AutoML Workshop

Abstract We present a new parameter-free algorithm for online linear optimization over any Hilbert space. It is theoretically optimal, with regret guarantees as good as with the best possible learning rate. The algorithm is simple and easy to implement. The analysis is given via the adversarial coin-betting game, Kelly betting and the Krichevsky-Trofimov estimator. Applications to obtain parameter-free convex optimization and machine learning algorithms are shown

CoinEM: Tuning-Free Particle-Based Variational Inference for Latent Variable Models

We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum likelihood estimation as an optimization problem: namely, as the minimization of a free energy functional. One way to solve this problem is to consider the discretization of a gradient flow associated with the free energy. We study one such approach, which resembles an extension of the popular Stein variational gradient descent algorithm. In particular, we establish a descent lemma for this algorithm, which guarantees that the free energy decreases at each iteration. This method, and any other obtained as the discretization of the gradient flow, will necessarily depend on a learning rate which must be carefully tuned by the practitioner in order to ensure convergence at a suitable rate. With this in mind, we also propose another algorithm for optimizing the free energy which is entirely learning rate free, based on coin betting techniques from convex optimization. We validate the performance of our algorithms across a broad range of numerical experiments, including several high-dimensional settings. Our results are competitive with existing particle-based methods, without the need for any hyperparameter tuning

CoinEM:Tuning-Free Particle-Based Variational Inference for Latent Variable Models

We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum likelihood estimation as an optimization problem: namely, as the minimization of a free energy functional. One way to solve this problem is to consider the discretization of a gradient flow associated with the free energy. We study one such approach, which resembles an extension of the popular Stein variational gradient descent algorithm. In particular, we establish a descent lemma for this algorithm, which guarantees that the free energy decreases at each iteration. This method, and any other obtained as the discretization of the gradient flow, will necessarily depend on a learning rate which must be carefully tuned by the practitioner in order to ensure convergence at a suitable rate. With this in mind, we also propose another algorithm for optimizing the free energy which is entirely learning rate free, based on coin betting techniques from convex optimization. We validate the performance of our algorithms across a broad range of numerical experiments, including several high-dimensional settings. Our results are competitive with existing particle-based methods, without the need for any hyperparameter tuning