# Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates

arXiv: https://arxiv.org/abs/2011.04225 · HTML: https://mlsanity.com/paper/2011.04225/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

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

- [Multi-channel Autobidding with Budget and ROI Constraints](https://mlsanity.com/paper/2302.01523/) (2023)
- [A general optimization solver based on OP-to-MaxSAT reduction](https://mlsanity.com/paper/2604.21961/) (2026)

## Abstract (arXiv)

This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under general constraints. The values of the objective and constraint functions are provided by a noisy blackbox, i.e., they can only be computed with random noise whose distribution is unknown. As in MADS, constraint violations are aggregated into a single constraint violation function. Since all functions values are numerically unavailable, StoMADS-PB uses estimates and introduces so-called probabilistic bounds for the violation. Such estimates and bounds obtained from stochastic observations are required to be accurate and reliable with high but fixed probabilities. The proposed method, which allows intermediate infeasible iterates, accepts new points using sufficient decrease conditions and imposing a threshold on the probabilistic bounds. Using Clarke nonsmooth calculus and martingale theory, Clarke stationarity convergence results for the objective and the violation function are derived with probability one.