  We use a deep neural network to generate controllers for optimal trading on
high frequency data. For the first time, a neural network learns the mapping
between the preferences of the trader, i.e. risk aversion parameters, and the
optimal controls. An important challenge in learning this mapping is that in
intraday trading, trader's actions influence price dynamics in closed loop via
the market impact. The exploration--exploitation tradeoff generated by the
efficient execution is addressed by tuning the trader's preferences to ensure
long enough trajectories are produced during the learning phase. The issue of
scarcity of financial data is solved by transfer learning: the neural network
is first trained on trajectories generated thanks to a Monte-Carlo scheme,
leading to a good initialization before training on historical trajectories.
Moreover, to answer to genuine requests of financial regulators on the
explainability of machine learning generated controls, we project the obtained
"blackbox controls" on the space usually spanned by the closed-form solution of
the stylized optimal trading problem, leading to a transparent structure. For
more realistic loss functions that have no closed-form solution, we show that
the average distance between the generated controls and their explainable
version remains small. This opens the door to the acceptance of ML-generated
controls by financial regulators.
