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

arXiv: https://arxiv.org/abs/2101.03821 · HTML: https://mlsanity.com/paper/2101.03821/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2021.

## Built on by (most cited first, 2 of 2)

- [A gradient estimator via L1-randomization for online zero-order optimization with two point feedback](https://mlsanity.com/paper/2205.13910/) (2022)
- [Stochastic Zeroth-Order Optimization under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity](https://mlsanity.com/paper/2406.19617/) (2024)

## Abstract (arXiv)

We consider β-smooth (satisfies the generalized Holder condition with parameter β > 2) stochastic convex optimization problem with zero-order one-point oracle. The best known result was arXiv:2006.07862: mathbbE left[f(overlinexN) - f(x^*)right] = tildeO left(dfracn2γ N^fracβ-1β right) in γ-strongly convex case, where n is the dimension. In this paper we improve this bound: mathbbE left[f(overlinexN) - f(x^*)right] = tildeO left(dfracn^2-frac1βγ N^fracβ-1β right).