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

Sergio Rozada; Santiago Paternain; Antonio G. Marques

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arXiv · 2201.09736

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

Sergio Rozada·Santiago Paternain·Antonio G. Marques

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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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Sergio Rozada, Santiago Paternain, Antonio G. Marques. 2022-01-21. Tensor and Matrix Low-Rank Value-Function Approximation in Reinforcement Learning. https://arxiv.org/abs/2201.09736

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