Recent advances in stochastic optimization have yielded the interactive particle Langevin algorithm (IPLA), which leverages the notion of interacting particle systems (IPS) to efficiently sample from approximate posterior densities. This becomes particularly crucial within 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 interactive particle Langevin algorithms (tIPLA). We obtain non-asymptotic convergence error estimates in Wasserstein-2 distance for the new class under an optimal rate.

翻译：近期随机优化领域的进展催生了交互式粒子朗之万算法（IPLA），该算法利用相互作用粒子系统（IPS）的概念，从近似后验分布中高效采样。这一特性在期望最大化（EM）框架中尤为重要——当E步骤面临计算挑战甚至不可行时尤为关键。尽管先前研究主要关注对数密度梯度最多呈线性增长的情形，本文的工作将该框架扩展至多项式增长情形。我们采用驯服技术构建显式离散化方案，由此衍生出一类在此类非线性条件下保持稳定的新算法，命名为驯服交互式粒子朗之万算法（tIPLA）。针对该新算法类别，我们获得了Wasserstein-2距离下的最优阶非渐近收敛误差估计。