Universal Reinforcement Learning

We consider an agent interacting with an unmodeled environment. At each time, the agent makes an observation, takes an action, and incurs a cost. Its actions can influence future observations and costs. The goal is to minimize the long-run average cost. We propose an algorithm for optimal control based on ideas from the Lempel-Ziv scheme for universal data compression and prediction. We establish that, if there exists an integer K such that the future is conditionally independent of the past given a window of K consecutive actions and observations, then the average cost converges to the optimum. Experimental results involving the game of Rock-Paper-Scissors illustrate merits of the algorithm.