An Analytical Study of Utility Functions in Multi-Objective Reinforcement Learning

Multi-objective reinforcement learning (MORL) is an excellent framework for multi-objective sequential decision-making. MORL employs a utility function to aggregate multiple objectives into one that expresses a user's preferences. However, MORL still misses two crucial theoretical analyses of the properties of utility functions: (1) a characterisation of the utility functions for which an associated optimal policy exists, and (2) a characterisation of the types of preferences that can be expressed as utility functions. In this paper, we contribute to both theoretical analyses. As a result, we formally characterise the families of preferences and utility functions that MORL should focus on: those for which an optimal policy is guaranteed to exist. We expect our theoretical results to foster the development of novel MORL algorithms that exploit our theoretical findings.