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Conformalized Decision Risk Assessment

Wenbin Zhou, Agni Orfanoudaki, Shixiang Zhu

TL;DR

CREDO introduces a distribution-free approach to auditing decision robustness under uncertainty by merging inverse optimization with conformal prediction. It reframes the problem through the inverse feasible region and uses generative CP balls to construct conservative, finite-sample guarantees on the probability that a prescribed decision remains optimal. The method provides a practical algorithm with closed-form solutions for linear problems and a scalable alternating scheme for convex problems, along with theoretical validity, consistency, and true positive rate guarantees. Empirical results across LP, QP, SOCP, IP, and real-grid data demonstrate strong validity, improved risk estimation accuracy with richer generative models, and effective risk-aware decision prescriptions in diverse settings.

Abstract

In many operational settings, decision-makers must commit to actions before uncertainty resolves, but existing optimization tools rarely quantify how consistently a chosen decision remains optimal across plausible scenarios. This paper introduces CREDO -- Conformalized Risk Estimation for Decision Optimization, a distribution-free framework that quantifies the probability that a prescribed decision remains (near-)optimal across realizations of uncertainty. CREDO reformulates decision risk through the inverse feasible region -- the set of outcomes under which a decision is optimal -- and estimates its probability using inner approximations constructed from conformal prediction balls generated by a conditional generative model. This approach yields finite-sample, distribution-free lower bounds on the probability of decision optimality. The framework is model-agnostic and broadly applicable across a wide range of optimization problems. Extensive numerical experiments demonstrate that CREDO provides accurate, efficient, and reliable evaluations of decision optimality across various optimization settings.

Conformalized Decision Risk Assessment

TL;DR

CREDO introduces a distribution-free approach to auditing decision robustness under uncertainty by merging inverse optimization with conformal prediction. It reframes the problem through the inverse feasible region and uses generative CP balls to construct conservative, finite-sample guarantees on the probability that a prescribed decision remains optimal. The method provides a practical algorithm with closed-form solutions for linear problems and a scalable alternating scheme for convex problems, along with theoretical validity, consistency, and true positive rate guarantees. Empirical results across LP, QP, SOCP, IP, and real-grid data demonstrate strong validity, improved risk estimation accuracy with richer generative models, and effective risk-aware decision prescriptions in diverse settings.

Abstract

In many operational settings, decision-makers must commit to actions before uncertainty resolves, but existing optimization tools rarely quantify how consistently a chosen decision remains optimal across plausible scenarios. This paper introduces CREDO -- Conformalized Risk Estimation for Decision Optimization, a distribution-free framework that quantifies the probability that a prescribed decision remains (near-)optimal across realizations of uncertainty. CREDO reformulates decision risk through the inverse feasible region -- the set of outcomes under which a decision is optimal -- and estimates its probability using inner approximations constructed from conformal prediction balls generated by a conditional generative model. This approach yields finite-sample, distribution-free lower bounds on the probability of decision optimality. The framework is model-agnostic and broadly applicable across a wide range of optimization problems. Extensive numerical experiments demonstrate that CREDO provides accurate, efficient, and reliable evaluations of decision optimality across various optimization settings.
Paper Structure (46 sections, 9 theorems, 91 equations, 6 figures, 6 tables, 4 algorithms)

This paper contains 46 sections, 9 theorems, 91 equations, 6 figures, 6 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Setup
  4. Motivating Examples
  5. The CREDO Framework
  6. Preliminary: Conformal Prediction
  7. Conformalized Decision Risk Assessment
  8. Reformulation with Inverse Feasible Region
  9. Risk Estimation via Generative Conformal Prediction
  10. Proposed Algorithm
  11. Theoretical Analysis
  12. Validity
  13. Consistency
  14. True Positive Rate
  15. Computational Implementation
  16. ...and 31 more sections

Key Result

Lemma 1

The probability in eq:risk-certificate can be equivalently expressed as:

Figures (6)

  • Figure 1: Our proposed framework (CREDO) compared against conventional predict-then-optimize (PTO).
  • Figure 2: Example of the CREDO procedure applied to a linear programming problem.
  • Figure 3: Comparison of risk estimation using a point model and generative models ($K = 3$ and $K = 4$) in CREDO.
  • Figure 4: Illustration of settings I and II.
  • Figure 5: Comparison of CREDO performance for three different calibrated radii.
  • ...and 1 more figures

Theorems & Definitions (21)

  • Example 1: Stylized Umbrella-Carrying Decision
  • Example 2: Clinical Triage
  • Lemma 1: Reformulation
  • Theorem 1: Conservativeness under $e$-value
  • Corollary 1: Conservativeness under $p$-value
  • Proposition 1: Asymptotic conditional consistency
  • Proposition 2: True positive rate
  • Proposition 3: Computation
  • Lemma 2
  • Remark 1
  • ...and 11 more