# COPF: An Online Framework for Deployment-Stable Counterfactual Fairness in Evolving Graphs

arXiv: https://arxiv.org/abs/2606.00700 · HTML: https://mlsanity.com/paper/2606.00700/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 43 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 26 of 26)

- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [Towards Better Evaluation for Dynamic Link Prediction](https://mlsanity.com/paper/2207.10128/) (2022)
- [How Algorithmic Confounding in Recommendation Systems Increases Homogeneity and Decreases Utility](https://mlsanity.com/paper/1710.11214/) (2017)
- [Runaway Feedback Loops in Predictive Policing](https://mlsanity.com/paper/1706.09847/) (2017)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [FairDrop: Biased Edge Dropout for Enhancing Fairness in Graph Representation Learning](https://mlsanity.com/paper/2104.14210/) (2021)
- [Counterfactual Risk Assessments, Evaluation, and Fairness](https://mlsanity.com/paper/1909.00066/) (2019)
- [Learning Fair Node Representations with Graph Counterfactual Fairness](https://mlsanity.com/paper/2201.03662/) (2022)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [CrossWalk: Fairness-enhanced Node Representation Learning](https://mlsanity.com/paper/2105.02725/) (2021)
- [Counterfactual Risk Minimization: Learning from Logged Bandit Feedback](https://mlsanity.com/paper/1502.02362/) (2015)
- [Fairness in Recommender Systems: Research Landscape and Future Directions](https://mlsanity.com/paper/2205.11127/) (2022)
- [Towards Fair Graph Neural Networks via Graph Counterfactual](https://mlsanity.com/paper/2307.04937/) (2023)
- [PageRank Bandits for Link Prediction](https://mlsanity.com/paper/2411.01410/) (2024)
- [From Fairness to Infinity: Outcome-Indistinguishable (Omni)Prediction in Evolving Graphs](https://mlsanity.com/paper/2411.17582/) (2024)
- [Fair When Trained, Unfair When Deployed: Observable Fairness Measures are Unstable in Performative Prediction Settings](https://mlsanity.com/paper/2202.05049/) (2022)
- [Link recommendations: Their impact on network structure and minorities](https://mlsanity.com/paper/2205.06048/) (2022)
- [Consistent End-to-End Estimation for Counterfactual Fairness](https://mlsanity.com/paper/2310.17687/) (2023)
- [A New Paradigm for Counterfactual Reasoning in Fairness and Recourse](https://mlsanity.com/paper/2401.13935/) (2024)
- [Recommendation Fairness in Social Networks Over Time](https://mlsanity.com/paper/2402.03450/) (2024)

## Abstract (arXiv)

Online link recommendation on evolving graphs is performative: by choosing which candidate links to show users, the system changes which links form and what feedback it later observes. Consequently, fairness estimates from logged outcomes can be misleading and may drift after deployment when the recommendation policy is updated. We introduce COPF (Counterfactual Online Performative Fairness), a decision-layer framework for deployment-stable fairness monitoring and control in online link recommendation. COPF (i) defines group-level opportunity gaps over exposure (shown vs. not shown) counterfactuals, (ii) makes them estimable by explicit exploration and by logging the probability (propensity) that each candidate is shown, and (iii) audits and controls fairness using residual outcome indistinguishability (OI) over a configurable auditor family with graph-aware doubly robust (GA-DR) estimators. We provide a noisy transfer theorem showing that Residual-OI on estimated GA-DR residuals implies bounds on exposure-counterfactual group gaps under temporal mixing and bounded local interference, and we instantiate an online multicalibration auditor together with a primal-dual controller. Experiments on two TGB streams and a controlled synthetic bipartite stream show that COPF reduces worst-case spikes in exposure-counterfactual group disparities with modest impact on ranking utility. Our code is available at https://github.com/lsnnnnnnnn/COPF.