The value function in reinforcement learning (RL) estimates the long-term return or cumulative reward an agent can expect to achieve starting from a given state, following a certain policy. The value function evaluates how good it is for an agent to be in a particular state, based on the rewards it is expected to receive in the future.
The value function is critical because it helps the agent predict which states are more beneficial to be in, even before taking actions. There are two primary types of value functions: the state-value function (V) and the action-value function (Q). The state-value function estimates the expected cumulative reward from a state, while the action-value function estimates the expected cumulative reward from a state-action pair.
The value function guides the agent to select actions that lead to high-value states. For instance, in a game, the value function might assign higher values to states closer to winning and lower values to states where the agent is in danger of losing.