Stochastic Linear Bandits Robust to Adversarial Attacks

• URL: http://arxiv.org/abs/2007.03285v2
• Date: Tue, 27 Oct 2020 20:18:09 GMT
• Title: Stochastic Linear Bandits Robust to Adversarial Attacks
• Authors: Ilija Bogunovic, Arpan Losalka, Andreas Krause, Jonathan Scarlett
• Abstract summary: We provide two variants of a Robust Phased Elimination algorithm, one that knows $C$ and one that does not. We show that both variants attain near-optimal regret in the non-corrupted case $C = 0$, while incurring additional additive terms respectively. In a contextual setting, we show that a simple greedy algorithm is provably robust with a near-optimal additive regret term, despite performing no explicit exploration and not knowing $C$.
• Score: 117.665995707568
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a stochastic linear bandit problem in which the rewards are not only subject to random noise, but also adversarial attacks subject to a suitable budget $C$ (i.e., an upper bound on the sum of corruption magnitudes across the time horizon). We provide two variants of a Robust Phased Elimination algorithm, one that knows $C$ and one that does not. Both variants are shown to attain near-optimal regret in the non-corrupted case $C = 0$, while incurring additional additive terms respectively having a linear and quadratic dependency on $C$ in general. We present algorithm independent lower bounds showing that these additive terms are near-optimal. In addition, in a contextual setting, we revisit a setup of diverse contexts, and show that a simple greedy algorithm is provably robust with a near-optimal additive regret term, despite performing no explicit exploration and not knowing $C$.

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