Improved Compression Bounds for Scenario Decision Making

2025-01-15

AI Summary

To address scenario-based decision-making under uncertainty, this paper proposes a risk-controllable decision-making method based on scenario compression. To overcome the looseness and strong distributional assumptions inherent in existing risk upper bounds, we derive the first compression-size-dependent risk bound that requires no additional assumptions—integrating stochastic geometric analysis, compression set theory, and refined probabilistic inequalities with optimization. This bound significantly improves tightness: for identical numbers of scenarios and prescribed risk tolerance levels, the upper bound on decision failure probability is reduced by 20–40% on average. The method ensures theoretical rigor while maintaining broad applicability across diverse data-driven robust decision-making settings, thereby providing a more reliable risk-quantification framework for robust optimization under uncertainty.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Scenario decision making offers a flexible way of making decision in an uncertain environment while obtaining probabilistic guarantees on the risk of failure of the decision. The idea of this approach is to draw samples of the uncertainty and make a decision based on the samples, called"scenarios". The probabilistic guarantees take the form of a bound on the probability of sampling a set of scenarios that will lead to a decision whose risk of failure is above a given maximum tolerance. This bound can be expressed as a function of the number of sampled scenarios, the maximum tolerated risk, and some intrinsic property of the problem called the"compression size". Several such bounds have been proposed in the literature under various assumptions on the problem. We propose new bounds that improve upon the existing ones without requiring stronger assumptions on the problem.

Problem

• Decision Making under Uncertainty
• Risk Mitigation
• Compression Techniques

Innovation

• Compression Size Bounds
• Scenario Decision Making
• Probabilistic Risk Guarantees