# Distributionally Robust Counterfactual Risk Minimization

## TL;DR

This paper proposes a distributionally robust optimization framework for counterfactual risk minimization, unifying existing methods and introducing new divergence-based estimators that improve performance on benchmark datasets.

## Contribution

It introduces a DRO-based framework for CRM, showing existing methods as special cases and proposing a new KL divergence-based estimator that outperforms state-of-the-art methods.

## Key findings

- The KL divergence-based estimator outperforms existing methods on benchmarks.
- Existing CRM solutions are special cases of the DRO framework.
- Using different probability divergences can improve counterfactual risk estimation.

## Abstract

This manuscript introduces the idea of using Distributionally Robust Optimization (DRO) for the Counterfactual Risk Minimization (CRM) problem. Tapping into a rich existing literature, we show that DRO is a principled tool for counterfactual decision making. We also show that well-established solutions to the CRM problem like sample variance penalization schemes are special instances of a more general DRO problem. In this unifying framework, a variety of distributionally robust counterfactual risk estimators can be constructed using various probability distances and divergences as uncertainty measures. We propose the use of Kullback-Leibler divergence as an alternative way to model uncertainty in CRM and derive a new robust counterfactual objective. In our experiments, we show that this approach outperforms the state-of-the-art on four benchmark datasets, validating the relevance of using other uncertainty measures in practical applications.