Projection-free Distributed Online Learning with Strongly Convex Losses
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To efficiently solve distributed online learning problems with complicated constraints, previous studies have proposed several distributed projection-free algorithms. The state-of-the-art one achieves the O(T^3/4) regret bound with O(√(T)) communication complexity. In this paper, we further exploit the strong convexity of loss functions to improve the regret bound and communication complexity. Specifically, we first propose a distributed projection-free algorithm for strongly convex loss functions, which enjoys a better regret bound of O(T^2/3log T) with smaller communication complexity of O(T^1/3). Furthermore, we demonstrate that the regret of distributed online algorithms with C communication rounds has a lower bound of Ω(T/C), even when the loss functions are strongly convex. This lower bound implies that the O(T^1/3) communication complexity of our algorithm is nearly optimal for obtaining the O(T^2/3log T) regret bound up to polylogarithmic factors. Finally, we extend our algorithm into the bandit setting and obtain similar theoretical guarantees.
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