Certified Training with Branch-and-Bound for Lyapunov-stable Neural Control

2024-11-27

AI Summary

To address the misalignment between training and verification objectives in neural controller certification—leading to small regions of attraction (ROAs) and low verification efficiency—this paper proposes the first certified training framework that embeds a branch-and-bound (BaB) mechanism directly into the training phase. The framework jointly optimizes Lyapunov stability constraint modeling, interval propagation, and adaptive dataset refinement, while dynamically partitioning hard-to-verify input subregions to tighten certification bounds, thereby aligning training and verification goals. Experiments on a 2D quadrotor output-feedback system demonstrate an 11× reduction in verification time and a 164× expansion of the certified ROA, significantly enhancing both the strength of stability guarantees and overall certification efficiency.

Technology Category

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Abstract

We study the problem of learning verifiably Lyapunov-stable neural controllers that provably satisfy the Lyapunov asymptotic stability condition within a region-of-attraction (ROA). Unlike previous works that adopted counterexample-guided training without considering the computation of verification in training, we introduce Certified Training with Branch-and-Bound (CT-BaB), a new certified training framework that optimizes certified bounds, thereby reducing the discrepancy between training and test-time verification that also computes certified bounds. To achieve a relatively global guarantee on an entire input region-of-interest, we propose a training-time BaB technique that maintains a dynamic training dataset and adaptively splits hard input subregions into smaller ones, to tighten certified bounds and ease the training. Meanwhile, subregions created by the training-time BaB also inform test-time verification, for a more efficient training-aware verification. We demonstrate that CT-BaB yields verification-friendly models that can be more efficiently verified at test time while achieving stronger verifiable guarantees with larger ROA. On the largest output-feedback 2D Quadrotor system experimented, CT-BaB reduces verification time by over 11X relative to the previous state-of-the-art baseline while achieving 164X larger ROA.

Problem

• Learning verifiably stable neural controllers with Lyapunov guarantees
• Reducing discrepancy between training and verification using certified bounds
• Achieving global stability guarantees with efficient training-aware verification

Innovation

• Certified training framework optimizes certified bounds
• Training-time branch-and-bound tightens certified bounds
• Dynamic dataset and adaptive subregion splitting ease training