Tensor and Matrix Low-Rank Value-Function Approximation in Reinforcement Learning

• URL: http://arxiv.org/abs/2201.09736v3
• Date: Mon, 27 May 2024 19:58:52 GMT
• Title: Tensor and Matrix Low-Rank Value-Function Approximation in Reinforcement Learning
• Authors: Sergio Rozada, Santiago Paternain, Antonio G. Marques,
• Abstract summary: Value-function approximation is a central problem in Reinforcement Learning (RL) This paper puts forth a parsimonious non-parametric approach, where we use low-rank algorithms to estimate the VF matrix in an online and model-free fashion. As VFs tend to be multi-dimensional, we propose replacing the classical VF matrix representation with a tensor representation and, then, use the PARAFAC decomposition to design an online model-free tensor low-rank algorithm.
• Score: 11.317136648551536
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Value-function (VF) approximation is a central problem in Reinforcement Learning (RL). Classical non-parametric VF estimation suffers from the curse of dimensionality. As a result, parsimonious parametric models have been adopted to approximate VFs in high-dimensional spaces, with most efforts being focused on linear and neural-network-based approaches. Differently, this paper puts forth a a parsimonious non-parametric approach, where we use stochastic low-rank algorithms to estimate the VF matrix in an online and model-free fashion. Furthermore, as VFs tend to be multi-dimensional, we propose replacing the classical VF matrix representation with a tensor (multi-way array) representation and, then, use the PARAFAC decomposition to design an online model-free tensor low-rank algorithm. Different versions of the algorithms are proposed, their complexity is analyzed, and their performance is assessed numerically using standardized RL environments.

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