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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…
Policy-Based Trajectory Clustering in Offline Reinforcement Learning
Hao Hu, Xinqi Wang, Simon Shaolei Du
We introduce a novel task of clustering trajectories from offline reinforcement learning (RL) datasets, where each cluster center represents the policy that generated its trajector…
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…
LoRe: Personalizing LLMs via Low-Rank Reward Modeling
Avinandan Bose, Zhihan Xiong, Yuejie Chi +3
Personalizing large language models (LLMs) to accommodate diverse user preferences is essential for enhancing alignment and user satisfaction. Traditional reinforcement learning fr…
A Minimalist Example of Edge-of-Stability and Progressive Sharpening
Liming Liu, Zixuan Zhang, Simon Du +1
Recent advances in deep learning optimization have unveiled two intriguing phenomena under large learning rates: Edge of Stability (EoS) and Progressive Sharpening (PS), challengin…
Extragradient Preference Optimization (EGPO): Beyond Last-Iterate Convergence for Nash Learning from Human Feedback
Runlong Zhou, Maryam Fazel, Simon S. Du
Reinforcement learning from human feedback (RLHF) has become essential for improving language model capabilities, but traditional approaches rely on the assumption that human prefe…
Towards Understanding the Benefit of Multitask Representation Learning in Decision Process
Rui Lu, Yang Yue, Andrew Zhao +2
Multitask Representation Learning (MRL) has emerged as a prevalent technique to improve sample efficiency in Reinforcement Learning (RL). Empirical studies have found that training…