Idempotent algorithms for discrete-time stochastic control through distributed dynamic programming

Previously, idempotent methods have been found to be extremely fast for solution of dynamic programming equations associated with deterministic control problems. The original methods exploited the idempotent (e.g., max-plus) linearity of the associated semigroup operator. However, it is now seen that the curse-of-dimensionality-free idempotent methods do not require this linearity. Here, we see that idempotent methods may be used to solve some classes of stochastic control problems. The key is the use of the idempotent distributive property.We demonstrate this approach for a class of nonlinear, discrete-time stochastic control problems.