An Adaptive Approach for Infinitely Many-armed Bandits under Generalized Rotting Constraints

In this study, we consider the infinitely many-armed bandit problems in a rested rotting setting, where the mean reward of an arm may decrease with each pull, while otherwise, it remains unchanged. We explore two scenarios regarding the rotting of rewards: one in which the cumulative amount of rotting is bounded by $V_T$, referred to as the slow-rotting case, and the other in which the cumulative number of rotting instances is bounded by $S_T$, referred to as the abrupt-rotting case. To address the challenge posed by rotting rewards, we introduce an algorithm that utilizes UCB with an adaptive sliding window, designed to manage the bias and variance trade-off arising due to rotting rewards. Our proposed algorithm achieves tight regret bounds for both slow and abrupt rotting scenarios. Lastly, we demonstrate the performance of our algorithm using numerical experiments.