Gradient-Based Nonlinear Rehearsal Learning with Multivariate Alterations

Machine learning (ML) has made significant advancements across various domains, with a shifting focus from purely predictive tasks to decision-making. The recent proposal by Zhou (2022) introduced a line of research known as rehearsal learning, which provides a novel perspective on modeling decision-making tasks. However, previous studies mainly focused on the linear Gaussian setting to constrain the modeling complexity. Furthermore, it has been demonstrated that finding exact optimal multivariate decisions within the sampling-based rehearsal framework is computationally infeasible in polynomial time, necessitating the development of approximate methods. In this work, we present Grad-Rh, the first gradient-based rehearsal learning method that can efficiently find multivariate decisions under non-linear and non-Gaussian settings. We address the uncertainty in decision-making tasks using flexible and expressive conditional normalizing flow models and derive four surrogate loss functions to enable efficient gradient-based optimization. Experimental results show that Grad-Rh performs comparably to exact baselines on linear data and significantly outperforms them on non-linear data in both decision quality and running time.