The main difference between tabular and function approximation methods in reinforcement learning lies in how they represent the value function or policy.
Tabular methods store explicit values for each state or state-action pair in a table. This approach works well when the state and action spaces are small and discrete, such as in simple grid-world environments. However, it becomes infeasible when the state space is large or continuous, as the table grows exponentially.
Function approximation methods, on the other hand, use a parametric function (like a neural network) to approximate the value function or policy. These methods allow the agent to scale to more complex environments with large or continuous state spaces by generalizing the knowledge from observed states to unvisited ones. Function approximation is more flexible and powerful but can be more challenging to train and optimize.