Stochastic Control and Optimal Learning

In classical stochastic control theory, a known model for the random noise in a system is given.

In many applications, however, the controller has only access to incomplete information; for example uncertainy about the model parameters, which leads to problems of simultaneous statistical inference and optimization,or strategic problems with asymmetric information.

A common feature then is that the optimizer needs to learn about the general conditions of the system (model parameters, competitors, et cetera) at the same time as optimization is performed.

The current project deals with stochastic control under incomplete information, in which the learning rate is controlled.

More specifically, we consider problems where the choice of control directly affects the learning rate, thus leading to problems of balancing exploration against exploitation.

The problem formulation is inspired by  applications in statistical problems of sequential analysis (where a controlled learning rate corresponds to the speed with which an experiment is run), in financial problems of learning-by-doing (where a higher degree of investment in a certain project gives more information about its profitability), in stochastic games with asymmetric information (the learning rate of one player is controlled by the other player), and in the study of sorting algorithms and optimal tournaments (where the choice of what matches to play corresponds to a choice of the learning rate).