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The Hedge Algorithm on a Continuum

2020-03-04 | |  69 |   46 |   0

Abstract We consider an online optimization problem on a compact subset 图片.png (not necessarily convex), in which a decision maker chooses, at each iteration t, a probability distribution 图片.png over S, and Pseeks T to minimize a cumulative expected loss, 图片.png, where 图片.png is a Lipschitz loss function revealed at the end of iteration t. Building on previous work, we propose a generalized Hedge algorithm and show a 图片.png bound on the regret when the losses are uniformly Lipschitz and S is uniformly fat (a weaker condition than convexity). Finally, we propose a generalization to the dual averaging method on the set of Lebesgue-continuous distributions over S.

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