Online Optimization Under Adversarial Perturbations

• Published in: IEEE journal of selected topics in signal processing Vol. 10; no. 2; pp. 256 - 269
• Main Authors: Donmez, Mehmet A., Raginsky, Maxim, Singer, Andrew C.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adversarial perturbations; Algorithm design and analysis; Algorithms; Fabrics; Games; Online; online optimization; Optimization; Perturbation methods; Players; Probability distribution; randomized algorithms; Regularity; repeated games; Robustness; Signal processing algorithms; Strategy
• ISSN: 1932-4553; 1941-0484
• DOI: 10.1109/JSTSP.2015.2496911

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 T 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 k of the T 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.