  Deep reinforcement learning (RL) is a data-driven, model-free method capable
of discovering complex control strategies for macroscopic objectives in
high-dimensional systems, making its application towards flow control
promising. Many systems of flow control interest possess symmetries that, when
neglected, can significantly inhibit the learning and performance of a naive
deep RL approach. Using a test-bed consisting of the Kuramoto-Sivashinsky
Equation (KSE), equally spaced actuators, and a goal of minimizing dissipation
and power cost, we demonstrate that by moving the deep RL problem to a
symmetry-reduced space, we can alleviate limitations inherent in the naive
application of deep RL. We demonstrate that symmetry-reduced deep RL yields
improved data efficiency as well as improved control policy efficacy compared
to policies found by naive deep RL. Interestingly, the policy learned by the
the symmetry aware control agent drives the system toward an equilibrium state
of the forced KSE that is connected by continuation to an equilibrium of the
unforced KSE, despite having been given no explicit information regarding its
existence. I.e., to achieve its goal, the RL algorithm discovers and stabilizes
an equilibrium state of the system. Finally, we demonstrate that the
symmetry-reduced control policy is robust to observation and actuation signal
noise, as well as to system parameters it has not observed before.
