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.

Humans have a remarkable ability to accurately reason about future events, including the behaviors and states of mind of other agents. Consider driving a car through a busy intersection: it is necessary to reason about the physics of the vehicle, the intentions of other drivers, and their beliefs about your own intentions. For example, if you signal a turn, another driver might yield to you; or if you enter the passing lane, another driver might decelerate to give you room to merge in front. Competent drivers must plan how they can safely react to a variety of potential future behaviors of other agents before they make their next move. This requires contingency planning: explicitly planning a set of conditional actions that depend on the stochastic outcome of future events. In this work, we develop a general-purpose contingency planner that is learned end-to-end using high-dimensional scene observations and low-dimensional behavioral observations. We use a conditional autoregressive flow model for contingency planning. We show how this model can tractably learn contingencies from behavioral observations. We developed a closed-loop control benchmark of realistic multi-agent scenarios in a driving simulator (CARLA), on which we compare our method to various noncontingent methods that reason about multi-agent future behavior, and find that our contingency planning method achieves qualitatively and quantitatively superior performance.