  We study the problem of adaptive control in partially observable linear
quadratic Gaussian control systems, where the model dynamics are unknown a
priori. We propose LqgOpt, a novel reinforcement learning algorithm based on
the principle of optimism in the face of uncertainty, to effectively minimize
the overall control cost. We employ the predictor state evolution
representation of the system dynamics and deploy a recently proposed
closed-loop system identification method, estimation, and confidence bound
construction. LqgOpt efficiently explores the system dynamics, estimates the
model parameters up to their confidence interval, and deploys the controller of
the most optimistic model for further exploration and exploitation. We provide
stability guarantees for LqgOpt and prove the regret upper bound of
$\tilde{\mathcal{O}}(\sqrt{T})$ for adaptive control of linear quadratic
Gaussian (LQG) systems, where $T$ is the time horizon of the problem.
