Primal-Dual Sequential Subspace Optimization for Saddle-point Problems

• URL: http://arxiv.org/abs/2008.09149v1
• Date: Thu, 20 Aug 2020 18:19:19 GMT
• Title: Primal-Dual Sequential Subspace Optimization for Saddle-point Problems
• Authors: Yoni Choukroun, Michael Zibulevsky, Pavel Kisilev
• Abstract summary: We introduce a new sequential subspace optimization method for large-scale saddle-point problems. It solves auxiliary saddle-point problems in low-dimensional subspaces, spanned by directions derived from first-order information over the primal emphand dual variables. Experimental results demonstrate significantly better convergence relative to popular first-order methods.
• Score: 3.9582154141918964
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a new sequential subspace optimization method for large-scale saddle-point problems. It solves iteratively a sequence of auxiliary saddle-point problems in low-dimensional subspaces, spanned by directions derived from first-order information over the primal \emph{and} dual variables. Proximal regularization is further deployed to stabilize the optimization process. Experimental results demonstrate significantly better convergence relative to popular first-order methods. We analyze the influence of the subspace on the convergence of the algorithm, and assess its performance in various deterministic optimization scenarios, such as bi-linear games, ADMM-based constrained optimization and generative adversarial networks.

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