How does dynamic programming work in reinforcement learning?

Dynamic programming (DP) in reinforcement learning (RL) provides a framework for solving Markov Decision Processes (MDPs) when the environment’s dynamics (transition probabilities and rewards) are fully known. DP algorithms break the problem into smaller subproblems by iteratively computing value functions, which estimate the expected long-term reward of states or state-action pairs. For example, methods like policy iteration and value iteration use these value functions to improve the agent’s policy—the strategy dictating which actions to take—until it converges to an optimal solution. These approaches rely on the Bellman equations, which define the recursive relationship between the value of a state and the values of its possible successor states.

A key example of DP in RL is policy iteration, which alternates between two steps: policy evaluation and policy improvement. During policy evaluation, the algorithm calculates the value of each state under the current policy by iteratively updating estimates until they stabilize. Once the values are accurate, policy improvement updates the policy by selecting actions that maximize the expected value in each state. For instance, in a grid world navigation task, the agent might compute the value of each grid cell based on its current policy (e.g., “move right”) and then adjust the policy to prioritize cells with higher values. Similarly, value iteration combines these steps by directly updating state values using the maximum possible reward from immediate actions, bypassing explicit policy evaluation cycles. This is useful in scenarios like inventory management, where states represent stock levels, and actions determine order quantities to minimize costs.

While DP is theoretically sound, its practical use in RL is limited by the assumption that the environment’s dynamics are fully known. Real-world RL problems often lack this information, leading to model-free methods like Q-learning. However, DP remains foundational for understanding RL concepts and is still applicable in controlled environments (e.g., simulations or games with known rules). For example, in a chess-playing agent, DP could precompute optimal moves if the game’s state transitions and rewards are modeled perfectly. Developers should also note that DP algorithms can be computationally intensive for large state spaces, prompting approximations like prioritized sweeping or using function approximators (e.g., neural networks) to generalize across states. These trade-offs highlight DP’s role as a building block for more scalable RL techniques.