Collaborative Linear Bandits with Adversarial Agents: Near-Optimal Regret Bounds

• URL: http://arxiv.org/abs/2206.02834v1
• Date: Mon, 6 Jun 2022 18:16:34 GMT
• Title: Collaborative Linear Bandits with Adversarial Agents: Near-Optimal Regret Bounds
• Authors: Aritra Mitra, Arman Adibi, George J. Pappas, and Hamed Hassani
• Abstract summary: We consider a linear bandit problem involving $M$ agents that can collaborate via a central server to minimize regret. A fraction $alpha$ of these agents are adversarial and can act arbitrarily, leading to the following tension. We design new algorithms that balance the exploration-exploitation trade-off via carefully constructed robust confidence intervals.
• Score: 31.5504566292927
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider a linear stochastic bandit problem involving $M$ agents that can collaborate via a central server to minimize regret. A fraction $\alpha$ of these agents are adversarial and can act arbitrarily, leading to the following tension: while collaboration can potentially reduce regret, it can also disrupt the process of learning due to adversaries. In this work, we provide a fundamental understanding of this tension by designing new algorithms that balance the exploration-exploitation trade-off via carefully constructed robust confidence intervals. We also complement our algorithms with tight analyses. First, we develop a robust collaborative phased elimination algorithm that achieves $\tilde{O}\left(\alpha+ 1/\sqrt{M}\right) \sqrt{dT}$ regret for each good agent; here, $d$ is the model-dimension and $T$ is the horizon. For small $\alpha$, our result thus reveals a clear benefit of collaboration despite adversaries. Using an information-theoretic argument, we then prove a matching lower bound, thereby providing the first set of tight, near-optimal regret bounds for collaborative linear bandits with adversaries. Furthermore, by leveraging recent advances in high-dimensional robust statistics, we significantly extend our algorithmic ideas and results to (i) the generalized linear bandit model that allows for non-linear observation maps; and (ii) the contextual bandit setting that allows for time-varying feature vectors.

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