17,178 research outputs found
Online Submodular Maximization via Online Convex Optimization
We study monotone submodular maximization under general matroid constraints
in the online setting. We prove that online optimization of a large class of
submodular functions, namely, weighted threshold potential functions, reduces
to online convex optimization (OCO). This is precisely because functions in
this class admit a concave relaxation; as a result, OCO policies, coupled with
an appropriate rounding scheme, can be used to achieve sublinear regret in the
combinatorial setting. We show that our reduction extends to many different
versions of the online learning problem, including the dynamic regret, bandit,
and optimistic-learning settings.Comment: Under revie
Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration
Stochastic approximation techniques have been used in various contexts in
data science. We propose a stochastic version of the forward-backward algorithm
for minimizing the sum of two convex functions, one of which is not necessarily
smooth. Our framework can handle stochastic approximations of the gradient of
the smooth function and allows for stochastic errors in the evaluation of the
proximity operator of the nonsmooth function. The almost sure convergence of
the iterates generated by the algorithm to a minimizer is established under
relatively mild assumptions. We also propose a stochastic version of a popular
primal-dual proximal splitting algorithm, establish its convergence, and apply
it to an online image restoration problem.Comment: 5 Figure
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