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

OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression