Improved Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandit

Vasilii Novitskii; Alexander Gasnikov

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arXiv · 2101.03821

Improved Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandit

Vasilii Novitskii·Alexander Gasnikov

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Abstract

We consider $\beta$-smooth (satisfies the generalized Holder condition with parameter $\beta > 2$) stochastic convex optimization problem with zero-order one-point oracle. The best known result was arXiv:2006.07862: $\mathbb{E} \left[f(\overline{x}_N) - f(x^*)\right] = \tilde{\mathcal{O}} \left(\dfrac{n^{2}}{\gamma N^{\frac{\beta-1}{\beta}}} \right)$ in $\gamma$-strongly convex case, where $n$ is the dimension. In this paper we improve this bound: $\mathbb{E} \left[f(\overline{x}_N) - f(x^*)\right] = \tilde{\mathcal{O}} \left(\dfrac{n^{2-\frac{1}{\beta}}}{\gamma N^{\frac{\beta-1}{\beta}}} \right).$

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BibTeX RIS

Vasilii Novitskii, Alexander Gasnikov. 2021-01-11. Improved Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandit. https://arxiv.org/abs/2101.03821

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