Online-information-based learning and decision making under uncertainty

In this work, we utilize information-based learning tools for learning in unknown and complex systems. Two problems are considered. First, we study the problem of stabilizing an unknown plant using switching supervisory control. We formulate the problem as an online decision problem and use "calibrated forecasts" as a mechanism for controller selection in supervisory control. The forecasted event is whether or not a controller will be effective over a finite implementation horizon. Controller selection is based on using the controller with the maximum calibrated forecast of the reward. Assuming the existence of a stabilizing controller within the set of candidate controllers, we show that with the proposed supervisory controller, the output of the system remains bounded for any bounded disturbance, even if the disturbance is chosen in an adversarial manner. Moreover, we show that the proposed formulation provides stability guarantees even when the reward received is corrupted with (possibly infinite) zero-mean finite-variance noise. The main results are obtained for a general class of system dynamics and specialized to linear systems.;Second, we propose an approach for systematic testing and learning in complex biological systems. The approach combines the use of a stochastic search algorithm and biological experiments to identify and study desired biological behaviors using external stimuli. As an example illustrating the validity of the proposed approach, we utilize the approach to study the effects of multiple drugs on the lytic-cycle induction of Kaposi's sarcoma-associated herpesvirus (KSHV). An alternate approach is also proposed where a relatively small set of sample data is experimentally evaluated and the results are used to construct a function map approximation of the input-output behavior of the biological system. To validate the alternate approach, we apply it to the same problem of KSHV reactivation. The results for the two proposed approaches indicate that they present a potential tool for systematic studying of the induced functions of complex biological systems by multiple external stimuli and for studying and developing drug therapies for several diseases.