Policy Learning under an Inequality Constraint

Yue Fang is an assistant professor at Chinese University of Hong Kong, Shenzhen. She graduated from University of Southern California this year. Her areas of interest include causal inference, machine learning, and policy learning.

In this paper, I consider the setting of maximizing mean income while maintaining a satisfactory equality level. The objective function is the mean income function, and the constraint is the inequality measure. I formulate the problem as a constrained optimization problem and try to solve the empirical problem with the information collected from the experiment. I first assume that the global optimum of the empirical problem could be found, and show the theoretical properties of the empirical solution, with regard to the population welfare and population inequality level when applying the empirical solution to the population. I also discuss how to use an enumeration method to find the global optimum to the empirical problem. I also use the data from the National Supported Work Demonstration to illustrate the performance of the proposed method.