Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers

• URL: http://arxiv.org/abs/2106.13067v1
• Date: Thu, 24 Jun 2021 14:48:43 GMT
• Title: Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers
• Authors: Patrick R. Johnstone, Jonathan Eckstein, Thomas Flynn, Shinjae Yoo
• Abstract summary: We present a new, variant of the projective splitting (PS) family of monotone algorithms for inclusion problems. It can solve min-max and noncooperative game formulations arising in applications such as robust ML without the convergence issues associated with gradient descent-ascent.
• Score: 4.568911586155097
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a new, stochastic variant of the projective splitting (PS) family of algorithms for monotone inclusion problems. It can solve min-max and noncooperative game formulations arising in applications such as robust ML without the convergence issues associated with gradient descent-ascent, the current de facto standard approach in such situations. Our proposal is the first version of PS able to use stochastic (as opposed to deterministic) gradient oracles. It is also the first stochastic method that can solve min-max games while easily handling multiple constraints and nonsmooth regularizers via projection and proximal operators. We close with numerical experiments on a distributionally robust sparse logistic regression problem.

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