R-max - a General Polynomial Time Algorithm for Near-Optimal Reinforcement Learning

R-MAX is a simple model-based reinforcement learning algorithm which can attain near-optimal average reward in polynomial time. In R-MAX, the agent always maintains a complete, but possibly inaccurate model of its environment and acts based on the optimal policy derived from this model. The model is initialized in an optimistic fashion: all actions in all states return the maximal possible reward (hence the name). During execution, the model is updated based on the agent's observations. R-MAX improves upon several previous algorithms: (1) It is simpler and more general than Kearns and Singh's E3 algorithm, covering zerosum stochastic games. (2) It has a built-in mechanism for resolving the exploration vs. exploitation dilemma. (3) It formally justifies the "optimism under uncertainty" bias used in many RL algorithms. (4) It is much simpler and more general than Brafman and Tennenholtz's LSG algorithmfor learning in single controller stochastic games. (5) It generalizes the algorithm by Monderer and Tennenholtz for learning in repeated games. (6) It is the only algorithm for near-optimal learning in repeated games known to be polynomial, providing a much simpler and more efficient alternative to previous algorithms by Banos and by Megiddo.