10 papers
Is Separation Necessary for Gradient EM to Learn Gaussian Mixtures in High Dimensions?
Yiran Zhang, Mo Zhou, Weihang Xu +2
Learning Gaussian mixture models (GMMs) using the Expectation-Maximization (EM) algorithm and its gradient-based variants is a fundamental problem in machine learning. It is known…
Learning Orthogonal Multi-Index Models Beyond Small Initialization: Incremental Learning, Competitive Dynamics and Symmetry
Mo Zhou, Weihang Xu, Simon S. Du +1
Recent work has identified incremental learning in shallow networks trained on single-index and multi-index models. However, existing analyses often rely on simplifying settings, s…
Asymptotically Optimal Regret for Reinforcement Learning without Horizon Dependence
Runlong Zhou, Zihan Zhang, Maryam Fazel +1
We study horizon-free regret minimization for finite-horizon time-homogeneous tabular Markov decision processes with states, actions, horizon , and per-trajectory total…
Dynamics of Learning under User Choice: Overspecialization and Peer-Model Probing
Adhyyan Narang, Sarah Dean, Lillian J Ratliff +1
In many economically relevant contexts where machine learning is deployed, multiple platforms obtain data from the same pool of users, each of whom selects the platform that best s…
Unregularized Linear Convergence in Zero-Sum Game from Preference Feedback
Shulun Chen, Runlong Zhou, Zihan Zhang +2
Aligning large language models (LLMs) with human preferences has proven effective for enhancing model capabilities, yet standard preference modeling using the Bradley-Terry model a…
Convergence Dynamics of Over-Parameterized Score Matching for a Single Gaussian
Yiran Zhang, Weihang Xu, Mo Zhou +2
Score matching has become a central training objective in modern generative modeling, particularly in diffusion models, where it is used to learn high-dimensional data distribution…
Global Convergence of Four-Layer Matrix Factorization under Random Initialization
Minrui Luo, Weihang Xu, Xiang Gao +2
Gradient descent dynamics on the deep matrix factorization problem is extensively studied as a simplified theoretical model for deep neural networks. Although the convergence theor…
Sharp Gap-Dependent Variance-Aware Regret Bounds for Tabular MDPs
Shulun Chen, Runlong Zhou, Zihan Zhang +2
We consider the gap-dependent regret bounds for episodic MDPs. We show that the Monotonic Value Propagation (MVP) algorithm achieves a variance-aware gap-dependent regret bound of…
Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixtures
Mo Zhou, Weihang Xu, Maryam Fazel +1
Learning Gaussian Mixture Models (GMMs) is a fundamental problem in statistics and machine learning, with the Expectation-Maximization (EM) algorithm and its popular variant gradie…
Understanding the Performance Gap in Preference Learning: A Dichotomy of RLHF and DPO
Ruizhe Shi, Minhak Song, Runlong Zhou +3
We present a fine-grained theoretical analysis of the performance gap between two-stage reinforcement learning from human feedback~(RLHF) and direct preference optimization~(DPO).…