Efficient Bisection Projection to Ensure Neural-Network Solution Feasibility for Optimization over General Set

Enming Liang, Minghua Chen

TL;DR: An efficient bisection-based projection scheme to ensure NN solution feasibility over general compact sets.

Abstract:

Neural networks (NNs) have emerged as promising tools for solving constrained optimization problems in real-time. However, ensuring constraint satisfaction for NN-generated solutions remains challenging due to prediction errors. Existing methods to ensure NN feasibility either suffer from high computational complexity or are limited to specific constraint types.
We present Bisection Projection, an efficient approach to ensure NN solution feasibility for optimization over general compact sets with non-empty interiors.
Our method comprises two key components:
(i) a dedicated NN (called IPNN) that predicts interior points (IPs) with low eccentricity, which naturally accounts for approximation errors;
(ii) a bisection algorithm that leverages these IPs to recover solution feasibility when initial NN solutions violate constraints.
We establish theoretical guarantees by providing sufficient conditions for IPNN feasibility and proving bounded optimality loss of the bisection operation under IP predictions.
Extensive evaluations on real-world non-convex problems demonstrate that Bisection Projection achieves superior feasibility and computational efficiency compared to existing methods, while maintaining comparable optimality gaps.

Lay Summary:

Neural networks can solve complex constrained optimization problems incredibly fast, but they sometimes produce solutions that violate critical safety constraints, such as predicting power generation beyond safe operational limits. While these predictions are often nearly optimal, ensuring they satisfy all necessary constraints remains challenging due to inherent prediction errors.

We developed Bisection Projection, a two-step method to correct constraint violations. First, we train a specialized neural network to predict "interior points" – safe positions well within constraints that naturally accommodate prediction errors. Second, when the main neural network produces an invalid solution, we use a bisection algorithm to find a valid solution along the line segment connecting the invalid prediction to our interior point.

Our method guarantees 100% constraint satisfaction while maintaining solution quality and achieving up to 10,000 times faster performance than traditional projection methods. Experiments on real-world problems like power grid management and inventory optimization demonstrate that Bisection Projection works for both simple and complex constraints, making neural network optimization both reliable and practical for time-critical applications.

Primary Area: General Machine Learning->Everything Else

Keywords: Neural Network, Constraint, Feasibility, Projection, Interior Point

Submission Number: 14540