Models of choice are a fundamental input to many now-canonical optimization
problems in the field of Operations Management, including assortment,
inventory, and price optimization. Naturally, accurate estimation of these
models from data is a critical step in the application of these optimization
problems in practice, and so it is perhaps surprising that such choice
estimation has to now been accomplished almost exclusively, both in theory and
in practice, (a) without the use of deep learning in any meaningful way, and
(b) via evaluation on limited data with constantly-changing metrics. This is in
stark contrast to the vast majority of similar learning applications, for which
the practice of machine learning suggests that (a) neural network-based models
are typically state-of-the-art, and (b) strict standardization on evaluation
procedures (datasets, metrics, etc.) is crucial. Thus motivated, we first
propose a choice model that is the first to successfully (both theoretically
and practically) leverage a modern neural network architectural concept
(self-attention). Theoretically, we show that our attention-based choice model
is a low-rank generalization of the Halo Multinomial Logit model, a recent
model that parsimoniously captures irrational choice effects and has seen
empirical success. We prove that whereas the Halo-MNL requires $\Omega(m^2)$
data samples to estimate, where $m$ is the number of products, our model
supports a natural nonconvex estimator (in particular, that which a standard
neural network implementation would apply) which admits a near-optimal
stationary point with $O(m)$ samples. We then establish the first
realistic-scale benchmark for choice estimation on real data and use this
benchmark to run the largest evaluation of existing choice models to date. We
find that the model we propose is dominant over both short-term and long-term
data periods.

通过引入自注意力的神经网络结构，本研究提出了第一个成功利用现代神经网络概念的选择模型，理论和实践都证明了该模型相对于现有模型在实际数据上更具优势。

用自注意力建模选择

Modeling Choice via Self-Attention

Providing users with alternatives to choose from is an essential component in
many online platforms, making the accurate prediction of choice vital to their
success. A renewed interest in learning choice models has led to significant
progress in modeling power, but most current methods are either limited in the
types of choice behavior they capture, cannot be applied to large-scale data,
or both.
Here we propose a learning framework for predicting choice that is accurate,
versatile, theoretically grounded, and scales well. Our key modeling point is
that to account for how humans choose, predictive models must capture certain
set-related invariances. Building on recent results in economics, we derive a
class of models that can express any behavioral choice pattern, enjoy favorable
sample complexity guarantees, and can be efficiently trained end-to-end.
Experiments on three large choice datasets demonstrate the utility of our
approach.

提供选择的替代方案是许多在线平台的重要组成部分，因此准确预测选择是其成功的关键。本文提出了一种学习框架，用于预测选择，具有准确性、多功能性、理论基础和良好的可扩展性。我们的建模要点是为了解释人类的选择，预测模型必须捕捉特定的集合相关的不变性，并且基于最近经济学研究成果，我们推导出一类可以表达任何行为选择模式的模型，具有良好的样本复杂性保证，并且可以高效地进行端到端训练。在三个大型选择数据集上的实验证明了我们方法的实用性。

基于集合依赖聚合的选择预测

Predicting Choice with Set-Dependent Aggregation

As datasets capturing human choices grow in richness and scale --
particularly in online domains -- there is an increasing need for choice models
that escape traditional choice-theoretic axioms such as regularity, stochastic
transitivity, and Luce's choice axiom. In this work we introduce the Pairwise
Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable
model that does not assume any of the above axioms while still satisfying the
foundational axiom of uniform expansion, a considerably weaker assumption than
Luce's choice axiom. We show that the PCMC model significantly outperforms the
Multinomial Logit (MNL) model in prediction tasks on both synthetic and
empirical datasets known to exhibit violations of Luce's axiom. Our analysis
also synthesizes several recent observations connecting the Multinomial Logit
model and Markov chains; the PCMC model retains the Multinomial Logit model as
a special case.

本研究引入了一种新的离散选择模型 Pairwise Choice Markov Chain (PCMC) 来预测人类的选择，该模型在不假设传统选择理论公理的情况下具有较好的预测性能，能够取得比 Multinomial Logit (MNL) 模型更好的效果。