Data parallel solutions of dimensionality problems in stochastic dynamic programming

Abstract

The authors develop fast and efficient methods to solve large stochastic optimal control problems in continuous time. The stochastic perturbations by both Gaussian and Poisson white noise are considered for modeling background fluctuations and the more severe random shocks. The treatment is through the partial differential equation of stochastic dynamic programming or Bellman equation, which simplifies the optimization of the stochastic dynamical system. Massive numbers of physical processors using the 64 K processor Connection Machine has been used. Techniques such as one-to-many broadcasting and operator decomposition are developed in terms of the special characteristics of the stochastic control problems. The improvements achieved show that the optimal stochastic dynamic control problem with a reasonable number of nodes per state can be solved with optimal system memory requirements. The timing performance further demonstrates that the Connection Machine helps to alleviate Bellman's curse of dimensionality if both the problem and the machine are sufficiently large. >