Approximate Dynamic Programming via Linear Programming

The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale 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 preselected basis functions to the dynamic programming costtogo 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.