Збережено в:
| Автори: | , |
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| Формат: | Preprint |
| Опубліковано: |
2024
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| Предмети: | |
| Онлайн доступ: | https://arxiv.org/abs/2403.08080 |
| Теги: |
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Зміст:
- This work provides the first convergence analysis for the Randomized Block Coordinate Descent method for minimizing a function that is both Hölder smooth and block Hölder smooth. Our analysis applies to objective functions that are non-convex, convex, and strongly convex. For non-convex functions, we show that the expected gradient norm reduces at an $O\left(k^{\fracγ{1+γ}}\right)$ rate, where $k$ is the iteration count and $γ$ is the Hölder exponent. For convex functions, we show that the expected suboptimality gap reduces at the rate $O\left(k^{-γ}\right)$. In the strongly convex setting, we show this rate for the expected suboptimality gap improves to $O\left(k^{-\frac{2γ}{1-γ}}\right)$ when $γ>1$ and to a linear rate when $γ=1$. Notably, these new convergence rates coincide with those furnished in the existing literature for the Lipschitz smooth setting.