Exponential convergence rate for Iterative Markovian Fitting

Two distributions µ, ν P ( X) with everywhere positive density are given. Recently the IMF algorithm [4] was proposed to solve problem (1), which consists of successive transformations interpreted as projections onto the sets of Markov and q -reciprocal processes (see [3, null2.5]): Here we for the first time prove exponential convergence of IMF . We rely on convergence analysis of iterations [1] minimizing a strongly convex function with a Lipschitz gradient. We recall from [3, Theorem 3.1] that the solution p The work was supported by the grant for research centers in the field of AI provided by the Ministry of Economic Development of the Russian Federation in accordance with the agreement 000000C313925P4F0002 and the agreement with Skoltech 139-10-2025-033.