Online Learning to Rank (OLTR) methods optimize ranking models by directly
interacting with users, which allows them to be very efficient and responsive.
All OLTR methods introduced during the past decade have extended on the
original OLTR method: Dueling Bandit Gradient Descent (DBGD). Recently, a
fundamentally different approach was introduced with the Pairwise
Differentiable Gradient Descent (PDGD) algorithm. To date the only comparisons
of the two approaches are limited to simulations with cascading click models
and low levels of noise. The main outcome so far is that PDGD converges at
higher levels of performance and learns considerably faster than DBGD-based
methods. However, the PDGD algorithm assumes cascading user behavior,
potentially giving it an unfair advantage. Furthermore, the robustness of both
methods to high levels of noise has not been investigated. Therefore, it is
unclear whether the reported advantages of PDGD over DBGD generalize to
different experimental conditions. In this paper, we investigate whether the
previous conclusions about the PDGD and DBGD comparison generalize from ideal
to worst-case circumstances. We do so in two ways. First, we compare the
theoretical properties of PDGD and DBGD, by taking a critical look at
previously proven properties in the context of ranking. Second, we estimate an
upper and lower bound on the performance of methods by simulating both ideal
user behavior and extremely difficult behavior, i.e., almost-random
non-cascading user models. Our findings show that the theoretical bounds of
DBGD do not apply to any common ranking model and, furthermore, that the
performance of DBGD is substantially worse than PDGD in both ideal and
worst-case circumstances. These results reproduce previously published findings
about the relative performance of PDGD vs. DBGD and generalize them to
extremely noisy and non-cascading circumstances.

本文介绍了在线学习排序的两种最新方法：Dueling Bandit Gradient Descent（DBGD）和 Pairwise Differentiable Gradient Descent（PDGD）的比较及其在极端嘈杂和非连锁用户模型情况下的性能。结果表明，PDGD 在理想和最坏情况下的性能都比 DBGD 好，并且 DBGD 的理论边界不适用于任何常见的排序模型。

在线环境中的排名模型优化

Optimizing Ranking Models in an Online Setting

Online Learning to Rank (OLTR) methods optimize rankers based on user
interactions. State-of-the-art OLTR methods are built specifically for linear
models. Their approaches do not extend well to non-linear models such as neural
networks. We introduce an entirely novel approach to OLTR that constructs a
weighted differentiable pairwise loss after each interaction: Pairwise
Differentiable Gradient Descent (PDGD). PDGD breaks away from the traditional
approach that relies on interleaving or multileaving and extensive sampling of
models to estimate gradients. Instead, its gradient is based on inferring
preferences between document pairs from user clicks and can optimize any
differentiable model. We prove that the gradient of PDGD is unbiased w.r.t.
user document pair preferences. Our experiments on the largest publicly
available Learning to Rank (LTR) datasets show considerable and significant
improvements under all levels of interaction noise. PDGD outperforms existing
OLTR methods both in terms of learning speed as well as final convergence.
Furthermore, unlike previous OLTR methods, PDGD also allows for non-linear
models to be optimized effectively. Our results show that using a neural
network leads to even better performance at convergence than a linear model. In
summary, PDGD is an efficient and unbiased OLTR approach that provides a better
user experience than previously possible.

Pairwise Differentiable Gradient Descent (PDGD) is an efficient and unbiased Online Learning to Rank approach that allows for effective optimization of non-linear models based on user interactions and preferences, providing a better user experience than previously possible.