Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adapting

Akshay Krishnamurthy; John Langford; Aleksandrs Slivkins; Chicheng Zhang

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arXiv · 1902.01520

Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adapting

Akshay Krishnamurthy·John Langford·Aleksandrs Slivkins·Chicheng Zhang

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Abstract

We study contextual bandit learning with an abstract policy class and continuous action space. We obtain two qualitatively different regret bounds: one competes with a smoothed version of the policy class under no continuity assumptions, while the other requires standard Lipschitz assumptions. Both bounds exhibit data-dependent "zooming" behavior and, with no tuning, yield improved guarantees for benign problems. We also study adapting to unknown smoothness parameters, establishing a price-of-adaptivity and deriving optimal adaptive algorithms that require no additional information.

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Akshay Krishnamurthy, John Langford, Aleksandrs Slivkins, Chicheng Zhang. 2019-02-05. Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adapting. https://arxiv.org/abs/1902.01520

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