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Recent work has proposed stochastic Plackett-Luce (PL) ranking models as arobust choice for optimizing relevance and fairness metrics. Unlike theirdeterministic counterparts that require heuristic optimization algorithms, PLmodels are fully differentiable. Theoretically, they can be used to optimizeranking metrics via stochastic gradient descent. However, in practice, thecomputation of the gradient is infeasible because it requires one to iterateover all possible permutations of items. Consequently, actual applications relyon approximating the gradient via sampling techniques. In this paper, weintroduce a novel algorithm: PL-Rank, that estimates the gradient of a PLranking model w.r.t. both relevance and fairness metrics. Unlike existingapproaches that are based on policy gradients, PL-Rank makes use of thespecific structure of PL models and ranking metrics. Our experimental analysisshows that PL-Rank has a greater sample-efficiency and is computationally lesscostly than existing policy gradients, resulting in faster convergence athigher performance. PL-Rank further enables the industry to apply PL models formore relevant and fairer real-world ranking systems.

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