A Near-optimal, Scalable and Corruption-tolerant Framework for Stochastic Bandits: From Single-Agent to Multi-Agent and Beyond

• URL: http://arxiv.org/abs/2502.07514v1
• Date: Tue, 11 Feb 2025 12:33:33 GMT
• Title: A Near-optimal, Scalable and Corruption-tolerant Framework for Stochastic Bandits: From Single-Agent to Multi-Agent and Beyond
• Authors: Zicheng Hu, Cheng Chen,
• Abstract summary: We propose a novel framework called BARBAT, which eliminates the factor of $K$ and achieves an optimal regret bound to a logarithmic factor. We also demonstrate how BARBAT can be extended to various settings, including graph bandits, semi-bandits, batched bandits and multi-agent bandits.
• Score: 2.5217803205496283
• License:
• Abstract: We investigate various stochastic bandit problems in the presence of adversarial corruption. A seminal contribution to this area is the BARBAR~\citep{gupta2019better} algorithm, which is both simple and efficient, tolerating significant levels of corruption with nearly no degradation in performance. However, its regret upper bound exhibits a complexity of $O(KC)$, while the lower bound is $\Omega(C)$. In this paper, we enhance the BARBAR algorithm by proposing a novel framework called BARBAT, which eliminates the factor of $K$ and achieves an optimal regret bound up to a logarithmic factor. We also demonstrate how BARBAT can be extended to various settings, including graph bandits, combinatorial semi-bandits, batched bandits and multi-agent bandits. In comparison to the Follow-The-Regularized-Leader (FTRL) family of methods, which provide a best-of-both-worlds guarantee, our approach is more efficient and parallelizable. Notably, FTRL-based methods face challenges in scaling to batched and multi-agent settings.

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