Policy Decomposition: Approximate Optimal Control with Suboptimality Estimates

TL;DR

This paper introduces policy decomposition, a novel approximation method for optimal control that provides explicit suboptimality estimates, enabling efficient control policy synthesis for complex systems with quantifiable performance bounds.

Contribution

The paper presents a new policy decomposition approach that decomposes complex control problems into subproblems with explicit suboptimality estimates, improving efficiency and performance prediction.

Findings

Estimates accurately identify the best control combinations.

Control policies are computed faster with minimal performance loss.

Method successfully applied to cart-pole, biped, and manipulator systems.

Abstract

Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify by how much the resulting control underperforms the elusive globally optimal solution. Here we propose policy decomposition, an approximation method with explicit suboptimality estimates. Our method decomposes the optimal control problem into lower-dimensional subproblems, whose optimal solutions are recombined to build a control policy for the entire system. Many such combinations exist, and we introduce the value error and its LQR and DDP estimates to predict the suboptimality of possible combinations and prioritize the ones that minimize it. Using a cart-pole, a 3-link balancing biped and N-link planar manipulators as example systems, we find that the estimates correctly identify the best combinations, yielding control policies in a fraction of the time it takes to compute the optimal control without a notable sacrifice in closed-loop performance. While more research will be needed to find ways of dealing with the combinatorics of policy decomposition, the results suggest this method could be an effective alternative for approximating optimal control in intractable systems.