Full error analysis of policy gradient learning algorithms for exploratory linear quadratic mean-field control problem in continuous time with common noise

Fuente: arXiv
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Main Authors: Frikha, Noufel, Pham, Huyên, Song, Xuanye
Format: Preprint
Published: 2024
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author Frikha, Noufel
Pham, Huyên
Song, Xuanye
author_facet Frikha, Noufel
Pham, Huyên
Song, Xuanye
contents We consider reinforcement learning (RL) methods for finding optimal policies in linear quadratic (LQ) mean field control (MFC) problems over an infinite horizon in continuous time, with common noise and entropy regularization. We study policy gradient (PG) learning and first demonstrate convergence in a model-based setting by establishing a suitable gradient domination condition.Next, our main contribution is a comprehensive error analysis, where we prove the global linear convergence and sample complexity of the PG algorithm with two-point gradient estimates in a model-free setting with unknown parameters. In this setting, the parameterized optimal policies are learned from samples of the states and population distribution.Finally, we provide numerical evidence supporting the convergence of our implemented algorithms.
format Preprint
id arxiv_https___arxiv_org_abs_2408_02489
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Full error analysis of policy gradient learning algorithms for exploratory linear quadratic mean-field control problem in continuous time with common noise
Frikha, Noufel
Pham, Huyên
Song, Xuanye
Optimization and Control
Machine Learning
We consider reinforcement learning (RL) methods for finding optimal policies in linear quadratic (LQ) mean field control (MFC) problems over an infinite horizon in continuous time, with common noise and entropy regularization. We study policy gradient (PG) learning and first demonstrate convergence in a model-based setting by establishing a suitable gradient domination condition.Next, our main contribution is a comprehensive error analysis, where we prove the global linear convergence and sample complexity of the PG algorithm with two-point gradient estimates in a model-free setting with unknown parameters. In this setting, the parameterized optimal policies are learned from samples of the states and population distribution.Finally, we provide numerical evidence supporting the convergence of our implemented algorithms.
title Full error analysis of policy gradient learning algorithms for exploratory linear quadratic mean-field control problem in continuous time with common noise
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2408.02489