# Counterfactual Risk Minimization with IPS-Weighted BPR and Self-Normalized Evaluation in Recommender Systems

## TL;DR

This paper introduces a robust IPS-weighted training pipeline with a Bayesian Personalized Ranking objective and Propensity Regularizer, improving stability and accuracy in recommender systems learned from implicit feedback.

## Contribution

It proposes a novel combination of IPS-weighted BPR with a Propensity Regularizer to reduce variance and improve robustness in counterfactual recommendation learning.

## Key findings

- Enhanced model robustness under biased exposure.
- Reduced variance in offline policy evaluation.
- Better generalization to unbiased exposure scenarios.

## Abstract

Learning and evaluating recommender systems from logged implicit feedback is challenging due to exposure bias. While inverse propensity scoring (IPS) corrects this bias, it often suffers from high variance and instability. In this paper, we present a simple and effective pipeline that integrates IPS-weighted training with an IPS-weighted Bayesian Personalized Ranking (BPR) objective augmented by a Propensity Regularizer (PR). We compare Direct Method (DM), IPS, and Self-Normalized IPS (SNIPS) for offline policy evaluation, and demonstrate how IPS-weighted training improves model robustness under biased exposure. The proposed PR further mitigates variance amplification from extreme propensity weights, leading to more stable estimates. Experiments on synthetic and MovieLens 100K data show that our approach generalizes better under unbiased exposure while reducing evaluation variance compared to naive and standard IPS methods, offering practical guidance for counterfactual learning and evaluation in real-world recommendation settings.