Primary Submission Category: Policy Learning
Policy Learning through Cooperative Bargaining
Authors: Eli Ben-Michael,
Presenting Author: Eli Ben-Michael*
Algorithmic decision making is increasing in importance in high stakes settings. Classical methods for data driven decision making and individualized treatment rules take a utilitarian, top down approach; if one decision leads to a higher expected utility than all others, then that decision is optimal. Under this approach if few individuals benefit greatly, that can outweigh many individuals being slightly harmed. In this paper, we consider learning policies with a bottom up approach, using ideas from public choice theory. We learn policies using an objective that finds a Nash equilibrium, meaning that any departure from the policy would lead to a worse outcome for some individuals. We show that the solution is a randomized policy that assigns an action according to the proportion of individuals that benefit from that action, irrespective of the scale of the benefit. For binary decisions, the objective results in a logistic loss function for a model that predicts wether or not individual treatment effects are positive. However, individual treatment effects are not identifiable and so it is not possible to estimate such policies even with unlimited data. To address this, we partially identify the objective function and derive the maximin and minimax optimal policies, and show how to estimate such policies empirically with data using flexible models for the treatment effect. We characterize the properties of such policies and demonstrate this approach via applications