  This paper presents a new regularization approach -- termed OpReg-Boost -- to
boost the convergence and lessen the asymptotic error of online optimization
and learning algorithms. In particular, the paper considers online algorithms
for optimization problems with a time-varying (weakly) convex composite cost.
For a given online algorithm, OpReg-Boost learns the closest algorithmic map
that yields linear convergence; to this end, the learning procedure hinges on
the concept of operator regression. We show how to formalize the operator
regression problem and propose a computationally-efficient Peaceman-Rachford
solver that exploits a closed-form solution of simple quadratically-constrained
quadratic programs (QCQPs). Simulation results showcase the superior properties
of OpReg-Boost w.r.t. the more classical forward-backward algorithm, FISTA, and
Anderson acceleration.
