Approximate Dynamic Programming via a Smoothed Linear Program

Approximate Dynamic Programming via a Smoothed Linear Program

We present a novel linear program for the approximation of the dynamic programming costto-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural ‘projection’ of a well studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go fun...

A Smoothed Approximate Linear Program

We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP naturally restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program – the ‘smoothed approximate linear program’ – relaxes this restriction in an appropriate fashion...

The Smoothed Approximate Linear Program

We present a novel linear program for the approximation of the dynamic programming costto-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural ‘projection’ of a well studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go fun...

Electronic Companion — “ Approximate Dynamic Programming via a Smoothed

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...