# What is the Bellman optimality equation?

Source: https://zilliz.com/ai-faq/what-is-the-bellman-optimality-equation
Author: zilliz

The Bellman optimality equation is a key equation in reinforcement learning that defines the value of a state under the optimal policy. It expresses the value of a state as the maximum expected return achievable by taking the best action from that state, considering future states.

The equation is written as:
( V^*(s) = \max_a \left( R(s, a) + \gamma \sum_{s'} P(s'