Interpolating Item and User Fairness in Multi-Sided Recommendations

TL;DR

This work addresses fairness across multiple stakeholders in online recommendations by formulating Problem (fair) as a constrained optimization that integrates item and user fairness with platform revenue. It introduces FORM, a low‑regret online algorithm that relaxes fairness constraints, explores decisions, and incrementally learns user and arrival statistics under bandit feedback. Theoretical results show sublinear revenue and fairness regrets, aided by local Lipschitzness assumptions and concentration bounds, while a real‑world Amazon case study demonstrates the method’s ability to balance fairness with revenue and quantify the price of fairness. Overall, the framework provides a flexible, tunable approach to achieving cross‑stakeholder fairness in dynamic online ecosystems with practical implications for platforms seeking sustainable, fair operation.

Abstract

Today's online platforms heavily lean on algorithmic recommendations for bolstering user engagement and driving revenue. However, these recommendations can impact multiple stakeholders simultaneously -- the platform, items (sellers), and users (customers) -- each with their unique objectives, making it difficult to find the right middle ground that accommodates all stakeholders. To address this, we introduce a novel fair recommendation framework, Problem (FAIR), that flexibly balances multi-stakeholder interests via a constrained optimization formulation. We next explore Problem (FAIR) in a dynamic online setting where data uncertainty further adds complexity, and propose a low-regret algorithm FORM that concurrently performs real-time learning and fair recommendations, two tasks that are often at odds. Via both theoretical analysis and a numerical case study on real-world data, we demonstrate the efficacy of our framework and method in maintaining platform revenue while ensuring desired levels of fairness for both items and users.

Figures (5)

• Figure 1: Experiment results for Amazon review data. $\textsc{fair-rev}(\delta^\texttt{I}, \delta^\texttt{U})$ is the platform’s revenue from solving Problem \ref{['eq:fair']} in hindsight with fairness parameters $\delta^{\texttt{I}}, \delta^{\texttt{U}}$ and $\texttt{FORM}\xspace(\delta^{\texttt{I}}, \delta^{\texttt{U}})$ is FORM when adopting fairness parameters $\delta^{\texttt{I}}, \delta^{\texttt{U}}$. In Figures \ref{['subfig:amazon-item']} and \ref{['subfig:amazon-user']}, item (user) outcomes are shown in ascending order. All results are averaged over $10$ simulations, with the line indicating the mean and shaded region showing mean $\pm$ std/$\sqrt{10}$.
• Figure 2: Price of Fairness (PoF) in our case study on the Amazon review data. Left: PoF when solving Problem \ref{['eq:fair-assort']} under different fairness parameters $(\delta^\texttt{I}, \delta^\texttt{U})$. The grid is colored black if the problem is infeasible. Upper-right: PoF when $\delta^\texttt{U} = 0$. Lower-right: PoF when $\delta^\texttt{I} = 0$.
• Figure 3: Additional experiment results for Amazon review data. Here, the item-fair solution adopts maxmin fairness w.r.t. item visibility.
• Figure 4: Additional experiment results for Amazon review data. Here, the item-fair solution adopts K-S fairness w.r.t. item revenue.
• Figure 5: Additional experiment results for Amazon review data. Here, the item-fair solution adopts K-S fairness w.r.t. item visibility.

Theorems & Definitions (20)

• Definition 1: Item-Fair Solution
• Definition 2: User-Fair Solution
• Proposition 1
• Remark 1: Constrained optimization versus fairness regularizers
• Remark 2: Price of Fairness
• Definition 3: Revenue and fairness regrets
• Theorem 1: Performance of FORM
• Example 1: A single-sided solution can be extremely unfair to the other sides.
• Definition 4: Price of Fairness
• Theorem 2