Section: New Results
Gains and Losses are Fundamentally Different in Regret Minimization: The Sparse Case
Participant : Vianney Perchet [correspondent] .
Collaboration with Joon Kwon.
In  , we demonstrate that, in the classical non-stochastic regret minimization problem with 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 decisions incur a nonzero outcome), we derive optimal regret bounds of different orders. Specifically, with gains, we obtain an optimal regret guarantee after stages of order , so the classical dependency in the dimension is replaced by the sparsity size. With losses, we provide matching upper and lower bounds of order , which is decreasing in . Eventually, we also study the bandit setting, and obtain an upper bound of order when outcomes are losses. This bound is proven to be optimal up to the logarithmic factor .