Learning and Control for Evolutionary Processes

Evolutionary selection can be interpreted as exerting an optimal control on population trajectories over many generations. As the field of synthetic biology grows, researchers are increasingly preoccupied with effectuating artificial selection on laboratory populations. However, many systems of interest exhibit unknown, or partially unknown, stochastic dynamics. In these settings it is desirable to learn the system dynamics while applying a knowledge-dependent optimal control subject to a cost function. Here we show that studying a deterministic analog of a stochastic system highlights the tradeoff between control and learning. This perspective will allow for the development of nearly optimal Bayesian algorithms for simultaneous learning and control, with applications to experiments to synthetic biology and immuno-therapy for HIV treatment.