Deep neural networks for choice analysis: Enhancing behavioral regularity with gradient regularization
Cornell University（康奈尔大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；University of Leeds（利兹大学）；University of California, Berkeley（加利福尼亚大学伯克利分校）；University of Florida（佛罗里达大学）
Siqi Feng, Rui Yao, Stephane Hess, Ricardo A. Daziano, Timothy Brathwaite, Joan Walker, Shenhao Wang
发表信息：
Transportation Research Part C: Emerging Technologies, Volume 166, 2024, 104767
Deep neural networks (DNNs) frequently present behaviorally irregular patterns, significantly limiting their practical potentials and theoretical validity in travel behavior modeling. This study proposes strong and weak behavioral regularities as novel metrics to evaluate the monotonicity of individual demand functions (known as the "law of demand"), and further designs a constrained optimization framework with six gradient regularizers to enhance DNNs' behavioral regularity. The proposed framework is applied to travel survey data from Chicago and London to examine the trade-off between predictive power and behavioral regularity for large vs. small sample scenarios and in-domain vs. out-of-domain generalizations. The results demonstrate that, unlike models with strong behavioral foundations such as the multinomial logit, the benchmark DNNs cannot guarantee behavioral regularity. However, gradient regularization (GR) increases DNNs' behavioral regularity by around 6 percentage points (pp) while retaining their relatively high predictive power. In the small sample scenario, GR is more effective than in the large sample scenario, simultaneously improving behavioral regularity by about 20 pp and log-likelihood by around 1.7%. Comparing with the in-domain generalization of DNNs, GR works more effectively in out-of-domain generalization: it drastically improves the behavioral regularity of poorly performing benchmark DNNs by around 65 pp, indicating the criticality of behavioral regularization for enhancing model transferability and application in forecasting. Moreover, the proposed framework is applicable to other NN-based choice models such as TasteNets. Future studies could use behavioral regularity as a metric along with log-likelihood in evaluating travel demand models, and investigate other methods to further enhance behavioral regularity when adopting complex machine learning models.
Regularity as Regularization: Smooth and Strongly Convex Brenier Potentials in Optimal Transport
CREST（法国国家科学研究中心经济与统计研究中心）；ENSAE（法国国家统计与经济管理学院）；Institut Polytechnique de Paris（巴黎综合理工学院）；CNRS（法国国家科学研究中心）；ENS, PSL Research University（巴黎高等师范学院，巴黎文理研究大学）；Google Brain（谷歌大脑）
Nonconvex Composite Functional Constraints via First-Order Augmented Lagrangian Methods under Local Regularity
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA（赫尔曼·米勒工程与系统工程学院，佐治亚理工学院，美国亚特兰大，GA）；Sauder School of Business, University of British Columbia, Vancouver, BC, Canada（萨德勒商学院，不列颠哥伦比亚大学，加拿大温哥华，BC）
The rate of convergence of Bregman proximal methods: Local geometry vs. regularity vs. sharpness
Univ. Grenoble Alpes（格勒诺布尔大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Grenoble INP（格勒诺布尔理工学院）；Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Université de Toulouse（图卢兹大学）；UPS（图卢兹第三大学）；LIG（格勒诺布尔信息与信号处理实验室）
