arXiv subjects

Antti Suominen

Publications and source records attributed to Antti Suominen.

2 recordsLinked to original sources

arXiv2026

Operator Calculus for Population-Based Optimization: Modular Convergence and Finite-Population Guarantees

Population-based optimizers combine update rules such as mutation, selection, and recombination. When one rule changes, it is often unclear which convergence guarantees survive or how the new combination should be assessed. We develop an operator calculus: an operator is a population-update rule, and the calculus specifies how separately checked effects can be combined. Under explicit regularity and small-step conditions, the leading changes caused by the updates add, yielding reusable building blocks for convergence analysis. The framework distinguishes finding and retaining a good solution, reducing the population's mean objective, and concentrating candidates near an optimizer, and identifies the extra approximation conditions needed for finite evaluation-budget guarantees. Applications include distribution adaptation, recombinative evolution, and consensus dynamics, with verified nonconvex cases. Controlled experiments on a common nonconvex problem collection show how component effects change with population geometry and the performance measure: a rule can worsen the mean objective yet produce better candidates.

math.OC↗

arXiv2025

Convex Regularization and Convergence of Policy Gradient Flows under Safety Constraints

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.

cs.LG↗