Exploitingeasydatainonlineoptimization-NIPSProceedings.PDFVIP

Exploiting easy data in online optimization Amir Sani Gergely Neu Alessandro Lazaric SequeL team, INRIA Lille – Nord Europe, France {amir.sani,gergely.neu,alessandro.lazaric}@inria.fr Abstract We consider the problem of online optimization, where a learner chooses a deci sion from a given decision set and suffers some loss associated with the decision and the state of the environment. The learner’s objective is to minimize its cu mulative regret against the best fixed decision in hindsight. Over the past few decades numerous variants have been considered, with many algorithms designed to achieve sub-linear regret in the worst case. However, this level of robustness comes at a cost. Proposed algorithms are often over-conservative, failing to adapt to the actual complexity of the loss sequence which is often far from the worst case. In this paper we introduce a general algorithm that, provided with a “safe” learning algorithm and an opportunistic “benchmark”, can effectively combine good worst-case guarantees with much improved performance on “easy” data. We derive general theoretical bounds on the regret of the proposed algorithm and discuss its implementation in a wide range of applications, notably in the prob lem of learning with shifting experts (a recent COLT open problem). Finally, we provide numerical simulations in the setting of prediction with expert advice with comparisons to the state of the art. 1 Introduction We consider a general class of online decision-making problems, where a learner sequentially de cides which actions to take from a given decision set and suffers so