Scaling Mixed-Integer Programming for Certification of Neural Network Controllers Using Bounds Tightening

Abstract

Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety, particularly in safety-critical domains such as autonomous vehicles. One approach to formally certify properties of neural networks is to solve a mixed-integer program based on the network. This approach suffers from scalability issues due to the complexity of solving the resulting mixed-integer programs. Nevertheless, these issues can be (partially) mitigated via bound-tightening techniques prior to forming the mixed-integer program, which results in tighter formulations and faster optimisation. This paper presents bound-tightening techniques in the context of neural network explicit control policies. Bound tightening is particularly important when considering problems spanning multiple time steps of a controlled system, as the bounds must be propagated through the problem depth. Several strategies for bound tightening are evaluated in terms of both computational complexity and tightness of the bounds.

Accepted to the 2024 63rd IEEE Conference on Decision and Control