While a number of algorithms for multiobjective reinforcement learning have been proposed, and a small number of applications developed, there has been very little rigorous empirical evaluation of the performance and limitations of these algorithms. This paper proposes standard methods for such empirical evaluation, to act as a foundation for future comparative studies. Two classes of multiobjective reinforcement learning algorithms are identified, and appropriate evaluation metrics and methodologies are proposed for each class. A suite of benchmark problems with known Pareto fronts is described, and future extensions and implementations of this benchmark suite are discussed. The utility of the proposed evaluation methods are demonstrated via an empirical comparison of two example learning algorithms.

For reinforcement learning tasks with multiple objectives, it may be advantageous to learn stochastic or non-stationary policies. This paper investigates two novel algorithms for learning non-stationary policies which produce Pareto-optimal behaviour (w-steering and Q-steering), by extending prior work based on the concept of geometric steering. Empirical results demonstrate that both new algorithms offer substantial performance improvements over stationary deterministic policies, while Q-steering significantly outperforms w-steering when the agent has no information about recurrent states within the environment. It is further demonstrated that Q-steering can be used interactively by providing a human decision-maker with a visualisation of the Pareto front and allowing them to adjust the agent's target point during learning. To demonstrate broader applicability, the use of Q-steering in combination with function approximation is also illustrated on a task involving control of local battery storage for a residential solar power system.

In this paper we provide empirical data of the performance of the two most commonly used multiobjective reinforcement learning algorithms against a set of benchmarks. First, we describe a methodology that was used in this paper. Then, we carefully describe the details and properties of the proposed problems and how those properties influence the behavior of tested algorithms. We also introduce a testing framework that will significantly improve future empirical comparisons of multiobjective reinforcement learning algorithms. We hope this testing environment eventually becomes a central repository of test problems and algorithms The empirical results clearly identify features of the test problems which impact on the performance of each algorithm, demonstrating the utility of empirical testing of algorithms on problems with known characteristics.

No abstract