Decision and Control with Uncertainty: What Problems Should We Aim to Solve?
There are four basic types of activity involving combinations of uncertainty and optimisation:
- Uncertainty propagation where the problem is to predict the behaviour of an uncertain system, where the uncertainty is in the initial state of the system or factors, such as properties, influencing the system evolution.
- Data assimilation, also known as ‘history matching’, ‘system identification’ or inverse problems.
- Decision making. Here a choice must be made between competing courses of action. For each choice of action the outcome is uncertain.
- Optimal control of an uncertain system. A system is only known in a probabilistic way. One has to design a control policy that optimises the system. The problem is particularly difficult when optimisation of the measurement system is included in the problem.
These problems are closely related to one another. However, the subject of decision theory is perhaps the most fundamental and well developed theory as it has a firm axiomatic basis and an extensive literature. In this talk we will examine the formulation of the problems and then discuss the matter of how close we are to solving any of these problems in a satisfactory way. The main points that will be defended are (i) we should always optimise our expected utility and (ii) sequential formulations are the most fruitful for practical progress.
Chris Farmer, University of Oxford, United Kingdom