  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.
