  Existing methods for optimal control struggle to deal with the complexity
commonly encountered in real-world systems, including dimensionality, process
error, model bias and data heterogeneity. Instead of tackling these system
complexities directly, researchers have typically sought to simplify models to
fit optimal control methods. But when is the optimal solution to an
approximate, stylized model better than an approximate solution to a more
accurate model? While this question has largely gone unanswered owing to the
difficulty of finding even approximate solutions for complex models, recent
algorithmic and computational advances in deep reinforcement learning (DRL)
might finally allow us to address these questions. DRL methods have to date
been applied primarily in the context of games or robotic mechanics, which
operate under precisely known rules. Here, we demonstrate the ability for DRL
algorithms using deep neural networks to successfully approximate solutions
(the "policy function" or control rule) in a non-linear three-variable model
for a fishery without knowing or ever attempting to infer a model for the
process itself. We find that the reinforcement learning agent discovers an
effective simplification of the problem to obtain an interpretable control
rule. We show that the policy obtained with DRL is both more profitable and
more sustainable than any constant mortality policy -- the standard family of
policies considered in fishery management.
