Conformal Predictive Programming for Chance Constrained Optimization
Yiqi Zhao, Xinyi Yu, Matteo Sesia, Jyotirmoy V. Deshmukh, Lars Lindemann
TL;DR
This work introduces Conformal Predictive Programming (CPP) to solve chance constrained optimization by reformulating probabilistic constraints as deterministic quantiles learned from data. CPP leverages conformal prediction to provide both a priori guarantees (via connections to SAA) and a posteriori feasibility guarantees through calibration, while accommodating robust and Mondrian variants. It offers three practical quantile-encodings (CPP-MIP, CPP-Bilevel, CPP-Discarding) and extends to joint chance constraints with union bounding or max-based approaches. Across convex, nonconvex, and stochastic control problems, CPP demonstrates competitive empirical coverage and favorable computational trade-offs, improving robustness to distribution shifts and class-conditional constraints. The framework enables flexible, scalable, and verifiable optimization under uncertainty with broad applicability in robotics, finance, and operations research.
Abstract
We propose conformal predictive programming (CPP), a framework to solve chance constrained optimization problems, i.e., optimization problems with constraints that are functions of random variables. CPP utilizes samples from these random variables along with the quantile lemma - central to conformal prediction - to transform the chance constrained optimization problem into a deterministic problem with a quantile reformulation. CPP inherits a priori guarantees on constraint satisfaction from existing sample average approximation approaches for a class of chance constrained optimization problems, and it provides a posteriori guarantees that are of conditional and marginal nature otherwise. The strength of CPP is that it can easily support different variants of conformal prediction which have been (or will be) proposed within the conformal prediction community. To illustrate this, we present robust CPP to deal with distribution shifts in the random variables and Mondrian CPP to deal with class conditional chance constraints. To enable tractable solutions to the quantile reformulation, we present a mixed integer programming method (CPP-MIP) encoding, a bilevel optimization strategy (CPP-Bilevel), and a sampling-and-discarding optimization strategy (CPP-Discarding). We also extend CPP to deal with joint chance constrained optimization (JCCO). In a series of case studies, we show the validity of the aforementioned approaches, empirically compare CPP-MIP, CPP-Bilevel, as well as CPP-Discarding, and illustrate the advantage of CPP as compared to scenario approach.