Distributional Uncertainty and Adaptive Decision-Making in System

2026-03-14

AI Summary

This work addresses the challenge of coordinating design in complex engineering systems under conflicting objectives and uncertain specifications, where existing co-design methods based on interval uncertainty fail to capture probabilistic risk and multi-stage adaptive decision-making. For the first time, distributional uncertainty is integrated into a monotone co-design framework by reparameterizing uncertain design outcomes as probability distributions over the design space via Markov kernels, thereby enabling adaptive decisions and compositional construction. Grounded in quasi-measurable space theory, the approach supports queries on probabilistic feasibility, confidence bounds, and resource demand distributions, overcoming the representational limitations of traditional interval models. In a mission-driven unmanned aerial vehicle case study, the framework successfully captures risk-sensitive and information-dependent design trade-offs, demonstrating its expressive power and effectiveness.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Complex engineered systems require coordinated design choices across heterogeneous components under multiple conflicting objectives and uncertain specifications. Monotone co-design provides a compositional framework for such problems by modeling each subsystem as a design problem: a feasible relation between provided functionalities and required resources in partially ordered sets. Existing uncertain co-design models rely on interval bounds, which support worst-case reasoning but cannot represent probabilistic risk or multi-stage adaptive decisions. We develop a distributional extension of co-design that models uncertain design outcomes as distributions over design problems and supports adaptive decision processes through Markov-kernel re-parameterizations. Using quasi-measurable and quasi-universal spaces, we show that the standard co-design interconnection operations remain compositional under this richer notion of uncertainty. We further introduce queries and observations that extract probabilistic design trade-offs, including feasibility probabilities, confidence bounds, and distributions of minimal required resources. A task-driven unmanned aerial vehicle case study illustrates how the framework captures risk-sensitive and information-dependent design choices that interval-based models cannot express.

Problem

• distributional uncertainty
• adaptive decision-making
• co-design
• probabilistic risk
• complex engineered systems

Innovation

• distributional uncertainty
• adaptive decision-making
• monotone co-design
• Markov kernels
• quasi-measurable spaces