Shrinkage estimation with reinforcement learning of large variance matrices for portfolio selection

A large amount of assets characterizes high-dimensional portfolio selection problems compared to temporal observation. In such a high-dimensional framework, the asset allocation is unfeasible because the covariance matrix obtained with the usual sample estimators cannot be inverted. This paper proposes a new shrinkage estimator based on reinforcement learning for large covariance matrices that is optimal in the context of portfolio selection. The resulting estimator is entirely data-driven since the optimal shrinkage intensity is given by optimizing neural network weights. This paper presents two different architectures: a standard fully connected network for a classical Policy Gradient Agent (PGA) and a Gated Recurrent Unit for a Recurrent Policy Gradient Agent (RPGA). To show the validity of the proposal, an application to asset allocation with Industry portfolios is provided. The results indicate that the RPGA-based approach in shrinkage estimation provides the best performance in out-of-sample comparison.