Computationally Efficient Optimization of Plackett-Luce Ranking Models for Relevance and Fairness

TL;DR

This paper introduces PL-Rank, a novel algorithm that efficiently estimates gradients for Plackett-Luce ranking models, improving relevance and fairness optimization with faster convergence and lower computational costs.

Contribution

The paper presents PL-Rank, a new gradient estimation method leveraging PL model structure, enhancing efficiency over policy gradient approaches for ranking optimization.

Findings

PL-Rank outperforms existing methods in sample-efficiency.

PL-Rank achieves faster convergence in experiments.

The approach enables practical application of PL models for fairness and relevance.

Abstract

Recent work has proposed stochastic Plackett-Luce (PL) ranking models as a robust choice for optimizing relevance and fairness metrics. Unlike their deterministic counterparts that require heuristic optimization algorithms, PL models are fully differentiable. Theoretically, they can be used to optimize ranking metrics via stochastic gradient descent. However, in practice, the computation of the gradient is infeasible because it requires one to iterate over all possible permutations of items. Consequently, actual applications rely on approximating the gradient via sampling techniques. In this paper, we introduce a novel algorithm: PL-Rank, that estimates the gradient of a PL ranking model w.r.t. both relevance and fairness metrics. Unlike existing approaches that are based on policy gradients, PL-Rank makes use of the specific structure of PL models and ranking metrics. Our experimental analysis shows that PL-Rank has a greater sample-efficiency and is computationally less costly than existing policy gradients, resulting in faster convergence at higher performance. PL-Rank further enables the industry to apply PL models for more relevant and fairer real-world ranking systems.