Expected Scalarised Returns Dominance: A New Solution Concept for Multi-Objective Decision Making

• URL: http://arxiv.org/abs/2106.01048v1
• Date: Wed, 2 Jun 2021 09:42:42 GMT
• Title: Expected Scalarised Returns Dominance: A New Solution Concept for Multi-Objective Decision Making
• Authors: Conor F. Hayes, Timothy Verstraeten, Diederik M. Roijers, Enda Howley, Patrick Mannion
• Abstract summary: In many real-world scenarios, the utility of a user is derived from the single execution of a policy. To apply multi-objective reinforcement learning, the expected utility of the returns must be optimised. We propose first-order dominance as a criterion to build solution sets to maximise expected utility. We then define a new solution concept called the ESR set, which is a set of policies that are ESR dominant.
• Score: 4.117597517886004
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In many real-world scenarios, the utility of a user is derived from the single execution of a policy. In this case, to apply multi-objective reinforcement learning, the expected utility of the returns must be optimised. Various scenarios exist where a user's preferences over objectives (also known as the utility function) are unknown or difficult to specify. In such scenarios, a set of optimal policies must be learned. However, settings where the expected utility must be maximised have been largely overlooked by the multi-objective reinforcement learning community and, as a consequence, a set of optimal solutions has yet to be defined. In this paper we address this challenge by proposing first-order stochastic dominance as a criterion to build solution sets to maximise expected utility. We also propose a new dominance criterion, known as expected scalarised returns (ESR) dominance, that extends first-order stochastic dominance to allow a set of optimal policies to be learned in practice. We then define a new solution concept called the ESR set, which is a set of policies that are ESR dominant. Finally, we define a new multi-objective distributional tabular reinforcement learning (MOT-DRL) algorithm to learn the ESR set in a multi-objective multi-armed bandit setting.

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