Many re-ranking strategies in search systems rely on stochastic ranking
policies, encoded as Doubly-Stochastic (DS) matrices, that satisfy desired
ranking constraints in expectation, e.g., Fairness of Exposure (FOE). These
strategies are generally two-stage pipelines: \emph{i)} an offline re-ranking
policy construction step and \emph{ii)} an online sampling of rankings step.
Building a re-ranking policy requires repeatedly solving a constrained
optimization problem, one for each issued query. Thus, it is necessary to
recompute the optimization procedure for any new/unseen query. Regarding
sampling, the Birkhoff-von-Neumann decomposition (BvND) is the favored approach
to draw rankings from any DS-based policy. However, the BvND is too costly to
compute online. Hence, the BvND as a sampling solution is memory-consuming as
it can grow as $\gO(N\, n^2)$ for $N$ queries and $n$ documents.
This paper offers a novel, fast, lightweight way to predict fair stochastic
re-ranking policies: Constrained Meta-Optimal Transport (CoMOT). This method
fits a neural network shared across queries like a learning-to-rank system. We
also introduce Gumbel-Matching Sampling (GumMS), an online sampling approach
from DS-based policies. Our proposed pipeline, CoMOT + GumMS, only needs to
store the parameters of a single model, and it generalizes to unseen queries.
We empirically evaluated our pipeline on the TREC 2019 and 2020 datasets under
FOE constraints. Our experiments show that CoMOT rapidly predicts fair
re-ranking policies on held-out data, with a speed-up proportional to the
average number of documents per query. It also displays fairness and ranking
performance similar to the original optimization-based policy. Furthermore, we
empirically validate the effectiveness of GumMS to approximate DS-based
policies in expectation.

本文提出了一种新的，快速，轻量级的用于预测公平随机重排序策略的方法：Constrained Meta-Optimal Transport (CoMOT) 及其在线采样方法 Gumbel-Matching Sampling (GumMS)，通过共享神经网络跨查询适配。在 TREC 2019 和 2020 数据集下，实验证明，该方法在保持公平性和排序性能不变的情况下，在不需要每个新查询重新计算优化过程的情况下，快速预测出公平的其余数据集上的重排序策略。

受限元最优输运下的重排学习

Learning to Re-rank with Constrained Meta-Optimal Transport

Fairness of exposure is a commonly used notion of fairness for ranking
systems. It is based on the idea that all items or item groups should get
exposure proportional to the merit of the item or the collective merit of the
items in the group. Often, stochastic ranking policies are used to ensure
fairness of exposure. Previous work unrealistically assumes that we can
reliably estimate the expected exposure for all items in each ranking produced
by the stochastic policy. In this work, we discuss how to approach fairness of
exposure in cases where the policy contains rankings of which, due to
inter-item dependencies, we cannot reliably estimate the exposure distribution.
In such cases, we cannot determine whether the policy can be considered fair.
Our contributions in this paper are twofold. First, we define a method called
FELIX for finding stochastic policies that avoid showing rankings with unknown
exposure distribution to the user without having to compromise user utility or
item fairness. Second, we extend the study of fairness of exposure to the top-k
setting and also assess FELIX in this setting. We find that FELIX can
significantly reduce the number of rankings with unknown exposure distribution
without a drop in user utility or fairness compared to existing fair ranking
methods, both for full-length and top-k rankings. This is an important first
step in developing fair ranking methods for cases where we have incomplete
knowledge about the user's behaviour.

本文讨论了在存在相互依赖的情况下，如何处理公正曝光问题，并提出了一种名为 FELIX 的方法来避免在不影响用户效用或商品公平性的情况下向用户展示具有未知曝光分布的排名，并扩展了公正曝光的研究到 top-k 设置中。实验表明，与现有的公正评级方法相比，FELIX 能够显著减少具有未知曝光分布的排名的数量，而不影响用户效用或公平性。