By Carlos Pérez Octavio Mendoza, Frédéric Godin
Estimating extreme risk in reinforcement learning becomes increasingly difficult as the confidence level increases, since only a small number of observations contribute to empirical estimates of Conditional Value-at-Risk (CVaR). In this paper, we extend an Extreme Value Theory (EVT) approach for CVaR optimization to high-dimensional neural-network policies. Using a peaks-over-threshold representation and method-of-moments estimation, we obtain a differentiable tail-risk objective and show that, conditional on the selected threshold, its finite-sample gradient can be computed directly through automatic differentiation. We first validate the approach in a controlled experiment with a known optimal solution and then investigate its performance in a deep-hedging problem with rare extreme market movements. Our results show similar hedging behavior for EVT- and empirical-CVaR-trained policies under normal conditions, while EVT-trained policies exhibit lower hedging losses under the extreme-scenario evaluation across the training sample sizes considered. These results suggest that EVT can provide a practical alternative for training neural policies when the observations relevant to extreme risk are scarce.
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