  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.
