Approximate dynamic programming via linear programming

The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits" a linear combination of pre-selected basis functions to the dynamic programming cost-to-go function. We develop bounds on the approximation error and present experimental results in the domain of queueing network control, providing empirical support for the methodology.