Nearly Optimal Exploration-Exploitation Decision Thresholds

While in general trading off exploration and exploitation in reinforcement learning is hard, under some formulations relatively simple solutions exist. Optimal decision thresholds for the multi-armed bandit problem, one for the infinite horizon discounted reward case and one for the finite horizon undiscounted reward case are derived, which make the link between the reward horizon, uncertainty and the need for exploration explicit. From this result follow two practical approximate algorithms, which are illustrated experimentally.