Low-variance estimation in the Plackett-Luce model via quasi-Monte Carlo sampling

TL;DR

This paper introduces a quasi-Monte Carlo sampling method combined with the Gumbel top-k trick to produce low-variance estimators for expectations in the Plackett-Luce model, improving efficiency in ranking tasks.

Contribution

The paper proposes a novel low-variance estimation technique for the Plackett-Luce model by integrating QMC sampling with the Gumbel top-k trick, enhancing sampling efficiency.

Findings

QMC-Gumbel method reduces estimator variance.

Empirical results show improved ranking evaluation accuracy.

Method demonstrates efficiency on real-world recommendation data.

Abstract

The Plackett-Luce (PL) model is ubiquitous in learning-to-rank (LTR) because it provides a useful and intuitive probabilistic model for sampling ranked lists. Counterfactual offline evaluation and optimization of ranking metrics are pivotal for using LTR methods in production. When adopting the PL model as a ranking policy, both tasks require the computation of expectations with respect to the model. These are usually approximated via Monte-Carlo (MC) sampling, since the combinatorial scaling in the number of items to be ranked makes their analytical computation intractable. Despite recent advances in improving the computational efficiency of the sampling process via the Gumbel top-k trick, the MC estimates can suffer from high variance. We develop a novel approach to producing more sample-efficient estimators of expectations in the PL model by combining the Gumbel top-k trick with quasi-Monte Carlo (QMC) sampling, a well-established technique for variance reduction. We illustrate our findings both theoretically and empirically using real-world recommendation data from Amazon Music and the Yahoo learning-to-rank challenge.