# Scenario Approach with Post-Design Certification of User-Specified Properties

arXiv: https://arxiv.org/abs/2602.15568 · HTML: https://mlsanity.com/paper/2602.15568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 12 of 12)

- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Compression, Generalization and Learning](https://mlsanity.com/paper/2301.12767/) (2023)
- [On the exact feasibility of convex scenario programs with discarded constraints](https://mlsanity.com/paper/2003.13433/) (2020)
- [Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs](https://mlsanity.com/paper/1307.0345/) (2013)
- [A scenario approach for non-convex control design](https://mlsanity.com/paper/1401.2200/) (2014)
- [Randomized Methods for Design of Uncertain Systems: Sample Complexity and Sequential Algorithms](https://mlsanity.com/paper/1304.0678/) (2013)
- [On the Sample Size of Random Convex Programs with Structured Dependence on the Uncertainty (Extended Version)](https://mlsanity.com/paper/1502.00803/) (2015)
- [A priori data-driven robustness guarantees on strategic deviations from generalised Nash equilibria](https://mlsanity.com/paper/2304.05308/) (2023)
- [A Posteriori Probabilistic Bounds of Convex Scenario Programs with Validation Tests](https://mlsanity.com/paper/1903.11734/) (2019)
- [Scenario approach for minmax optimization with emphasis on the nonconvex case: positive results and caveats](https://mlsanity.com/paper/1906.01476/) (2019)
- [On the sensitivity of linear resource sharing problems to the arrival of new agents](https://mlsanity.com/paper/2109.13580/) (2021)
- [Distributed Safe Control Design and Probabilistic Safety Verification for Multi-Agent Systems](https://mlsanity.com/paper/2303.12610/) (2023)

## Abstract (arXiv)

The scenario approach is an established data-driven design framework that comes equipped with a powerful theory linking design complexity to generalization properties. In this approach, data are simultaneously used both for design and for certifying the design's reliability, without resorting to a separate test dataset. This paper takes a step further by guaranteeing additional properties, useful in post-design usage but not considered during the design phase. To this end, we introduce a two-level framework of appropriateness: baseline appropriateness, which guides the design process, and post-design appropriateness, which serves as a criterion for a posteriori evaluation. We provide distribution-free upper bounds on the risk of failing to meet the post-design appropriateness; these bounds are computable without using any additional test data. Under additional assumptions, lower bounds are also derived. As part of an effort to demonstrate the usefulness of the proposed methodology, the paper presents two practical examples in H2 and pole-placement problems. Moreover, a method is provided to infer comprehensive distributional knowledge of relevant performance indexes from the available dataset.