End-to-end Stochastic Optimization with Energy-based Model

Lingkai Kong, Jiaming Cui, Yuchen Zhuang, Rui Feng, B. Aditya Prakash, Chao Zhang

Keywords: end-to-end stochastic optimization, energy-based model, decision-focused learning

Abstract: Decision-focused learning (DFL) was recently proposed for stochastic optimization problems that involve unknown parameters. By integrating predictive modeling with an implicitly differentiable optimization layer, DFL has shown superior performance to the standard two-stage predict-then-optimize pipeline. However, most existing DFL methods are only applicable to convex problems or a subset of nonconvex problems that can be easily relaxed to convex ones. Further, they can be inefficient in training due to the requirement of solving and differentiating through the optimization problem in every training iteration. We propose SO-EBM, a general and efficient DFL method for stochastic optimization using energy-based models. Instead of relying on KKT conditions to induce an implicit optimization layer, SO-EBM explicitly parameterizes the original optimization problem using a differentiable optimization layer based on energy functions. To better approximate the optimization landscape, we propose a coupled training objective that uses a maximum likelihood loss to capture the optimum location and a distribution-based regularizer to capture the overall energy landscape. Finally, we propose an efficient training procedure for SO-EBM with a self-normalized importance sampler based on a Gaussian mixture proposal. We evaluate SO-EBM in three applications: power scheduling, COVID-19 resource allocation, and non-convex adversarial security game, demonstrating the effectiveness and efficiency of SO-EBM.

TL;DR: an new end-to-end stochastic optimization method with energy-based model