Value Functions and the Bellman Equation — Thinking Ahead
The key idea that makes reinforcement learning work is deceptively simple: instead of chasing immediate reward, estimate the long-term value of being in a situation, and act to move toward high-value situations. Value functions are how an agent "thinks ahead," and the Bellman equation is the elegant recursive relationship that makes computing them possible. This is the conceptual core of RL — grasp it and the algorithms become obvious.
The idea that makes RL work: estimate the long-term value of a situation and move toward high-value ones. State-value and Q-functions, the Bellman equation (value = reward + γ × value-of-next) that turns infinite look-ahead into a recursion and solves credit assignment, and planning vs learning.