Lauri Viitasaari

Mahdi Dehshiri, Kerlyns Martinez, Lauri Viitasaari

This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization, coefficient approximation, and model fitting error -- within a unified framework. Through Sobolev-type norms, we derive convergence rates that incorporate the regularity of trajectories, thereby capturing the interaction of these error components. To demonstrate the applicability of the theory, we introduce a training scheme for coefficient function estimation based on shallow neural networks and a recurrent architecture. Numerical experiments validate the theoretical findings and illustrate the effectiveness of the approach.

Benny Avelin, Lauri Viitasaari

In this article we prove that estimator stability is enough to show that leave-one-out cross validation is a sound procedure, by providing concentration bounds in a general framework. In particular, we provide concentration bounds beyond Lipschitz continuity assumptions on the loss or on the estimator. We obtain our results by relying on random variables with distribution satisfying the logarithmic Sobolev inequality, providing us a relatively rich class of distributions. We illustrate our method by considering several interesting examples, including linear regression, kernel density estimation, and stabilized/truncated estimators such as stabilized kernel regression.

Pekka Malo, Lauri Viitasaari, Antti Suominen et al.

This paper examines reinforcement learning (RL) in infinite-horizon decision processes with almost-sure safety constraints, crucial for applications like autonomous systems, finance, and resource management. We propose a doubly-regularized RL framework combining reward and parameter regularization to address safety constraints in continuous state-action spaces. The problem is formulated as a convex regularized objective with parametrized policies in the mean-field regime. Leveraging mean-field theory and Wasserstein gradient flows, policies are modeled on an infinite-dimensional statistical manifold, with updates governed by parameter distribution gradient flows. Key contributions include solvability conditions for safety-constrained problems, smooth bounded approximations for gradient flows, and exponential convergence guarantees under sufficient regularization. General regularization conditions, including entropy regularization, support practical particle method implementations. This framework provides robust theoretical insights and guarantees for safe RL in complex, high-dimensional settings.