Abstract
This work describes MPQ-learning, an algorithm that approximates the set of all deterministic non-dominated policies in multi-objective Markov decision problems, where rewards are vectors and each component stands for an objective to maximize. MPQ-learning generalizes directly the ideas of Q-learning to the multi-objective case. It can be applied to non-convex Pareto frontiers and finds both supported and unsupported solutions. We present the results of the application of MPQ-learning to some benchmark problems. The algorithm solves successfully these problems, so showing the feasibility of this approach. We also compare MPQ-learning to a standard linearization procedure that computes only supported solutions and show that in some cases MPQ-learning can be as effective as the scalarization method.
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