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Mean-field Langevin dynamics (MLFD) is a class of interacting particle methods that tackle convex optimization over probability measures on a manifold, which are scalable, versatile, and enjoy computational guarantees. However, some…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…

In this paper we propose a new approach for sampling from probability measures in, possibly, high dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the…

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…

The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from…

In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for…

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of…

Our work is motivated by a desire to study the theoretical underpinning for the convergence of stochastic gradient type algorithms widely used for non-convex learning tasks such as training of neural networks. The key insight, already…

We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in…

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity…

Exploration in environments with sparse rewards has been a persistent problem in reinforcement learning (RL). Many tasks are natural to specify with a sparse reward, and manually shaping a reward function can result in suboptimal…

We present an iterative active constraint learning (ACL) algorithm, within the learning from demonstrations (LfD) paradigm, which intelligently solicits informative demonstration trajectories for inferring an unknown constraint in the…

Stochastic gradient methods (SGMs) are predominant approaches for solving stochastic optimization. On smooth nonconvex problems, a few acceleration techniques have been applied to improve the convergence rate of SGMs. However, little…

Generative Flow Networks (GFlowNets) are a class of generative models that sample objects in proportion to a specified reward function through a learned policy. They can be trained either on-policy or off-policy, needing a balance between…

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated remarkable potential in enhancing the reasoning capability of Large Reasoning Models (LRMs). However, RLVR often drives the policy toward over-determinism,…

We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save…

Distributed optimization methods are often applied to solving huge-scale problems like training neural networks with millions and even billions of parameters. In such applications, communicating full vectors, e.g., (stochastic) gradients,…

This paper studies the constrained/safe reinforcement learning (RL) problem with sparse indicator signals for constraint violations. We propose a model-based approach to enable RL agents to effectively explore the environment with unknown…