Banker Online Mirror Descent

06/16/2021

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by   Jiatai Huang, et al.

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We propose Banker-OMD, a novel framework generalizing the classical Online Mirror Descent (OMD) technique in online learning algorithm design. Banker-OMD allows algorithms to robustly handle delayed feedback, and offers a general methodology for achieving Õ(√(T) + √(D))-style regret bounds in various delayed-feedback online learning tasks, where T is the time horizon length and D is the total feedback delay. We demonstrate the power of Banker-OMD with applications to three important bandit scenarios with delayed feedback, including delayed adversarial Multi-armed bandits (MAB), delayed adversarial linear bandits, and a novel delayed best-of-both-worlds MAB setting. Banker-OMD achieves nearly-optimal performance in all the three settings. In particular, it leads to the first delayed adversarial linear bandit algorithm achieving Õ(poly(n)(√(T) + √(D))) regret.