Crush Optimism with Pessimism: Structured Bandits Beyond Asymptotic Optimality (NeurIPS 2020 Paper)

NeurIPS 2020

Crush Optimism with Pessimism: Structured Bandits Beyond Asymptotic Optimality (NeurIPS 2020 Paper)

Nov 08, 2020
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Kwang-Sung Jun (U. Arizona) talks about their paper "Crush Optimism with Pessimism: Structured Bandits Beyond Asymptotic Optimality" coauthored with Chicheng Zhang. (paper accepted at NeurIPS 2020) Abstract: 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 alluded researchers. On the other hand, it is known that one can achieve 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 ω(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 case 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 K but with an effective number of arms Kψ that we introduce. We also discuss a problem class where CROP can be exponentially better than existing algorithms in \textit{nonasymptotic} regimes. This problem class also reveals a surprising fact that even a clairvoyant oracle who plays according to the asymptotically optimal arm pull scheme may suffer a linear worst-case regret. Link to paper: https://arxiv.org/abs/2006.08754 Slides: https://drive.google.com/file/d/11iMEpFMlwONLNzuvM-V2HSX_C95ZA1cb/view?usp=sharing

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