Limits to learning in reinforcement learning hyper-heuristics

Learning mechanisms in selection hyper-heuristics are used to identify the most appropriate subset of heuristics when solving a given problem. Several experimental studies have used additive reinforcement learning mechanisms, however, these are inconclusive with regard to the performance of selection hyper-heuristics with these learningmechanisms. This paper points out limitations to learning with additive reinforcement learning mechanisms. Our theoretical results show that if the probability of improving the candidate solution in each point of the search process is less than 1/2 which is a mild assumption, then additive reinforcement learning mechanisms perform asymptotically similar to the simple random mechanism which chooses heuristics uniformly at random. In addition, frequently used adaptation schemes can affect the memory of reinforcement learning mechanisms negatively. We also conducted experiments on two well-known combinatorial optimisation problems, bin-packing and flowshop, and the obtained results confirm the theoretical findings. This study suggests that alternatives to the additive updates in reinforcement learning mechanisms should be considered.