Stochastic Coordinate Minimization with Progressive Precision for Stochastic Convex Optimization

• URL: http://arxiv.org/abs/2003.05482v1
• Date: Wed, 11 Mar 2020 18:42:40 GMT
• Title: Stochastic Coordinate Minimization with Progressive Precision for Stochastic Convex Optimization
• Authors: Sudeep Salgia, Qing Zhao, Sattar Vakili
• Abstract summary: A framework based on iterative coordinate minimization (CM) is developed for convex optimization. We establish the optimal precision control and the resulting order-optimal regret performance. The proposed algorithm is amenable to online implementation and inherits the scalability and parallelizability properties of CM for large-scale optimization.
• Score: 16.0251555430107
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A framework based on iterative coordinate minimization (CM) is developed for stochastic convex optimization. Given that exact coordinate minimization is impossible due to the unknown stochastic nature of the objective function, the crux of the proposed optimization algorithm is an optimal control of the minimization precision in each iteration. We establish the optimal precision control and the resulting order-optimal regret performance for strongly convex and separably nonsmooth functions. An interesting finding is that the optimal progression of precision across iterations is independent of the low-dimensional CM routine employed, suggesting a general framework for extending low-dimensional optimization routines to high-dimensional problems. The proposed algorithm is amenable to online implementation and inherits the scalability and parallelizability properties of CM for large-scale optimization. Requiring only a sublinear order of message exchanges, it also lends itself well to distributed computing as compared with the alternative approach of coordinate gradient descent.

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