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Value functions are central to Dynamic Programming and Reinforcement Learning but their exact estimation suffers from the curse of dimensionality, challenging the development of practical value-function (VF) estimation algorithms. Several approaches have been proposed to overcome this issue, from non-parametric schemes that aggregate states or actions to parametric approximations of state and action VFs via, e.g., linear estimators or deep neural networks. Relevantly, several high-dimensional state problems can be well-approximated by an intrinsic low-rank structure. Motivated by this and leveraging results from low-rank optimization, this paper proposes different stochastic algorithms to estimate a low-rank factorization of the Q(s, a) matrix. This is a non-parametric alternative to VF approximation that dramatically reduces the computational and sample complexities relative to classical Q-learning methods that estimate Q(s, a) separately for each state-action pair.

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The rise of microgrid-based architectures is modifying significantly the energy control landscape in distribution systems, making distributed control mechanisms necessary to ensure reliable power system operations. In this article, the use of Reinforcement Learning techniques is proposed to implement load frequency control (LFC) without requiring a central authority. To this end, a detailed model of power system dynamic behaviour is formulated by representing individual generator dynamics, generator rate and network constraints, renewable-based generation, and realistic load realisations. The LFC problem is recast as a Markov Decision Process, and the Multi-Agent Deep Deterministic Policy Gradient algorithm is used to approximate the optimal solution of all LFC layers, that is, primary, secondary and tertiary. The proposed LFC framework operates through centralised learning and distributed implementation. In particular, there is no information interchange between generating units during operation. Thus, no communication infrastructure is necessary and information privacy between them is respected. The proposed framework is validated through numerical results and it is shown that it can be used to implement LFC in a distributed and cost-efficient manner.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.