Learning Dynamic Utility

We consider the problem of reconstructing an agent's dynamic utility random field from observed decisions at discrete, possibly random, times. This inverse revealed-utility problem originates from Samuelson's revealed preference theory and is revisited here within the framework of forward dynamic utilities introduced by Musiela and Zariphopoulou and extended by El Karoui and Mrad. We propose a constructive learning-based methodology for recovering a time-consistent utility random field. The approach relies on the characterization of the utility through its marginal utility process and the associated adjoint dynamics, which yields an explicit representation of the revealed utility. The numerical study is structured into two learning regimes. First, for fixed ω, the problem reduces to the approximation of a deterministic function on a finite-dimensional domain. In this setting, we compare classical supervised learning methods, Support Vector Regression (SVR) and ν-SVR, with a multilayer perceptron (MLP). Second, we address the fully parametric problem by learning the nonlinear operator mapping ω to the utility field. We then compare three neural network architectures with distinct inductive biases to assess their ability to approximate the underlying solution operator. The results show that neural-network-based approaches substantially outperform kernel-based methods, and that operator-oriented architectures provide the most accurate and robust approximations. This work illustrates the effectiveness of combining stochastic control theory with modern learning techniques for solving inverse problems in dynamic preference modeling.