We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures. To handle the superlinear regime, taming techniques are employed to produce a stable, explicit scheme. We derive non-asymptotic convergence bounds in Wasserstein-2 distance, with all constants tracked explicitly in terms of dimension and inverse temperature, improving upon the currently known rates for subgradient-based Langevin algorithms. We further provide excess risk estimates for the associated optimisation problem. We verify the assumptions, with explicit constants, for the regularized pretraining potential of a LLM in the GPT-2 lineage and the boosted coordinate-wise variant of SG-TULA pretrains the former competitively against finetuned AdamW and Muon, for which no comparable non-asymptotic guarantees are presently available.
Stochastic Gradient Langevin Dynamics (SGLD) reduces the cost of Langevin-based sampling by replacing full-dataset drift evaluations with mini-batch approximations, but the resulting subsampling error may offset this computational saving. We study this trade-off for stochastic differential equations with finite-sum dri...
Mateusz B. Majka, Tigran Nagapetyan, Łukasz Szpruch et al.· 0 citations
As a fundamental task across computational statistics, scientific computing and machine learning, sampling from high-dimensional probability distributions has received increasing attention in recent years. Numerous sampling algorithms have been proposed, among which underdamped Langevin Monte Carlo (ULMC) methods based...
As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its variants. We show that a preconditioned SGD step is the posterior-mean update of a Gaussian Bayes model, and that its one-step regret splits into an intrinsic-time cost and...
We consider the problem of sampling from Gibbs distributions on matrix spaces whose potential energies are neither convex nor globally gradient-Lipschitz. We introduce a family of non-quadratic kinetic energies that lead to a new underdamped Langevin system with momentum preconditioning, in which the gradient of the ki...
This work proposes Batched SGD, a simple variant that partitions online samples into epochs and performs a single update per epoch using a refined, low-variance gradient estimate, and provides the first high-probability guarantees for FL.
Feng Zhu, Robert W. Heath, Aritra Mitra· 0 citations
In sampling problems, gradient-based schemes such as Langevin Monte Carlo (LMC) mix faster than non-gradient-based methods, but their applicability is limited by access to the gradient of the target log-density. In practice, gradients are often unavailable and function evaluations are noisy, e.g., stochastic simulators...
Hongbo Li, J. Spall· 0 citations
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