  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.
