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arXiv · 2511.00257

A Tight Lower Bound for Non-stochastic Multi-armed Bandits with Expert Advice

Zachary Chase·Shinji Ito·Idan Mehalel
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Abstract

We determine the minimax optimal expected regret in the classic non-stochastic multi-armed bandit with expert advice problem, by proving a lower bound that matches the upper bound of Kale (2014). The two bounds determine the minimax optimal expected regret to be $\Theta\left( \sqrt{T K \log (N/K) } \right)$, where $K$ is the number of arms, $N$ is the number of experts, and $T$ is the time horizon.

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Zachary Chase, Shinji Ito, Idan Mehalel. 2025-10-31. A Tight Lower Bound for Non-stochastic Multi-armed Bandits with Expert Advice. https://arxiv.org/abs/2511.00257

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