Crush optimism with pessimism: Structured bandits beyond asymptotic optimality

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Abstract

In this paper, we study stochastic structured bandits for minimizing regret. The fact that the popular optimistic algorithms do not achieve the asymptotic instance-dependent regret optimality (asymptotic optimality for short) has recently allured researchers. On the other hand, it is known that one can achieve a bounded regret (i.e., does not grow indefinitely with n) in certain instances. Unfortunately, existing asymptotically optimal algorithms rely on forced sampling that introduces an ?(1) term w.r.t. the time horizon n in their regret, failing to adapt to the “easiness” of the instance. In this paper, we focus on the finite hypothesis class and ask if one can achieve the asymptotic optimality while enjoying bounded regret whenever possible. We provide a positive answer by introducing a new algorithm called CRush Optimism with Pessimism (CROP) that eliminates optimistic hypotheses by pulling the informative arms indicated by a pessimistic hypothesis. Our finite-time analysis shows that CROP (i) achieves a constant-factor asymptotic optimality and, thanks to the forced-exploration-free design, (ii) adapts to bounded regret, and (iii) its regret bound scales not with the number of arms K but with an effective number of arms K? that we introduce. We also discuss a problem class where CROP can be exponentially better than existing algorithms in nonasymptotic regimes. Finally, we observe that even a clairvoyant oracle who plays according to the asymptotically optimal arm pull scheme may suffer a linear worst-case regret, indicating that it may not be the end of optimism.

Original languageEnglish (US)
JournalAdvances in Neural Information Processing Systems
Volume2020-December
StatePublished - 2020
Externally publishedYes
Event34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
Duration: Dec 6 2020Dec 12 2020

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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