  Synthesizing optimal controllers for dynamical systems often involves solving
optimization problems with hard real-time constraints. These constraints
determine the class of numerical methods that can be applied: computationally
expensive but accurate numerical routines are replaced by fast and inaccurate
methods, trading inference time for solution accuracy. This paper provides
techniques to improve the quality of optimized control policies given a fixed
computational budget. We achieve the above via a hypersolvers approach, which
hybridizes a differential equation solver and a neural network. The performance
is evaluated in direct and receding-horizon optimal control tasks in both low
and high dimensions, where the proposed approach shows consistent Pareto
improvements in solution accuracy and control performance.
