Learning predictive models from observations using deep neural networks (DNNs) is a promising new approach to many real-world planning and control problems. However, common DNNs are too unstructured for effective planning, and current control methods typically rely on extensive sampling or local gradient descent. In this paper, we propose a new framework for integrated model learning and predictive control that is amenable to efficient optimization algorithms. Specifically, we start with a ReLU neural model of the system dynamics and, with minimal losses in prediction accuracy, we gradually sparsify it by removing redundant neurons. This discrete sparsification process is approximated as a continuous problem, enabling an end-to-end optimization of both the model architecture and the weight parameters. The sparsified model is subsequently used by a mixed-integer predictive controller, which represents the neuron activations as binary variables and employs efficient branch-and-bound algorithms. Our framework is applicable to a wide variety of DNNs, from simple multilayer perceptrons to complex graph neural dynamics. It can efficiently handle tasks involving complicated contact dynamics, such as object pushing, compositional object sorting, and manipulation of deformable objects. Numerical and hardware experiments show that, despite the aggressive sparsification, our framework can deliver better closed-loop performance than existing state-of-the-art methods.

翻译：利用深度神经网络（DNN）从观测数据中学习预测模型，是解决许多现实世界规划与控制问题的一种有前景的新方法。然而，常见的DNN结构过于无序，难以进行有效规划，且当前的控制方法通常依赖于大量采样或局部梯度下降。在本文中，我们提出了一种集成的模型学习与预测控制新框架，该框架适用于高效的优化算法。具体来说，我们从系统动力学的ReLU神经网络模型出发，在预测精度损失最小的情况下，通过移除冗余神经元逐步使其稀疏化。这一离散的稀疏化过程被近似为连续问题，从而实现了模型架构与权重参数的端到端优化。随后，稀疏化模型被用于混合整数预测控制器，该控制器将神经元激活状态表示为二元变量，并采用高效的分支定界算法。我们的框架适用于多种DNN，从简单的多层感知器到复杂的图神经动力学模型。它可以高效处理涉及复杂接触动力学的任务，例如物体推挤、组合物体分类以及可变形物体的操作。数值与硬件实验表明，尽管进行了激进的稀疏化，我们的框架相比现有最优方法，仍能实现更优的闭环性能。