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A number of learning problems can be cast as an Online Convex Game: on each round, a learner makes a prediction x from a convex set, the environment plays a loss function f, and the learner’s long-term goal is to minimize regret. Algorithms have been proposed by Zinkevich, when f is assumed to be convex, and Hazan et al., when f is assumed to be strongly convex, that have provably low regret. We consider these two settings and analyze such games from a minimax perspective, proving minimax strategies and lower bounds in each case. These results prove that the existing algorithms are essentially optimal.
Abernethy, J., Bartlett, P. L., Rakhlin, A., & Tewari, A. (2008). Optimal Strategies and Minimax Lower Bounds for Online Convex Games. Retrieved from https://repository.upenn.edu/statistics_papers/164
Date Posted: 27 November 2017