Using Machine Learning to compute constrained Pareto optimal carbon tax rules in a stochastic OLG model

Abstract

We present a computational framework for deriving constrained Pareto optimal carbon tax rules within a stochastic overlapping generations (OLG) model. By integrating deep reinforcement learning, Deep Equilibrium Networks for fast policy evaluation, and Gaussian Process surrogate modelling with Bayesian active learning, the framework systematically locates optimal carbon tax schedules for heterogeneous agents exposed to climate risk. The economic environment is a 12 period OLG model in which exogenous shocks perturb emissions, the carbon–temperature link, and climate damage functions, generating asymmetric risks—including rare climate disasters. Constrained Pareto efficiency is pursued by jointly designing tax and revenue sharing rules that raise welfare despite market imperfections. A single surrogate model evaluation constructs the complete constrained Pareto frontier, uncovering non trivial trade offs between intergenerational welfare and carbon taxation. Optimal taxes substantially reduce climate risk and improve welfare across cohorts, demonstrating that the proposed approach yields scalable, high precision tools for macro policy design in complex stochastic settings. Beyond climate economics, the framework offers a versatile template for analysing heterogeneous agent problems in which reinforcement learning and surrogate modelling can accelerate the search for welfare improving policies.