating multiple actual experiences, while the temporal difference method uses the difference between the current estimate and the estimate of the next state to update the expected reward value. The purpose of updating the current state value function is to find a better state value function to replace the current function, which can be achieved through the Bellman equation. The Bellman equation calculates the value function of the current state by accumulating the reward of the current state with the expected reward of the next state. By continuously applying the Bellman equation, the state value function can be gradually updated until a stable state value function is reached. Value iteration is an efficient method for finding optimal policies in reinforcement learning. By gradually updating the state value function, value iteration can find an optimal policy that maximizes the cumulative reward.

The difference between policy iteration and value iteration

Although policy iteration and value iteration are both commonly used methods in reinforcement learning, they are implemented in There are clear differences in means and goals.

1. Implementation method

Strategy iteration is a strategy-based method that finds the optimal strategy by continuously updating the strategy. Specifically, strategy iteration consists of two steps: strategy evaluation and strategy improvement. In policy evaluation, we evaluate the value function of each state through the current policy; in policy improvement, we update the policy based on the value function of the current state to make the policy closer to the optimal policy.

Value iteration is a method based on value function, which finds the optimal strategy by continuously updating the value function. Specifically, value iteration updates the value function of each state iteratively until the value function converges. Then, we can get the optimal strategy based on the final value function.

2. Goal

The goal of strategy iteration is to directly optimize the strategy and approach the optimal strategy by continuously updating the strategy iteratively. However, since each iteration requires policy evaluation and policy improvement, the calculation amount is large.

The goal of value iteration is to obtain the optimal strategy by optimizing the state value function. It approximates the optimal value function by continuously updating the value function of each state, and then derives the optimal strategy based on this optimal value function. Compared with policy iteration, value iteration requires less calculation.

3. Convergence speed

Generally speaking, policy iteration usually converges to the optimal policy faster, but each iteration usually requires More calculations. Value iteration may require more iterations to converge.

4. Interaction with other techniques

Value iteration is easier to combine with function approximation methods (such as deep learning) because it focuses on is the optimization value function. Policy iteration is more commonly used in scenarios with clear models.

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