Low-variance estimation in the Plackett-Luce model via quasi-Monte Carlo sampling
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Alexander Buchholz, Jan Malte Lichtenberg, Giuseppe Di Benedetto, Yannik Stein, Vito Bellini, Matteo Ruffini
2022
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.
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