# Dynamic Programming#

Dynamic programming is a mathematical method for solving complex problems by breaking them down into smaller sub-problems, solving those sub-problems, and combining the solutions to form the solution to the original problem. In the context of reinforcement learning, dynamic programming can be used to find the value of a given state using the estimated values of next states. It can also be used to find the optimal value function (the value function that arises from following the optimal policy).

Dynamic programming for reinforcement learning is mainly used in problems where the environment dynamics are known. The basic idea is to use the knowledge of the environment’s state transitions and rewards to build a mathematical model of the environment and then use this model to find an optimal policy.

There are two main approaches to dynamic programming in reinforcement learning: value iteration and policy iteration. In value iteration, the goal is to find the state-value function, which gives the expected return of an agent in a given state. This is done by iteratively updating the state-value function until it converges to the optimal solution. In policy iteration, the goal is to find the optimal policy directly. This is done by alternating between evaluating the current policy and improving it, until convergence to the optimal policy.

Dynamic programming approaches have the advantage of being computationally efficient, but they can be limited in their applicability due to the need for a complete and accurate model of the environment. Additionally, these approaches may not be suitable for problems with large state spaces or problems where the environment dynamics cannot be accurately modeled.