arXiv subjects

Nikolaos Makras

Publications and source records attributed to Nikolaos Makras.

3 recordsLinked to original sources

arXiv2026

The Tamed Subgradient Unadjusted Langevin Algorithm beyond Convexity

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.

cs.LG↗

arXiv2025

The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions

In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging techniques, such as the Moreau-Yosida envelope or Gaussian smoothing, and show consequently that the performance of samplers like ULA does not necessarily degenerate arbitrarily with low regularity. In particular, we show that the Lipschitz or Hölder continuity assumption can be replaced by a geometric one-sided Lipschitz condition that allows even for discontinuous log-gradients. We derive non-asymptotic guarantees for the convergence of the algorithm to the target distribution in Wasserstein distances. Non-asymptotic bounds are also provided for the performance of the algorithm as an optimizer, specifically for the solution of associated excess risk optimization problems.

stat.ML↗

arXiv2025

Taming the Interacting Particle Langevin Algorithm: The Superlinear case

Recent advances in stochastic optimization have yielded the interacting particle Langevin algorithm (IPLA), which leverages the notion of interacting particle systems (IPS) to efficiently sample from approximate posterior densities. This becomes particularly crucial in relation to the framework of Expectation-Maximization (EM), where the E-step is computationally challenging or even intractable. Although prior research has focused on scenarios involving convex cases with gradients of log densities that grow at most linearly, our work extends this framework to include polynomial growth. Taming techniques are employed to produce an explicit discretization scheme that yields a new class of stable, under such non-linearities, algorithms which are called tamed interacting particle Langevin algorithms (tIPLA). We obtain non-asymptotic convergence error estimates in Wasserstein-2 distance for the new class under the best known rate.

math.PR↗