On Function Approximation in Reinforcement Learning: Optimism in the Face of Large State Spaces

Understand

The classical theory of reinforcement learning (RL) has focused on tabular and linear representations of value functions.

• Further progress hinges on combining RL with modern function approximators such as kernel functions and deep neural networks, and indeed there have been many empirical successes that have exploited such combinations in large-scale applications.
• There are profound challenges, however, in developing a theory to support this enterprise, most notably the need to take into consideration the exploration-exploitation tradeoff at the core of RL in conjunction with the computational and statistical tradeoffs that arise in modern function-approximation-based learning systems.
• We approach these challenges by studying an optimistic modification of the least-squares value iteration algorithm, in the context of the action-value function represented by a kernel function or an overparameterized neural network.