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We introduce two new particle-based algorithms for learning latent variablemodels via marginal maximum likelihood estimation, including one which isentirely tuning-free. Our methods are based on the perspective of marginalmaximum likelihood estimation as an optimization problem: namely, as theminimization of a free energy functional. One way to solve this problem is viathe discretization of a gradient flow associated with the free energy. We studyone such approach, which resembles an extension of Stein variational gradientdescent, establishing a descent lemma which guarantees that the free energydecreases at each iteration. This method, and any other obtained as thediscretization of the gradient flow, necessarily depends on a learning ratewhich must be carefully tuned by the practitioner in order to ensureconvergence at a suitable rate. With this in mind, we also propose anotheralgorithm for optimizing the free energy which is entirely learning rate free,based on coin betting techniques from convex optimization. We validate theperformance of our algorithms across several numerical experiments, includingseveral high-dimensional settings. Our results are competitive with existingparticle-based methods, without the need for any hyperparameter tuning.

Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Betting