  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.
