  In this paper, we consider the problem of finding a meta-learning online
control algorithm that can learn across the tasks when faced with a sequence of
$N$ (similar) control tasks. Each task involves controlling a linear dynamical
system for a finite horizon of $T$ time steps. The cost function and system
noise at each time step are adversarial and unknown to the controller before
taking the control action. Meta-learning is a broad approach where the goal is
to prescribe an online policy for any new unseen task exploiting the
information from other tasks and the similarity between the tasks. We propose a
meta-learning online control algorithm for the control setting and characterize
its performance by \textit{meta-regret}, the average cumulative regret across
the tasks. We show that when the number of tasks are sufficiently large, our
proposed approach achieves a meta-regret that is smaller by a factor $D/D^{*}$
compared to an independent-learning online control algorithm which does not
perform learning across the tasks, where $D$ is a problem constant and $D^{*}$
is a scalar that decreases with increase in the similarity between tasks. Thus,
when the sequence of tasks are similar the regret of the proposed meta-learning
online control is significantly lower than that of the naive approaches without
meta-learning. We also present experiment results to demonstrate the superior
performance achieved by our meta-learning algorithm.
