Bias-Variance Trade-off and Overlearning in Dynamic Decision Problems

Modern Monte Carlo-type approaches to dynamic decision problems face the classical bias-variance trade-off. Deep neural networks can overlearn the data and construct feedback actions which are non-adapted to the information flow and hence, become susceptible to generalization error. We prove asymptotic overlearning for fixed training sets, but also provide a non-asymptotic upper bound on overperformance based on the Rademacher complexity demonstrating the convergence of these algorithms for sufficiently large training sets. Numerically studied stylized examples illustrate these possibilities, the dependence on the dimension and the effectiveness of this approach.