Technology Category
Reasoning under Uncertainty: Stochastic OptimizationMachine Learning: Calibration & Uncertainty QuantificationIntelligent Robots: Learning & Optimization for ROB
Distribution-Free Robust Predict-Then-Optimize in Function Spaces
🤖 AI Summary
This work addresses the lack of distribution-agnostic uncertainty quantification in existing neural operator surrogate models for decision-making tasks, which hinders reliable robust optimization. To overcome this limitation, the study introduces conformal prediction into the function space of neural operator outputs for the first time, leveraging an infinite-dimensional Danskin’s theorem and variational analysis to construct a scalable, robust decision framework that requires no strong distributional assumptions. The proposed method effectively controls regret in downstream tasks and demonstrates significant performance gains over traditional approaches such as Gaussian processes across multiple engineering benchmarks. By providing rigorous theoretical guarantees while enhancing both reliability and computational efficiency, this framework advances the state of the art in robust decision-making under uncertainty.
Technology Category
Application Category
📝 Abstract
The need to rapidly solve PDEs in engineering design workflows has spurred the rise of neural surrogate models. In particular, neural operator models provide a discretization-invariant surrogate by retaining the infinite-dimensional, functional form of their arguments. Despite improved throughput, such methods lack guarantees on accuracy, unlike classical numerical PDE solvers. Optimizing engineering designs under these potentially miscalibrated surrogates thus runs the risk of producing designs that perform poorly upon deployment. In a similar vein, there is growing interest in automated decision-making under black-box predictors in the finite-dimensional setting, where a similar risk of suboptimality exists under poorly calibrated models. For this reason, methods have emerged that produce adversarially robust decisions under uncertainty estimates of the upstream model. One such framework leverages conformal prediction, a distribution-free post-hoc uncertainty quantification method, to provide these estimates due to its natural pairing with black-box predictors. We herein extend this line of conformally robust decision-making to infinite-dimensional function spaces. We first extend the typical conformal prediction guarantees over finite-dimensional spaces to infinite-dimensional Sobolev spaces. We then demonstrate how such uncertainty can be leveraged to robustly formulate engineering design tasks and characterize the suboptimality of the resulting robust optimal designs. We then empirically demonstrate the generality of our functional conformal coverage method across a diverse collection of PDEs, including the Poisson and heat equations, and showcase the significant improvement of such robust design in a quantum state discrimination task.
Problem
Research questions and friction points this paper is trying to address.
uncertainty quantification
neural operators
distribution-free
robust decision-making
PDE surrogate models
Innovation
Methods, ideas, or system contributions that make the work stand out.
conformal prediction
neural operators
distribution-free uncertainty quantification
robust decision-making
infinite-dimensional optimization
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