What is function approximation in reinforcement learning?

Function approximation in reinforcement learning is the technique of approximating the value function or policy when the state or action space is too large to represent explicitly in a table. Instead of maintaining a table of values for all states or state-action pairs, function approximation uses a parameterized model, such as a neural network, to estimate the value function or policy.

For example, in Deep Q-learning, the Q-function is approximated by a deep neural network that maps states and actions to their corresponding Q-values. This allows the agent to scale to more complex environments where tabular methods would be inefficient or impractical.

Function approximation is essential in high-dimensional state spaces (e.g., pixel data in games or images), allowing RL to work on tasks that are beyond the reach of traditional tabular methods.