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Online Optimization Under Adversarial Perturbations
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DOI：10.1109/JSTSP.2015.2496911.png)
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Abstract
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We investigate the problem of online optimization under adversarial perturbations. In each round of this repeated game, a player selects an action from a decision set using a randomized strategy, and then Nature reveals a loss function for this action, for which the player incurs a loss. The game then repeats for a total of rounds, over which the player seeks to minimize the total incurred loss, or more specifically, the excess incurred loss with respect to a fixed comparison class. The added challenge over traditional online optimization, is that for of the rounds, after the player selects an action, an adversarial agent perturbs this action arbitrarily. Through a worst case adversary framework to model the perturbations, we introduce a randomized algorithm that is provably robust against such adversarial attacks. In particular, we show that this algorithm is Hannan consistent with respect to a rich class of randomized strategies under mild regularity conditions.
Keywords:
Adversarial perturbations
online optimization
randomized algorithms
repeated games
robustness
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