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

2026-02-17

AI Summary

This work addresses the challenge of certifying performance attributes that emerge as user concerns after deployment but were not considered during the design phase in data-driven control. To this end, the paper proposes a two-layer adaptability framework that extends the scenario approach by introducing a post-design adaptability concept, enabling reliable certification without requiring additional test data. It is the first to formally incorporate user-specified a posteriori performance properties into the scenario optimization framework, deriving computable, distribution-free upper and lower bounds on the violation risk. Moreover, the method allows full reconstruction of the performance metric’s distribution from existing data. Experimental validation on H₂ control and pole placement problems demonstrates that the approach effectively certifies a posteriori properties and accurately infers critical performance distributions, offering both theoretical rigor and practical utility.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

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.

Problem

• scenario approach
• post-design certification
• user-specified properties
• generalization
• distribution-free bounds

Innovation

• scenario approach
• post-design certification
• distribution-free bounds
• two-level appropriateness
• data-driven design