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The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [2] of this work we established that agents cluster around a network…

Performance of distributed optimization and learning systems is bottlenecked by "straggler" nodes and slow communication links, which significantly delay computation. We propose a distributed optimization framework where the dataset is…

Stochastic gradient Langevin dynamics (SGLD) and stochastic gradient Hamiltonian Monte Carlo (SGHMC) are two popular Markov Chain Monte Carlo (MCMC) algorithms for Bayesian inference that can scale to large datasets, allowing to sample from…

Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems so called recurrent models are used. In this article we…

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…

Sampling the parameter space of artificial neural networks according to a Boltzmann distribution provides insight into the geometry of low-loss solutions and offers an alternative to conventional loss minimization for training. However,…

A number of results have recently demonstrated the benefits of incorporating various constraints when training deep architectures in vision and machine learning. The advantages range from guarantees for statistical generalization to better…

Stochastic Gradient Descent Langevin Dynamics (SGLD) algorithms, which add noise to the classic gradient descent, are known to improve the training of neural networks in some cases where the neural network is very deep. In this paper we…

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…

Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

We study a class of constrained reinforcement learning (RL) problems in which multiple constraint specifications are not identified before training. It is challenging to identify appropriate constraint specifications due to the undefined…

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…

In reinforcement learning (RL), it is often advantageous to consider additional constraints on the action space to ensure safety or action relevance. Existing work on such action-constrained RL faces challenges regarding effective policy…

Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…

3D Gaussian Splatting (3DGS) has emerged as a leading framework for novel view synthesis, yet its core optimization challenges remain underexplored. We identify two key issues in 3DGS optimization: entrapment in suboptimal local optima and…

The method of complex Langevin simulations is a tool that can be used to tackle the complex-action problem encountered, for instance, in finite-density lattice quantum chromodynamics or real-time lattice field theories. The method is based…

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…

In this paper, we establish well-posedness of reflected McKean-Vlasov SDEs and their particle approximations in smooth non-convex domains. We prove convergence of the interacting particle system to the corresponding mean-field limit with…

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

Stochastic distributed optimization methods that solve an optimization problem over a multi-agent network have played an important role in a variety of large-scale signal processing and machine leaning applications. Among the existing…