Cheap Thrills: Effective Amortized Optimization Using Inexpensive Labels

TL;DR

This paper introduces a three-stage framework for optimization using inexpensive, imperfect labels, combining supervised pretraining and self-supervised refinement to achieve faster convergence and significant cost reductions.

Contribution

It presents a novel approach that leverages cheap labels and a merit loss-based scheme to improve surrogate models for complex optimization tasks.

Findings

Up to 59x reduction in offline computational cost.

Faster convergence and improved accuracy in challenging domains.

Small amounts of cheap labels suffice for effective self-supervised refinement.

Abstract

To scale optimization and simulation, prior work has explored training machine-learning surrogates that map problem parameters to solutions inexpensively at inference time. Unfortunately, commonly used approaches, including supervised and self-supervised learning with either soft or hard feasibility enforcement, face inherent challenges such as reliance on expensive high-quality labels or difficult optimization landscapes. To address their trade-offs, we propose a novel framework that collects "cheap" imperfect labels, performs supervised model pretraining with a merit loss-based termination scheme, and finally refines the model through self-supervised learning to improve final performance. Empirical validation across challenging domains -- including nonconvex constrained optimization, power-grid operation, and stiff dynamical systems -- shows that this three-stage strategy yields faster convergence; improved accuracy, feasibility, and optimality; and up to 59x reductions in total offline computational cost. We further analyze why and when our framework improves surrogate model training, finding that (i) merit loss is an informative signal and (ii) only small numbers of cheap, inexact labels are needed to place the model in a favorable regime for self-supervised learning.