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- W3127913533 abstract "We study the problem of nonstochastic bandits with infinitely many experts: A learner aims to maximize the total reward by taking actions sequentially based on bandit feedback while benchmarking against a countably infinite set of experts. We propose a variant of Exp4.P that, for finitely many experts, enables inference of correct expert rankings while preserving the order of the regret upper bound. We then incorporate the variant into a meta-algorithm that works on infinitely many experts. We prove a high-probability upper bound of $tilde{mathcal{O}} big( i^*K + sqrt{KT} big)$ on the regret, up to polylog factors, where $i^*$ is the unknown position of the best expert, $K$ is the number of actions, and $T$ is the time horizon. We also provide an example of structured experts and discuss how to expedite learning in such case. Our meta-learning algorithm achieves the tightest regret upper bound for the setting considered when $i^* = tilde{mathcal{O}} big( sqrt{T/K} big)$. If a prior distribution is assumed to exist for $i^*$, the probability of satisfying a tight regret bound increases with $T$, the rate of which can be fast." @default.
- W3127913533 created "2021-02-15" @default.
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- W3127913533 date "2021-02-09" @default.
- W3127913533 modified "2023-09-25" @default.
- W3127913533 title "Nonstochastic Bandits with Infinitely Many Experts." @default.
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