Rotting Infinitely Many-armed Bandits

• URL: http://arxiv.org/abs/2201.12975v3
• Date: Sun, 17 Dec 2023 10:16:48 GMT
• Title: Rotting Infinitely Many-armed Bandits
• Authors: Jung-hun Kim, Milan Vojnovic, Se-Young Yun
• Abstract summary: We show an $Omega(maxvarrho2/3T,sqrtT)$ worst-case regret lower bound where $T$ is the horizon time. An algorithm that does not know the value of $varrho$ can be achieved by using an adaptive UCB index along with an adaptive threshold value.
• Score: 33.26370721280417
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the infinitely many-armed bandit problem with rotting rewards, where the mean reward of an arm decreases at each pull of the arm according to an arbitrary trend with maximum rotting rate $\varrho=o(1)$. We show that this learning problem has an $\Omega(\max\{\varrho^{1/3}T,\sqrt{T}\})$ worst-case regret lower bound where $T$ is the horizon time. We show that a matching upper bound $\tilde{O}(\max\{\varrho^{1/3}T,\sqrt{T}\})$, up to a poly-logarithmic factor, can be achieved by an algorithm that uses a UCB index for each arm and a threshold value to decide whether to continue pulling an arm or remove the arm from further consideration, when the algorithm knows the value of the maximum rotting rate $\varrho$. We also show that an $\tilde{O}(\max\{\varrho^{1/3}T,T^{3/4}\})$ regret upper bound can be achieved by an algorithm that does not know the value of $\varrho$, by using an adaptive UCB index along with an adaptive threshold value.

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