Adaptive-resolution reinforcement learning with polynomial exploration in deterministic domains

We propose a model-based learning algorithm, the Adaptive-resolution Reinforcement Learning (ARL) algorithm, that aims to solve the online, continuous state space reinforcement learning problem in a deterministic domain. Our goal is to combine adaptive-resolution approximation schemes with efficient exploration in order to obtain polynomial learning rates. The proposed algorithm uses an adaptive approximation of the optimal value function using kernel-based averaging, going from coarse to fine kernel-based representation of the state space, which enables us to use finer resolution in the "important" areas of the state space, and coarser resolution elsewhere. We consider an online learning approach, in which we discover these important areas online, using an uncertainty intervals exploration technique. In addition, we introduce an incremental variant of the ARL (IARL), which is a more practical version of the original algorithm with reduced computational complexity at each stage. Polynomial learning rates in terms of mistake bound (in a PAC framework) are established for these algorithms, under appropriate continuity assumptions.