  Learning to make decisions from observed data in dynamic environments remains
a problem of fundamental importance in a number of fields, from artificial
intelligence and robotics, to medicine and finance. This paper concerns the
problem of learning control policies for unknown linear dynamical systems so as
to maximize a quadratic reward function. We present a method to optimize the
expected value of the reward over the posterior distribution of the unknown
system parameters, given data. The algorithm involves sequential convex
programing, and enjoys reliable local convergence and robust stability
guarantees. Numerical simulations and stabilization of a real-world inverted
pendulum are used to demonstrate the approach, with strong performance and
robustness properties observed in both.
