# Dimensional Peeking for Low-Variance Gradients in Zeroth-Order Discrete Optimization via Simulation

arXiv: https://arxiv.org/abs/2602.00075 · HTML: https://mlsanity.com/paper/2602.00075/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 21 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator](https://mlsanity.com/paper/1807.01695/) (2018)
- [CityFlow: A Multi-Agent Reinforcement Learning Environment for Large Scale City Traffic Scenario](https://mlsanity.com/paper/1905.05217/) (2019)
- [Improved Zeroth-Order Variance Reduced Algorithms and Analysis for Nonconvex Optimization](https://mlsanity.com/paper/1910.12166/) (2019)
- [Automatic Differentiation of Programs with Discrete Randomness](https://mlsanity.com/paper/2210.08572/) (2022)
- [Zeroth order optimization with orthogonal random directions](https://mlsanity.com/paper/2107.03941/) (2021)
- [ASTRO-DF: A Class of Adaptive Sampling Trust-Region Algorithms for Derivative-Free Stochastic Optimization](https://mlsanity.com/paper/1610.06506/) (2016)
- [Stochastic Zeroth Order Gradient and Hessian Estimators: Variance Reduction and Refined Bias Bounds](https://mlsanity.com/paper/2205.14737/) (2022)
- [Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?](https://mlsanity.com/paper/2207.05060/) (2022)
- [Smoothing Methods for Automatic Differentiation Across Conditional Branches](https://mlsanity.com/paper/2310.03585/) (2023)
- [Gradient-based Algorithms for Convex Discrete Optimization via Simulation](https://mlsanity.com/paper/2010.16250/) (2020)
- [Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation](https://mlsanity.com/paper/2410.08125/) (2024)
- [Automatic Gradient Estimation for Calibrating Crowd Models with Discrete Decision Making](https://mlsanity.com/paper/2404.04678/) (2024)

## Abstract (arXiv)

Gradient-based optimization methods are commonly used to identify local optima in high-dimensional spaces. When derivatives cannot be evaluated directly, stochastic estimators can provide approximate gradients. However, these estimators' perturbation-based sampling of the objective function introduces variance that can lead to slow convergence. In this paper, we present dimensional peeking, a variance reduction method for gradient estimation in discrete optimization via simulation. By lifting the sampling granularity from scalar values to classes of values that follow the same control flow path, we increase the information gathered per simulation evaluation. Our derivation from an established smoothed gradient estimator shows that the method does not introduce any bias. We present an implementation via a custom numerical data type to transparently carry out dimensional peeking over C++ programs. Variance reductions by factors of up to 7.9 are observed for three simulation-based optimization problems with high-dimensional input. The optimization progress compared to three meta-heuristics shows that dimensional peeking increases the competitiveness of zeroth-order optimization for discrete and non-convex simulations.