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arXiv · 2301.02511

Stochastic Primal Dual Hybrid Gradient Algorithm with Adaptive Step-Sizes

Antonin Chambolle·Claire Delplancke·Matthias J. Ehrhardt·Carola-Bibiane Schönlieb·Junqi Tang
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Abstract

In this work we propose a new primal-dual algorithm with adaptive step-sizes. The stochastic primal-dual hybrid gradient (SPDHG) algorithm with constant step-sizes has become widely applied in large-scale convex optimization across many scientific fields due to its scalability. While the product of the primal and dual step-sizes is subject to an upper-bound in order to ensure convergence, the selection of the ratio of the step-sizes is critical in applications. Up-to-now there is no systematic and successful way of selecting the primal and dual step-sizes for SPDHG. In this work, we propose a general class of adaptive SPDHG (A-SPDHG) algorithms, and prove their convergence under weak assumptions. We also propose concrete parameters-updating strategies which satisfy the assumptions of our theory and thereby lead to convergent algorithms. Numerical examples on computed tomography demonstrate the effectiveness of the proposed schemes.

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Antonin Chambolle, Claire Delplancke, Matthias J. Ehrhardt, Carola-Bibiane Schönlieb, Junqi Tang. 2023-01-06. Stochastic Primal Dual Hybrid Gradient Algorithm with Adaptive Step-Sizes. https://arxiv.org/abs/2301.02511

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