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

arXiv: https://arxiv.org/abs/2509.00333 · HTML: https://mlsanity.com/paper/2509.00333/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 30 Aug 2025.

## Builds on (most cited first, 2 of 2)

- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Unbiased Learning-to-Rank with Biased Feedback](https://mlsanity.com/paper/1608.04468/) (2016)

## Abstract (arXiv)

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.