Almost Sure Convergence and Non-asymptotic Concentration Bounds for Stochastic Mirror Descent Algorithm
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909246359076864 |
|---|---|
| author | Paul, Anik Kumar Mahindrakar, Arun D Kalaimani, Rachel K |
| author_facet | Paul, Anik Kumar Mahindrakar, Arun D Kalaimani, Rachel K |
| contents | This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the assumption of diminishing bias. Furthermore, we derive concentration bounds for the discrepancy between the iterates' function values and the optimal value, based on standard assumptions. Subsequently, leveraging the assumption of Sub-Gaussian noise in stochastic subgradients, we present refined concentration bounds for this discrepancy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost Sure Convergence and Non-asymptotic Concentration Bounds for Stochastic Mirror Descent Algorithm Paul, Anik Kumar Mahindrakar, Arun D Kalaimani, Rachel K Optimization and Control This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the assumption of diminishing bias. Furthermore, we derive concentration bounds for the discrepancy between the iterates' function values and the optimal value, based on standard assumptions. Subsequently, leveraging the assumption of Sub-Gaussian noise in stochastic subgradients, we present refined concentration bounds for this discrepancy. |
| title | Almost Sure Convergence and Non-asymptotic Concentration Bounds for Stochastic Mirror Descent Algorithm |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2407.05863 |