Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909983523733504 |
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| author | Lara, Felipe Vega, Cristian |
| author_facet | Lara, Felipe Vega, Cristian |
| contents | We study non-convex delayed-noise online optimization problems by evaluating dynamic regret in the non-stationary setting when the loss functions are quasar-convex. In particular, we consider scenarios involving quasar-convex functions either with a Lipschitz gradient or weakly smooth and, for each case, we ensure bounded dynamic regret in terms of cumulative path variation achieving sub-linear regret rates. Furthermore, we illustrate the flexibility of our framework by applying it to both theoretical settings such as zeroth-order (bandit) and also to practical applications with quadratic fractional functions. Moreover, we provide new examples of non-convex functions that are quasar-convex by proving that the class of differentiable strongly quasiconvex functions (Polyak 1966) are strongly quasar-convex on convex compact sets. Finally, several numerical experiments validate our theoretical findings, illustrating the effectiveness of our approach. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_14506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications Lara, Felipe Vega, Cristian Optimization and Control 90C26, 65K05, 90C56, 90C30, 68W27 We study non-convex delayed-noise online optimization problems by evaluating dynamic regret in the non-stationary setting when the loss functions are quasar-convex. In particular, we consider scenarios involving quasar-convex functions either with a Lipschitz gradient or weakly smooth and, for each case, we ensure bounded dynamic regret in terms of cumulative path variation achieving sub-linear regret rates. Furthermore, we illustrate the flexibility of our framework by applying it to both theoretical settings such as zeroth-order (bandit) and also to practical applications with quadratic fractional functions. Moreover, we provide new examples of non-convex functions that are quasar-convex by proving that the class of differentiable strongly quasiconvex functions (Polyak 1966) are strongly quasar-convex on convex compact sets. Finally, several numerical experiments validate our theoretical findings, illustrating the effectiveness of our approach. |
| title | Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications |
| topic | Optimization and Control 90C26, 65K05, 90C56, 90C30, 68W27 |
| url | https://arxiv.org/abs/2412.14506 |