Efficient and Robust Algorithms for Adversarial Linear Contextual Bandits

• URL: http://arxiv.org/abs/2002.00287v3
• Date: Tue, 24 May 2022 14:05:52 GMT
• Title: Efficient and Robust Algorithms for Adversarial Linear Contextual Bandits
• Authors: Gergely Neu, Julia Olkhovskaya
• Abstract summary: We consider an adversarial variant of the classic $K$-armed linear contextual bandit problem. Under the assumption that the $d$-dimensional contexts are generated i.i.d.at random, we develop efficient algorithms based on the classic Exp3 algorithm.
• Score: 13.32560004325655
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider an adversarial variant of the classic $K$-armed linear contextual bandit problem where the sequence of loss functions associated with each arm are allowed to change without restriction over time. Under the assumption that the $d$-dimensional contexts are generated i.i.d.~at random from a known distributions, we develop computationally efficient algorithms based on the classic Exp3 algorithm. Our first algorithm, RealLinExp3, is shown to achieve a regret guarantee of $\widetilde{O}(\sqrt{KdT})$ over $T$ rounds, which matches the best available bound for this problem. Our second algorithm, RobustLinExp3, is shown to be robust to misspecification, in that it achieves a regret bound of $\widetilde{O}((Kd)^{1/3}T^{2/3}) + \varepsilon \sqrt{d} T$ if the true reward function is linear up to an additive nonlinear error uniformly bounded in absolute value by $\varepsilon$. To our knowledge, our performance guarantees constitute the very first results on this problem setting.

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