  Self-tuning optical systems are of growing importance in technological
applications such as mode-locked fiber lasers. Such self-tuning paradigms
require {\em intelligent} algorithms capable of inferring approximate models of
the underlying physics and discovering appropriate control laws in order to
maintain robust performance for a given objective. In this work, we demonstrate
the first integration of a {\em deep learning} (DL) architecture with {\em
model predictive control} (MPC) in order to self-tune a mode-locked fiber
laser. Not only can our DL-MPC algorithmic architecture approximate the unknown
fiber birefringence, it also builds a dynamical model of the laser and
appropriate control law for maintaining robust, high-energy pulses despite a
stochastically drifting birefringence. We demonstrate the effectiveness of this
method on a fiber laser which is mode-locked by nonlinear polarization
rotation. The method advocated can be broadly applied to a variety of optical
systems that require robust controllers.
