Solving Complex Optimisation Problems by Machine Learning

Most optimisation research focuses on relatively simple cases: one decision maker, one objective, and possibly a set of constraints. However, real-world optimisation problems often come with complications: they might be multi-objective, multi-agent, multi-stage or multi-level, and they might have uncertainty, partial knowledge or nonlinear objectives. Each has led to research areas with dedicated solution methods. However, when new hybrid problems are encountered, there is typically no solver available. We define a broad class of discrete optimisation problem called an influence program, and describe a lightweight algorithm based on multi-agent multi-objective reinforcement learning with sampling. We show that it can be used to solve problems from a wide range of literatures: constraint programming, Bayesian networks, stochastic programming, influence diagrams (standard, limited memory and multi-objective), and game theory (multi-level programming, Bayesian games and level-k reasoning). We expect it to be useful for the rapid prototyping of solution methods for new hybrid problems.