Bellman Equation
The Bellman equation is a fundamental concept in dynamic programming and reinforcement learning that expresses the value of a decision problem in terms of the value of its subproblems. It breaks down complex optimization problems into simpler recursive relationships, enabling efficient computation of optimal policies. Named after Richard Bellman, it is central to solving Markov decision processes (MDPs) by defining the optimal value function recursively.
Developers should learn the Bellman equation when working on optimization problems in fields like reinforcement learning, robotics, or economics, as it provides a mathematical framework for decision-making under uncertainty. It is essential for implementing algorithms such as value iteration, policy iteration, and Q-learning, which are used to train AI agents in environments like games or autonomous systems. Understanding this equation helps in designing efficient solutions for sequential decision problems where actions have long-term consequences.