Efficient Bisection Projection to Ensure NN Solution Feasibility for Optimization over General Set

Enming Liang, Minghua Chen

Keywords: Constrained Optimization, Neural Network, Feasibility, Bisection, Learning based Optimization

TL;DR: An efficient bisection-based algorithm to recover NN solution feasibility for constrained optimization over non-convex sets.

Abstract:

Neural networks (NNs) have shown promise in solving constrained optimization problems in real-time. However, ensuring that NN-generated solutions strictly adhere to constraints is challenging due to NN prediction errors. Recent methods have achieved feasibility guarantees over ball-homeomorphic sets with low complexity and bounded optimality loss, yet extending these guarantees to more general sets remains largely open.
In this paper, we develop **Bisection Projection**, an efficient approach to ensure NN solution feasibility for optimization over general compact sets with non-empty interiors, irrespective of their ball-homeomorphic properties.
Our method begins by identifying multiple interior points (IPs) within the constraint set, chosen based on their eccentricity modulated by the NN infeasibility region.
We utilize another unsupervised-trained NN (called IPNN) to map inputs to these interior points, thereby reducing the complexity of computing these IPs in run-time.
For NN solutions initially deemed infeasible, we apply a bisection procedure that adjusts these solutions towards the identified interior points, ensuring feasibility with minor projection-induced optimality loss. We prove the feasibility guarantee and bound the optimality loss of our approach under mild conditions.
Extensive simulations, including non-convex optimal power flow problems in large-scale networks, demonstrate that bisection projection outperforms existing methods in solution feasibility and computational efficiency with comparable optimality losses.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 9527