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

• URL: http://arxiv.org/abs/2105.13271v1
• Date: Thu, 27 May 2021 16:17:38 GMT
• Title: OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression
• Authors: Nicola Bastianello, Andrea Simonetto, Emiliano Dall'Anese
• Abstract summary: This paper presents a new regularization approach -- OpReg-Boost -- to boost the convergence of online optimization and learning algorithms. We show how to formalize the operator regression problem and propose a computationally-efficient Peaceman-Rachford solver.
• Score: 5.457279006229211
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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, and with respect to its close relative convex-regression-boost (CvxReg-Boost) which is also novel but less performing.

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