Cheap Thrills: Effective Amortized Optimization Using Inexpensive Labels
This work offers a more cost-effective method for training machine learning surrogates for optimization and simulation problems, which is beneficial for researchers and practitioners dealing with expensive label generation.
This paper proposes a three-stage framework for amortized optimization that uses inexpensive, imperfect labels for initial supervised pretraining, followed by self-supervised refinement. This approach significantly reduces offline costs by up to 59x while improving convergence speed, accuracy, feasibility, and optimality across various challenging domains.
To scale the solution of optimization and simulation problems, prior work has explored machine-learning surrogates that inexpensively map problem parameters to corresponding solutions. 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 first collects "cheap" imperfect labels, then performs supervised pretraining, and finally refines the model through self-supervised learning to improve overall performance. Our theoretical analysis and merit-based criterion show that labeled data need only place the model within a basin of attraction, confirming that only modest numbers of inexact labels and training epochs are required. We empirically validate our simple three-stage strategy across challenging domains, including nonconvex constrained optimization, power-grid operation, and stiff dynamical systems, and show that it yields faster convergence; improved accuracy, feasibility, and optimality; and up to 59x reductions in total offline cost.