Policy Invariance under Reward Transformations for Multi-Objective Reinforcement Learning

Patrick Mannion, Sam Devlin, Karl Mason, Jim Duggan, Enda Howley

Research output: Contribution to journalArticlepeer-review


Reinforcement Learning (RL) is a powerful and well-studied Machine Learning paradigm, where an agent learns to improve its performance in an environment by maximising a reward signal. In multi-objective Reinforcement Learning (MORL) the reward signal is a vector, where each component represents the performance on a different objective. Reward shaping is a well-established family of techniques that have been successfully used to improve the performance and learning speed of RL agents in single-objective problems. The basic premise of reward shaping is to add an additional shaping reward to the reward naturally received from the environment, to incorporate domain knowledge and guide an agent’s exploration. Potential-Based Reward Shaping (PBRS) is a specific form of reward shaping that offers additional guarantees. In this paper, we extend the theoretical guarantees of PBRS to MORL problems. Specifically, we provide theoretical proof that PBRS does not alter the true Pareto front in both single- and multi-agent MORL. We also contribute the first published empirical studies of the effect of PBRS in single- and multi-agent MORL problems.
Original languageEnglish
Article number263
Pages (from-to)60-73
Number of pages14
Early online date16 Jun 2017
Publication statusPublished - 8 Nov 2017

Bibliographical note

© 2017 Elsevier B.V. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.


  • Reinforcement Learning
  • Multi-Objective
  • Reward Shaping

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