Evolving Multimodal Robot Behavior via Many Stepping Stones with the Combinatorial Multi-Objective Evolutionary Algorithm

An important challenge in reinforcement learning is to solve multimodal problems, where agents have to act in qualitatively different ways depending on the circumstances. Because multimodal problems are often too difficult to solve directly, it is often helpful to define a curriculum, which is an ordered set of sub-tasks that can serve as the stepping stones for solving the overall problem. Unfortunately, choosing an effective ordering for these subtasks is difficult, and a poor ordering can reduce the performance of the learning process. Here, we provide a thorough introduction and investigation of the Combinatorial Multi-Objective Evolutionary Algorithm (CMOEA), which allows all combinations of subtasks to be explored simultaneously. We compare CMOEA against three algorithms that can similarly optimize on multiple subtasks simultaneously: NSGA-II, NSGA-III and ϵ-Lexicase Selection. The algorithms are tested on a function-optimization problem with two subtasks, a simulated multimodal robot locomotion problem with six subtasks and a simulated robot maze navigation problem where a hundred random mazes are treated as subtasks. On these problems, CMOEA either outperforms or is competitive with the controls. As a separate contribution, we show that adding a linear combination over all objectives can improve the ability of the control algorithms to solve these multimodal problems. Lastly, we show that CMOEA can leverage auxiliary objectives more effectively than the controls on the multimodal locomotion task. In general, our experiments suggest that CMOEA is a promising algorithm for solving multimodal problems.