State-Separated SARSA: A Practical Sequential Decision-Making Algorithm with Recovering Rewards

While many multi-armed bandit algorithms assume that rewards for all arms are constant across rounds, this assumption does not hold in many real-world scenarios. This paper considers the setting of recovering bandits, where the reward depends on the number of rounds elapsed since the last time an arm was pulled. We propose a new reinforcement learning (RL) algorithm tailored to this setting, named the State-Separated SARSA (SS-SARSA) algorithm, which treats the elapsed rounds as states. The SS-SARSA algorithm achieves efficient learning by reducing the number of state combinations required for Q-learning/SARSA, which often suffers from combinatorial explosion for large-scale RL problems. Additionally, it makes minimal assumptions about the reward structure and has lower computational complexity. Furthermore, we prove asymptotic convergence to an optimal policy under mild assumptions. Simulation studies demonstrate the superior performance of our algorithm across various settings.