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 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 .