Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.01633 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916694942810112 |
|---|---|
| author | Pougkakiotis, Spyridon Kalogerias, Dionysios S. |
| author_facet | Pougkakiotis, Spyridon Kalogerias, Dionysios S. |
| contents | In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which (sub-)gradient information might be unavailable. The proposed algorithm utilizes the well-known Gaussian smoothing technique, which yields unbiased zeroth-order gradient estimators of a related partially smooth surrogate problem (in which one of the two nonsmooth terms in the original problem's objective is replaced by a smooth approximation). This allows us to employ a standard proximal stochastic gradient scheme for the approximate solution of the surrogate problem, which is determined by a single smoothing parameter, and without the utilization of first-order information. We provide state-of-the-art convergence rates for the proposed zeroth-order method using minimal assumptions. The proposed scheme is numerically compared against alternative zeroth-order methods as well as a stochastic sub-gradient scheme on a standard phase retrieval problem. Further, we showcase the usefulness and effectiveness of our method for the unique setting of automated hyper-parameter tuning. In particular, we focus on automatically tuning the parameters of optimization algorithms by minimizing a novel heuristic model. The proposed approach is tested on a proximal alternating direction method of multipliers for the solution of $\mathcal{L}_1/\mathcal{L}_2$-regularized PDE-constrained optimal control problems, with evident empirical success. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_01633 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Zeroth-order Proximal Stochastic Gradient Method for Weakly Convex Stochastic Optimization Pougkakiotis, Spyridon Kalogerias, Dionysios S. Optimization and Control In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which (sub-)gradient information might be unavailable. The proposed algorithm utilizes the well-known Gaussian smoothing technique, which yields unbiased zeroth-order gradient estimators of a related partially smooth surrogate problem (in which one of the two nonsmooth terms in the original problem's objective is replaced by a smooth approximation). This allows us to employ a standard proximal stochastic gradient scheme for the approximate solution of the surrogate problem, which is determined by a single smoothing parameter, and without the utilization of first-order information. We provide state-of-the-art convergence rates for the proposed zeroth-order method using minimal assumptions. The proposed scheme is numerically compared against alternative zeroth-order methods as well as a stochastic sub-gradient scheme on a standard phase retrieval problem. Further, we showcase the usefulness and effectiveness of our method for the unique setting of automated hyper-parameter tuning. In particular, we focus on automatically tuning the parameters of optimization algorithms by minimizing a novel heuristic model. The proposed approach is tested on a proximal alternating direction method of multipliers for the solution of $\mathcal{L}_1/\mathcal{L}_2$-regularized PDE-constrained optimal control problems, with evident empirical success. |
| title | A Zeroth-order Proximal Stochastic Gradient Method for Weakly Convex Stochastic Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2205.01633 |