Learning as Energy Dissipation: Handling Inexact Surrogate Gradients in Decision-focused Training

Shunyu Wu, Jingcheng Wang, Jun Rao, Xinwei Xiao, Yanjiu Zhong

Keywords: Energy Dissipative, Inexact Surrogate Gradients, Decision-focused Training

TL;DR: Adam may not be the most suitable optimizer for decision-focused training.

Abstract:

Learning is often imagined as a descent along a smooth surface, where each step steadily lowers the energy. Decision-focused learning (DFL) challenges this picture. Instead of optimizing prediction error, it optimizes the quality of downstream decisions, which requires surrogate losses to approximate decision regret. The gradients of these surrogates are not exact: the ideal gradient of the surrogate vanishes at its optimum, while the computed directions are noisy and misaligned. In practice, this breaks the energy-dissipative nature of learning, producing unstable training curves and erratic decision quality.

We reinterpret this difficulty through the lens of energy dissipation. If training is viewed as the evolution of a dissipative system, then instability arises precisely when inexact gradients violate the energy law. To restore this structure, we introduce EDO (Energy-Dissipative Optimizer), which reformulates updates as implicit descent steps that guarantee monotone energy decrease even under gradient inexactness. EDO integrates simple stabilizing mechanisms—scaled weight decay, parameter averaging, and adaptive momentum—without altering the modeling pipeline. We show that three widely used surrogate families admit valid subgradients under this formulation, and provide theoretical guarantees of monotone energy descent with uniform error bounds. Across four benchmark tasks, EDO produces smoother training trajectories, lower regret, and more reliable decisions than existing methods.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Submission Number: 2347