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Overall Objectives
Application Domains
New Results
Bilateral Contracts and Grants with Industry
Bibliography
Overall Objectives
Application Domains
New Results
Bilateral Contracts and Grants with Industry
Bibliography


Section: New Results

Gains and Losses are Fundamentally Different in Regret Minimization: The Sparse Case

Participant : Vianney Perchet [correspondent] .

Collaboration with Joon Kwon.

In [38] , we demonstrate that, in the classical non-stochastic regret minimization problem with d decisions, gains and losses to be respectively maximized or minimized are fundamentally different. Indeed, by considering the additional sparsity assumption (at each stage, at most s decisions incur a nonzero outcome), we derive optimal regret bounds of different orders. Specifically, with gains, we obtain an optimal regret guarantee after T stages of order Tlogs, so the classical dependency in the dimension is replaced by the sparsity size. With losses, we provide matching upper and lower bounds of order Tslog(d)/d, which is decreasing in d. Eventually, we also study the bandit setting, and obtain an upper bound of order Tslog(d/s) when outcomes are losses. This bound is proven to be optimal up to the logarithmic factor log(d/s).