Nathan Hatch

Nathan Hatch, Byron Boots

Model Predictive Control (MPC) is a classic tool for optimal control of complex, real-world systems. Although it has been successfully applied to a wide range of challenging tasks in robotics, it is fundamentally limited by the prediction horizon, which, if too short, will result in myopic decisions. Recently, several papers have suggested using a learned value function as the terminal cost for MPC. If the value function is accurate, it effectively allows MPC to reason over an infinite horizon. Unfortunately, Reinforcement Learning (RL) solutions to value function approximation can be difficult to realize for robotics tasks. In this paper, we suggest a more efficient method for value function approximation that applies to goal-directed problems, like reaching and navigation. In these problems, MPC is often formulated to track a path or trajectory returned by a planner. However, this strategy is brittle in that unexpected perturbations to the robot will require replanning, which can be costly at runtime. Instead, we show how the intermediate data structures used by modern planners can be interpreted as an approximate value function. We show that that this value function can be used by MPC directly, resulting in more efficient and resilient behavior at runtime.

Amirreza Shaban, Ching-An Cheng, Nathan Hatch et al.

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is computationally challenging. One heuristic to circumvent this difficulty is to use the approximate gradient given by performing truncated back-propagation through the iterative optimization procedure that solves the lower-level problem. Although promising empirical performance has been reported, its theoretical properties are still unclear. In this paper, we analyze the properties of this family of approximate gradients and establish sufficient conditions for convergence. We validate this on several hyperparameter tuning and meta learning tasks. We find that optimization with the approximate gradient computed using few-step back-propagation often performs comparably to optimization with the exact gradient, while requiring far less memory and half the computation time.