# Smooth Convex Optimization using Sub-Zeroth-Order Oracles

arXiv: https://arxiv.org/abs/2103.00667 · HTML: https://mlsanity.com/paper/2103.00667/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2021.

## Built on by (most cited first, 3 of 3)

- [Finding Stationary Points by Comparisons](https://mlsanity.com/paper/2606.27082/) (2026)
- [Gradient Testing and Estimation by Comparisons](https://mlsanity.com/paper/2405.11454/) (2024)
- [Sequential Resource Trading Using Comparison-Based Gradient Estimation](https://mlsanity.com/paper/2408.11186/) (2024)

## Abstract (arXiv)

We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an oracle that compares the function values for a given pair of points, and an oracle that outputs a noisy function value for a given point. We show that the sample complexity of optimization using these oracles is polynomial in the relevant parameters. The optimization algorithm that we provide for the comparator oracle is the first algorithm with a known rate of convergence that is polynomial in the number of dimensions. We also give an algorithm for the noisy-value oracle that incurs a regret of tildeO(n3.75 T0.75) (ignoring the other factors and logarithmic dependencies) where n is the number of dimensions and T is the number of queries.