  We present a reinforcement learning (RL) approach for robust optimisation of
risk-aware performance criteria. To allow agents to express a wide variety of
risk-reward profiles, we assess the value of a policy using rank dependent
expected utility (RDEU). RDEU allows the agent to seek gains, while
simultaneously protecting themselves against downside risk. To robustify
optimal policies against model uncertainty, we assess a policy not by its
distribution, but rather, by the worst possible distribution that lies within a
Wasserstein ball around it. Thus, our problem formulation may be viewed as an
actor/agent choosing a policy (the outer problem), and the adversary then
acting to worsen the performance of that strategy (the inner problem). We
develop explicit policy gradient formulae for the inner and outer problems, and
show its efficacy on three prototypical financial problems: robust portfolio
allocation, optimising a benchmark, and statistical arbitrage.
