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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.03507 |
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Table of Contents:
- This paper is devoted to the study (common in many applications) of the black-box optimization problem, where the black-box represents a gradient-free oracle $\tilde{f} = f(x) + ξ$ providing the objective function value with some stochastic noise. Assuming that the objective function is $μ$-strongly convex, and also not just $L$-smooth, but has a higher order of smoothness ($β\geq 2$) we provide a novel optimization method: Zero-Order Accelerated Batched Stochastic Gradient Descent, whose theoretical analysis closes the question regarding the iteration complexity, achieving optimal estimates. Moreover, we provide a thorough analysis of the maximum noise level, and show under which condition the maximum noise level will take into account information about batch size $B$ as well as information about the smoothness order of the function $β$.