Ensuring DNN Solution Feasibility for Optimization Problems with Linear Constraints

Tianyu Zhao, Xiang Pan, Minghua Chen, Steven Low

Keywords: Deep learning, Deep neural network, Constrained optimization, Solution feasibility guarantee, Optimal power flow

TL;DR: This paper proposes a preventive learning framework to ensure DNN solution feasibility for optimization problems with linear constraints without post-processing.

Abstract: We propose preventive learning as the first framework to guarantee Deep Neural Network (DNN) solution feasibility for optimization problems with linear constraints without post-processing, upon satisfying a mild condition on constraint calibration. Without loss of generality, we focus on problems with only inequality constraints. We systematically calibrate the inequality constraints used in training, thereby anticipating DNN prediction errors and ensuring the obtained solutions remain feasible. We characterize the calibration rate and a critical DNN size, based on which we can directly construct a DNN with provable solution feasibility guarantee. We further propose an Adversarial-Sample Aware training algorithm to improve its optimality performance. We apply the framework to develop DeepOPF+ for solving essential DC optimal power flow problems in grid operation. Simulation results over IEEE test cases show that it outperforms existing strong DNN baselines in ensuring 100\% feasibility and attaining consistent optimality loss (<0.19%) and speedup (up to x228) in both light-load and heavy-load regimes, as compared to a state-of-the-art solver. We also apply our framework to a non-convex problem and show its performance advantage over existing schemes.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Deep Learning and representational learning