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arXiv · 2008.09149

Primal-Dual Sequential Subspace Optimization for Saddle-point Problems

Yoni Choukroun·Michael Zibulevsky·Pavel Kisilev
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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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Yoni Choukroun, Michael Zibulevsky, Pavel Kisilev. 2020-08-20. Primal-Dual Sequential Subspace Optimization for Saddle-point Problems. https://arxiv.org/abs/2008.09149

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