We derive finite-sample generalization bounds for Transformers trained with dynamic programming recursions. Building on the doubly lifted, measure-valued formulation of Transformer dynamics, we view data sets as probability laws on pairs of empirical input-output measures, allowing us to interpret the training problem as a finite-horizon Markovian control problem.
arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.
By Linglingzhi Zhu, Yunqin Zhu, Yao Xie
arXiv:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.
By Xiuyuan Cheng, Yunqin Zhu, Yao Xie
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.
By Chiwun Yang
arXiv:2506. 07040v4 Announce Type: replace-cross Abstract: We study model-free methods for distributionally robust infinite-horizon average-reward Markov decision processes (MDPs).
By Yang Xu, Swetha Ganesh, Vaneet Aggarwal
arXiv:2606. 19117v1 Announce Type: cross Abstract: Offline policy learning has received growing attention in causal inference.
By Yiyan Huang, Cheuk Hang Leung, Qi Wu, Zhiheng Zhang
arXiv:2605. 26078v3 Announce Type: replace Abstract: Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions.
By Zhaoyu Zhu, Rui Gao, Shuang Li
arXiv:2606. 28281v1 Announce Type: cross Abstract: PAC-Bayesian bounds provide finite-sample guarantees for data-dependent randomized predictors, but applying them to learning-based control is difficult because the natural objective is a quadratic trajectory cost.
By Domagoj Herceg
arXiv:2404. 03578v3 Announce Type: replace Abstract: The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL).
By Miao Lu, Han Zhong, Tong Zhang, Jose Blanchet
arXiv:2606. 07600v1 Announce Type: cross Abstract: We formulate data propagation through the Transformer, the machine learning architecture powering large language models, as a nonlinear control system on the space of probability measures.
By Albert Alcalde, Zhengping Ji, Enrique Zuazua
arXiv:2606. 06855v1 Announce Type: cross Abstract: While algorithmic stability is a central tool for understanding generalization of learning algorithms, existing high-probability guarantees typically rely on uniform boundedness or sub-Gaussian/sub-Weibull tail assumptions, which can be overly restrictive for modern settings with heavy-tailed or unbounded losses.
By Qianqian Lei, Soham Bonnerjee, Yuefeng Han, Wei Biao Wu
arXiv:2311. 15365v3 Announce Type: replace Abstract: We study an idealized training process for deep neural networks in a continuous-depth, mean-field model in which each layer is parameterized by a probability measure on a Euclidean parameter space.
By Noboru Isobe