用正交投影层让神经网络自动满足凸约束，训练快、解得准、调参稳。
Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers
- 在输出层引入正交投影，确保模型输出始终满足凸约束
- 单问题求解速度比传统方法快，批量求解提速显著，训练时间降数个量级
- 适用于需要快速可靠解的场景，如多车路径规划
我们提出一种新型神经网络输出层Πnet，可确保满足凸约束。该方法利用算子分裂实现前向传播中的快速可靠投影，并通过隐函数定理完成反向传播。将Πnet作为参数化约束优化问题的可行设计优化代理，在求解单个问题时获得中等精度解的速度优于传统求解器，批量问题求解速度优势更显著。相比现有学习方法，Πnet在训练时间、解的质量和对超参数的鲁棒性上均提升数个数量级，同时保持相近的推理时间。最后，我们在具有非凸轨迹偏好的一组多车运动规划任务中验证了其有效性，并提供基于JAX的GPU就绪实现包。
原文摘要 · Abstract (English)
We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $Π$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $Π$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches by orders of magnitude in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $Π$net as a GPU-ready package implemented in JAX.
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