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Poster
Minimax Optimal Algorithms for Unconstrained Linear Optimization
Brendan McMahan · Jacob D Abernethy

Sun Dec 08 02:00 PM -- 06:00 PM (PST) @ Harrah's Special Events Center, 2nd Floor #None

We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark strategy. The standard benchmark is the loss of the best strategy chosen from a bounded comparator set, whereas we consider a broad range of benchmark functions. We consider the problem as a sequential multi-stage zero-sum game, and we give a thorough analysis of the minimax behavior of the game, providing characterizations for the value of the game, as well as both the player's and the adversary's optimal strategy. We show how these objects can be computed efficiently under certain circumstances, and by selecting an appropriate benchmark, we construct a novel hedging strategy for an unconstrained betting game.

Author Information

Brendan McMahan (Google)
Jacob D Abernethy (University of Michigan)

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