Inverse optimization in countably infinite linear programs

Given the costs and a feasible solution for a linear program, inverse optimization involves finding new costs that are close to the original ones and make the given solution optimal. We develop an inverse optimization framework for countably infinite linear programs using the weighted absolute sum metric. We reformulate this as an infinite-dimensional mathematical program using duality. We propose a convergent algorithm that solves a sequence of finite-dimensional LPs to tackle it. We apply this to non-stationary Markov decision processes.