# Can a One-Point Feedback Zeroth-order Algorithm Achieve Linear Dimension Dependent Sample Complexity?

arXiv: https://arxiv.org/abs/2508.12228 · HTML: https://mlsanity.com/paper/2508.12228/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [Accelerating Evolutionary Strategy via Rao-Blackwellizing Realization of Uncertain Input](https://mlsanity.com/paper/2608.02073/) (2026)

## Abstract (arXiv)

We revisit the one-point feedback zeroth-order (ZO) optimization problem, a classical setting in derivative-free optimization where only a single noisy function evaluation is available per query. Compared to their two-point counterparts, existing one-point feedback ZO algorithms typically suffer from poor dimension dependence in their sample complexities -- often quadratic or worse -- even for convex problems. This gap has led to the open question of whether one-point feedback ZO algorithms can match the optimal linear dimension dependence achieved by two-point methods. In this work, we answer this question affirmatively.