Skip to Main content Skip to Navigation
Journal articles

Stochastic proximal subgradient descent oscillates in the vicinity of its accumulation set

Abstract : We analyze the stochastic proximal subgradient descent in the case where the objective functions are path differentiable and verify a Sard-type condition. While the accumulation set may not be reduced to unique point, we show that the time spent by the iterates to move from one accumulation point to another goes to infinity. An oscillation-type behavior of the drift is established. These results show a strong stability property of the proximal subgradient descent. Using the theory of closed measures, Bolte, Pauwels and Ríos-Zertuche [6] established this type of behavior for the deterministic subgradient descent. Our technique of proof relies on the classical works on stochastic approximation of differential inclusions, which allows us to extend results in the deterministic case to a stochastic and proximal setting, as well as to treat these different cases in a unified manner.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03676675
Contributor : Sholom Schechtman Connect in order to contact the contributor
Submitted on : Tuesday, May 24, 2022 - 10:59:28 AM
Last modification on : Friday, June 24, 2022 - 4:05:31 AM

File

oscillations.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Sholom Schechtman. Stochastic proximal subgradient descent oscillates in the vicinity of its accumulation set. Optimization Letters, Springer Verlag, 2022, ⟨10.1007/s11590-022-01884-8⟩. ⟨hal-03676675⟩

Share

Metrics

Record views

8

Files downloads

3