Multi-objective dynamic programming with limited precision

This paper addresses the problem of approximating the set of all solutions for Multi-objective Markov Decision Processes. We show that in the vast majority of interesting cases, the number of solutions is exponential or even infinite. In order to overcome this difficulty we propose to approximate the set of all solutions by means of a limited precision approach based on White’s multi-objective value-iteration dynamic programming algorithm. We prove that the number of calculated solutions is tractable and show experimentally that the solutions obtained are a good approximation of the true Pareto front.Funding for open access charge: Universidad de Málaga / CBUA. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Funded by the Spanish Government, Agencia Estatal de Investigación (AEI) and European Union, Fondo Europeo de Desarrollo Regional (FEDER), Grant TIN2016-80774-R (AEI/FEDER, UE)