Stochastic Optimisation

Stochastic optimisation encompasses many diverse areas including control theory, reinforcement learning, multiarmed bandit problems, simulation optimisation, and neural networks. Stochastic optimisation can be succinctly described as sequential decision making under uncertainty. In a sequential decision problem, the system being modelled progresses through a finite or infinite number of stages. At each stage, the system is in a particular state taken from a discrete or continuous state space, and decision (action) is taken which may depend on the stage and/or state. The aim is to design a set of decisions or actions (a policy) at each stage, so that an objective function is optimised. Randomness is incorporated into the problem by exogeneous information that is only realised once a decision is made at each stage. Topics include Markov decision processes, approximate dynamic programming, reinforcement learning, simulation optimisation, and robust optimisation. This subject provides a rigorous mathematical treatment of stochastic optimisation, and will include applications selected from logistics, finance, transportation, health, resource allocation, e-commerce, and supply chain management.