# Reduced Sample Complexity in Scenario-Based Control System Design via Constraint Scaling

arXiv: https://arxiv.org/abs/2411.07361 · HTML: https://mlsanity.com/paper/2411.07361/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2024.

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

- [An Extreme Value Perspective on Learning Stress Laws](https://mlsanity.com/paper/2607.10700/) (2026)

## Abstract (arXiv)

The scenario approach is widely used in robust control system design and chance-constrained optimization, maintaining convexity without requiring assumptions about the probability distribution of uncertain parameters. However, the approach can demand large sample sizes, making it intractable for safety-critical applications that require very low levels of constraint violation. To address this challenge, we propose a novel yet simple constraint scaling method, inspired by large deviations theory. Under mild nonparametric conditions on the underlying probability distribution, we show that our method yields an exponential reduction in sample size requirements for bilinear constraints with low violation levels compared to the classical approach, thereby significantly improving computational tractability. Numerical experiments on robust pole assignment problems support our theoretical findings.