Beyond Exposure: Optimizing Ranking Fairness with Non-linear Time-Income Functions

TL;DR

The paper tackles ranking fairness in settings where provider income is a nonlinear function of exposure and context, notably time. It formalizes Income Fairness, introduces a time-aware income function, and proposes DIDRF, a dynamic, derivative-aware ranking method that uses a Taylor-expanded marginal objective to jointly optimize effectiveness and income fairness. DIDRF operates in offline and online modes, leveraging a first-order term for effectiveness and second-order terms for fairness, with online relevance uncertainty handled via an uncertainty penalty. Across simulated offline and online experiments on public datasets, DIDRF consistently improves income fairness while maintaining high user-facing ranking performance, and does so with practical time complexity. The work provides a principled, scalable framework for time-aware, fairness-aware ranking in real-world IR systems, with clear avenues for broader empirical validation and extensions to other contextual factors beyond time.

Abstract

Ranking is central to information distribution in web search and recommendation. Nowadays, in ranking optimization, the fairness to item providers is viewed as a crucial factor alongside ranking relevance for users. There are currently numerous concepts of fairness and one widely recognized fairness concept is Exposure Fairness. However, it relies primarily on exposure determined solely by position, overlooking other factors that significantly influence income, such as time. To address this limitation, we propose to study ranking fairness when the provider utility is influenced by other contextual factors and is neither equal to nor proportional to item exposure. We give a formal definition of Income Fairness and develop a corresponding measurement metric. Simulated experiments show that existing-exposure-fairness-based ranking algorithms fail to optimize the proposed income fairness. Therefore, we propose the Dynamic-Income-Derivative-aware Ranking Fairness algorithm, which, based on the marginal income gain at the present timestep, uses Taylor-expansion-based gradients to simultaneously optimize effectiveness and income fairness. In both offline and online settings with diverse time-income functions, DIDRF consistently outperforms state-of-the-art methods.

Figures (3)

• Figure 1: $cNDCG_{avg}@5$ vs. unfairness in the offline setting. Given the same unfairness, the higher curves or points lie, the better their performances are.
• Figure 2: $cNDCG_{avg}@5$ vs. unfairness in the offline setting with the income function equal to 1. Given the same unfairness, the higher curves or points lie, the better their performances are.
• Figure 3: $cNDCG_{avg}@5$ vs. unfairness in the online setting. Given the same unfairness, the higher curves or points lie, the better their performances are.

Theorems & Definitions (2)

• definition 1: Income Fairness
• definition 2: Amortized Income Fairness