  We investigate the adaptive robust control framework for portfolio
optimization and loss-based hedging under drift and volatility uncertainty.
Adaptive robust problems offer many advantages but require handling a double
optimization problem (infimum over market measures, supremum over the control)
at each instance. Moreover, the underlying Bellman equations are intrinsically
multi-dimensional. We propose a novel machine learning approach that solves for
the local saddle-point at a chosen set of inputs and then uses a nonparametric
(Gaussian process) regression to obtain a functional representation of the
value function. Our algorithm resembles control randomization and regression
Monte Carlo techniques but also brings multiple innovations, including adaptive
experimental design, separate surrogates for optimal control and the local
worst-case measure, and computational speed-ups for the sup-inf optimization.
Thanks to the new scheme we are able to consider settings that have been
previously computationally intractable and provide several new financial
insights about learning and optimal trading under unknown market parameters. In
particular, we demonstrate the financial advantages of adaptive robust
framework compared to adaptive and static robust alternatives.
