How does policy iteration work in reinforcement learning?

Policy iteration is a fundamental algorithm in reinforcement learning used to find the optimal policy—a strategy that tells an agent what action to take in each state to maximize cumulative rewards. It works by iteratively improving the policy through two alternating phases: policy evaluation and policy improvement. The process starts with an initial policy (often random), calculates how good each state is under that policy (value function), then updates the policy to choose better actions based on those values. This cycle repeats until the policy no longer changes, indicating convergence to the optimal strategy.

The first phase, policy evaluation, estimates the value of each state under the current policy. This is done by solving the Bellman equations, which express the expected long-term reward of a state as the immediate reward plus the discounted future rewards from following the policy. For example, if a robot is navigating a grid world, policy evaluation would calculate how valuable each grid cell is, assuming the robot follows its current movement rules (e.g., always move left). This step is often implemented iteratively, updating the value estimates until they stabilize. The second phase, policy improvement, updates the policy to select actions that maximize the newly computed state values. Using the grid world example, the robot might switch from moving left to moving upward if that direction leads to higher-value cells. This ensures the policy becomes greedier with respect to the latest value estimates.

Policy iteration guarantees convergence to the optimal policy if given sufficient iterations, as each update either improves the policy or leaves it unchanged. However, it can be computationally expensive for large state spaces because policy evaluation requires solving a system of equations iteratively. In practice, developers often use approximations, like stopping evaluation after a fixed number of iterations or using a small error threshold. For instance, in a game with millions of states, exact policy evaluation might be infeasible, so truncated iterations or parallel computing techniques are employed. Despite its computational demands, policy iteration remains a foundational method because it clearly separates evaluation and improvement, making it easier to understand and adapt to variants like modified policy iteration.