| Autor: |
Charles Audet, Jean Bigeon, Romain Couderc, Michael Kokkolaras |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 8, Iss 11, Pp 25922-25956 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20231321?viewType=HTML |
| Popis: |
This work considers stochastic optimization problems in which the objective function values can only be computed by a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on sequential stochastic optimization (SSO), i.e., the original problem is decomposed into a sequence of subproblems. Each subproblem is solved by using a zeroth-order version of a sign stochastic gradient descent with momentum algorithm (i.e., ZO-signum) and with increasingly fine precision. This decomposition allows a good exploration of the space while maintaining the efficiency of the algorithm once it gets close to the solution. Under the Lipschitz continuity assumption on the blackbox, a convergence rate in mean is derived for the ZO-signum algorithm. Moreover, if the blackbox is smooth and convex or locally convex around its minima, the rate of convergence to an $ \epsilon $-optimal point of the problem may be obtained for the SSO algorithm. Numerical experiments are conducted to compare the SSO algorithm with other state-of-the-art algorithms and to demonstrate its competitiveness. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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