Actor-critic multi-objective reinforcement learning for non-linear utility functions

We propose a novel multi-objective reinforcement learning algorithm that successfully learns the optimal policy even for non-linear utility functions. Non-linear utility functions pose a challenge for SOTA approaches, both in terms of learning efficiency as well as the solution concept. A key insight is that, by proposing a critic that learns a multi-variate distribution over the returns, which is then combined with accumulated rewards, we can directly optimize on the utility function, even if it is non-linear. This allows us to vastly increase the range of problems that can be solved compared to those which can be handled by single-objective methods or multi-objective methods requiring linear utility functions, yet avoiding the need to learn the full Pareto front. We demonstrate our method on multiple multi-objective benchmarks, and show that it learns effectively where baseline approaches fail.