Newest papers

Continuous-Time Policy Gradient from Discrete Data: Convergence Analysis and Model-Free Algorithms

Martin Hernandez, Xinyan Qing, Mo Zhou, Yuhua Zhu · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28580 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

El aprendizaje de reforzamiento de datos en tiempo continuo busca una política óptima bajo dinámicas desconocidas impulsadas por ecuaciones diferenciales estocásticas utilizando observaciones recopiladas en tiempos discretos. Desarrollamos un marco de gradientes de políticas que combina el análisis de convergencia riguroso con el aprendizaje de datos discretos. Primero establecemos una diferencia de rendimiento y derivamos fórmulas de gradientes de políticas para políticas aleatorias y paramétricas. Luego demostramos la convergencia exponencial de un flujo de políticas reguladas por entropía al óptimo regularizado. Para las actualizaciones de parámetros discretos, derivamos un vínculo de convergencia que separa explícitamente las contribuciones del error crítico, el error de regresión de políticas y el tamaño del paso de aprendizaje.

Machine translation (Meta M2M100); the English original follows.

Abstract

Continuous-time reinforcement learning seeks an optimal policy under unknown dynamics driven by stochastic differential equations using observations collected at discrete times. We develop a policy gradient framework that combines rigorous convergence analysis with learning from discrete data. We first establish a performance difference lemma and derive policy gradient formulas for randomized and parametrized policies. We then prove exponential convergence of an entropy-regularized policy flow to the regularized optimum. For discrete parametrized updates, we derive a convergence bound that explicitly separates the contributions of critic error, policy-regression error, and the learning step size. To enable learning under unknown dynamics, we integrate this framework with PhiBE, which constructs a continuous-time surrogate generator from discrete transition data. The resulting on-policy and off-policy model-free actor-critic algorithms preserve the continuous-time structure of the control problem. Numerical experiments on an entropy-regularized linear-quadratic regulator and a nonlinear wheeled robot demonstrate the performance and stability of the proposed methods with both known and data-driven dynamics.

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Topics: Convergence (economics), Reinforcement learning, Mathematics, Lemma (botany), Stability (learning theory), Discrete time and continuous time

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