Mini-batch stochastic subgradient for functional constrained optimization
| Autor: | Singh, Nitesh Kumar, Necoara, Ion |
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| Rok vydání: | 2024 |
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| Zdroj: | Optimization, 2023 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1080/02331934.2023.2189015 |
| Popis: | In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the other is amenable to proximal evaluations. We assume a generalized bounded gradient condition on the objective which allows us to simultaneously tackle both smooth and nonsmooth problems. We also consider the cases of both with and without a strong convexity property. Further, we assume that each constraint set is given as the level set of a convex but not necessarily differentiable function. We reformulate the constrained finite sum problem into a stochastic optimization problem for which the stochastic subgradient projection method from [17] specializes to a collection of mini-batch variants, with different mini-batch sizes for the objective function and functional constraints, respectively. More specifically, at each iteration, our algorithm takes a mini-batch stochastic proximal subgradient step aimed at minimizing the objective function and then a subsequent mini-batch subgradient projection step minimizing the feasibility violation. By specializing different mini-batching strategies, we derive exact expressions for the stepsizes as a function of the mini-batch size and in some cases we also derive insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime. We also prove sublinear convergence rates for the mini-batch subgradient projection algorithm which depend explicitly on the mini-batch sizes and on the properties of the objective function. Numerical results also show a better performance of our mini-batch scheme over its single-batch counterpart. Comment: 24 pages |
| Databáze: | arXiv |
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