Universal Reinforcement Learning
Vivek F. Farias, Ciamac C. Moallemi, Benjamin Van Roy, Tsachy Weissman · IEEE Transactions on Information Theory · 2010
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-term average cost. We propose a novel algorithm, known as the active LZ algorithm, for optimal control based on ideas from the Lempel-Ziv scheme for universal data compression and prediction. We establish that, under the active LZ algorithm, if there exists an integerKsuch that the future is conditionally independent of the past given a window ofKconsecutive 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.