Optimisation under uncertainty covers a broad framework of problems at the interface of applied probability and optimisation. The main focus of work is on Markov decision processes, game theory, reinforcement learning and multi-agent systems. The underlying aim is to use a combination of models, techniques and theory from stochastic control, equilibrium selection and learning to determine behaviour that is optimal with regard to some given reward structure, for example to problems in behavioural biology. Markov decision processes describe a class of single decision-maker optimisation problems that arise when applied probability models (e.g. Markov chains) are extended to allow for action-dependent transition distributions and associated rewards. Game Theory problems are more complex in that they involve two or more decision makers (players), so the optimal action for each player will depend on the actions of other players. Here, interest focuses on Nash equilibria - strategies that are conditionally optimal in the sense that no player can do better by changing their strategy while other players stay with their current strategy. The problem is even more complicated when the transition probabilities or expected rewards are not fully known or the actions of the other players are not fully observable. Reinforcement learning algorithms use simulation based techniques to “learn” the appropriate optimal or equilibrium behaviour. More generally, multi-agent systems address problems where, for example, decision makers are essentially distributed in time or space, and each single agent has only partial information about the process. Now the objective is to find ways of collaborating that will enable the agents to reach optimal or near-optimal solutions. Current research in the group includes: Decentralised control and optimisation, Nonstandard problems and algorithms for fluctuating environments, Convergence of reinforcement learning algorithms for game theory, Applications in behavioural biology and the optimal control of queues.