An Analytic Solution to Discrete . . .

Reinforcement learning (RL) was originally proposed as a framework to allow agents to learn in an online fashion as they interact with their environment. Existing RL algorithms come short of achieving this goal because the amount of exploration required is often too costly and/or too time consuming for online learning. As a result, RL is mostly used for o#ine learning in simulated environments. We propose a new algorithm, called BEETLE, for e#ective online learning that is computationally e#cient while minimizing the amount of exploration. We take a Bayesian model-based approach, framing RL as a partially observable Markov decision process. Our two main contributions are the analytical derivation that the optimal value function is the upper envelope of a set of multivariate polynomials, and an e#cient pointbased value iteration algorithm that exploits this simple parameterization