Algorithmes de bandits stochastiques pour la gestion de la demande électrique

As electricity is hard to store, the balance between production and consumption must be strictly maintained. With the integration of intermittent renewable energies into the production mix, the management of the balance becomes complex. At the same time, the deployment of smart meters suggests demand response. More precisely, sending signals - such as changes in the price of electricity - would encourage users to modulate their consumption according to the production of electricity. The algorithms used to choose these signals have to learn consumer reactions and, in the same time, to optimize them (exploration-exploration trade-off). Our approach is based on bandit theory and formalizes this sequential learning problem. We propose a first algorithm to control the electrical demand of a homogeneous population of consumers and offer T⅔ upper bound on its regret. Experiments on a real data set in which price incentives were offered illustrate these theoretical results. As a “full information” dataset is required to test bandit algorithms, a consumption data generator based on variational autoencoders is built. In order to drop the assumption of the population homogeneity, we propose an approach to cluster households according to their consumption profile. These different works are finally combined to propose and test a bandit algorithm for personalized demand side management.L'électricité se stockant difficilement à grande échelle, l'équilibre entre la production et la consommation doit être rigoureusement maintenu. Une gestion par anticipation de la demande se complexifie avec l'intégration au mix de production des énergies renouvelables intermittentes. Parallèlement, le déploiement des compteurs communicants permet d'envisager un pilotage dynamique de la consommation électrique. Plus concrètement, l'envoi de signaux - tels que des changements du prix de l'électricité – permettrait d'inciter les usagers à moduler leur consommation afin qu'elle s'ajuste au mieux à la production d'électricité. Les algorithmes choisissant ces signaux devront apprendre la réaction des consommateurs face aux envois tout en les optimisant (compromis exploration-exploitation). Notre approche, fondée sur la théorie des bandits, a permis de formaliser ce problème d'apprentissage séquentiel et de proposer un premier algorithme pour piloter la demande électrique d'une population homogène de consommateurs. Une borne supérieure d'ordre T⅔ a été obtenue sur le regret de cet algorithme. Des expériences réalisées sur des données de consommation de foyers soumis à des changements dynamiques du prix de l'électricité illustrent ce résultat théorique. Un jeu de données en « information complète » étant nécessaire pour tester un algorithme de bandits, un simulateur de données de consommation fondé sur les auto-encodeurs variationnels a ensuite été construit. Afin de s'affranchir de l'hypothèse d'homogénéité de la population, une approche pour segmenter les foyers en fonction de leurs habitudes de consommation est aussi proposée. Ces différents travaux sont finalement combinés pour proposer et tester des algorithmes de bandits pour un pilotage personnalisé de la consommation électrique

Target Tracking for Contextual Bandits: Application to Demand Side Management

We propose a contextual-bandit approach for demand side management by offering price incentives. More precisely, a target mean consumption is set at each round and the mean consumption is modeled as a complex function of the distribution of prices sent and of some contextual variables such as the temperature, weather, and so on. The performance of our strategies is measured in quadratic losses through a regret criterion. We offer $T^{2/3}$ upper bounds on this regret (up to poly-logarithmic terms)---and even faster rates under stronger assumptions---for strategies inspired by standard strategies for contextual bandits (like LinUCB, see Li et al., 2010). Simulations on a real data set gathered by UK Power Networks, in which price incentives were offered, show that our strategies are effective and may indeed manage demand response by suitably picking the price levels

Efficient Model-Based Concave Utility Reinforcement Learning through Greedy Mirror Descent

Many machine learning tasks can be solved by minimizing a convex function of an occupancy measure over the policies that generate them. These include reinforcement learning, imitation learning, among others. This more general paradigm is called the Concave Utility Reinforcement Learning problem (CURL). Since CURL invalidates classical Bellman equations, it requires new algorithms. We introduce MD-CURL, a new algorithm for CURL in a finite horizon Markov decision process. MD-CURL is inspired by mirror descent and uses a non-standard regularization to achieve convergence guarantees and a simple closed-form solution, eliminating the need for computationally expensive projection steps typically found in mirror descent approaches. We then extend CURL to an online learning scenario and present Greedy MD-CURL, a new method adapting MD-CURL to an online, episode-based setting with partially unknown dynamics. Like MD-CURL, the online version Greedy MD-CURL benefits from low computational complexity, while guaranteeing sub-linear or even logarithmic regret, depending on the level of information available on the underlying dynamics

A mirror descent approach for Mean Field Control applied to Demande-Side management

We consider a finite-horizon Mean Field Control problem for Markovian models. The objective function is composed of a sum of convex and Lipschitz functions taking their values on a space of state-action distributions. We introduce an iterative algorithm which we prove to be a Mirror Descent associated with a non-standard Bregman divergence, having a convergence rate of order 1/ \sqrt K. It requires the solution of a simple dynamic programming problem at each iteration. We compare this algorithm with learning methods for Mean Field Games after providing a reformulation of our control problem as a game problem. These theoretical contributions are illustrated with numerical examples applied to a demand-side management problem for power systems aimed at controlling the average power consumption profile of a population of flexible devices contributing to the power system balance

Target Tracking for Contextual Bandits: Application to Demand Side Management

International audienceWe propose a contextual-bandit approach for demand side management by offering price incentives. More precisely, a target mean consumption is set at each round and the mean consumption is modeled as a complex function of the distribution of prices sent and of some contextual variables such as the temperature, weather, and so on. The performance of our strategies is measured in quadratic losses through a regret criterion. We offer $T^{2/3}$ upper bounds on this regret (up to poly-logarithmic terms)---and even faster rates under stronger assumptions---for strategies inspired by standard strategies for contextual bandits (like LinUCB, see Li et al., 2010). Simulations on a real data set gathered by UK Power Networks, in which price incentives were offered, show that our strategies are effective and may indeed manage demand response by suitably picking the price levels

Algorithmes de bandits stochastiques pour la gestion de la demande électrique

As electricity is hard to store, the balance between production and consumption must be strictly maintained. With the integration of intermittent renewable energies into the production mix, the management of the balance becomes complex. At the same time, the deployment of smart meters suggests demand response. More precisely, sending signals - such as changes in the price of electricity - would encourage users to modulate their consumption according to the production of electricity. The algorithms used to choose these signals have to learn consumer reactions and, in the same time, to optimize them (exploration-exploration trade-off). Our approach is based on bandit theory and formalizes this sequential learning problem. We propose a first algorithm to control the electrical demand of a homogeneous population of consumers and offer T⅔ upper bound on its regret. Experiments on a real data set in which price incentives were offered illustrate these theoretical results. As a “full information” dataset is required to test bandit algorithms, a consumption data generator based on variational autoencoders is built. In order to drop the assumption of the population homogeneity, we propose an approach to cluster households according to their consumption profile. These different works are finally combined to propose and test a bandit algorithm for personalized demand side management.L'électricité se stockant difficilement à grande échelle, l'équilibre entre la production et la consommation doit être rigoureusement maintenu. Une gestion par anticipation de la demande se complexifie avec l'intégration au mix de production des énergies renouvelables intermittentes. Parallèlement, le déploiement des compteurs communicants permet d'envisager un pilotage dynamique de la consommation électrique. Plus concrètement, l'envoi de signaux - tels que des changements du prix de l'électricité – permettrait d'inciter les usagers à moduler leur consommation afin qu'elle s'ajuste au mieux à la production d'électricité. Les algorithmes choisissant ces signaux devront apprendre la réaction des consommateurs face aux envois tout en les optimisant (compromis exploration-exploitation). Notre approche, fondée sur la théorie des bandits, a permis de formaliser ce problème d'apprentissage séquentiel et de proposer un premier algorithme pour piloter la demande électrique d'une population homogène de consommateurs. Une borne supérieure d'ordre T⅔ a été obtenue sur le regret de cet algorithme. Des expériences réalisées sur des données de consommation de foyers soumis à des changements dynamiques du prix de l'électricité illustrent ce résultat théorique. Un jeu de données en « information complète » étant nécessaire pour tester un algorithme de bandits, un simulateur de données de consommation fondé sur les auto-encodeurs variationnels a ensuite été construit. Afin de s'affranchir de l'hypothèse d'homogénéité de la population, une approche pour segmenter les foyers en fonction de leurs habitudes de consommation est aussi proposée. Ces différents travaux sont finalement combinés pour proposer et tester des algorithmes de bandits pour un pilotage personnalisé de la consommation électrique

Online hierarchical forecasting for power consumption data

International audienceThis paper proposes a three-step approach to forecasting time series of electricity consumption at different levels of household aggregation. These series are linked by hierarchical constraintsglobal consumption is the sum of regional consumption, for example. First, benchmark forecasts are generated for all series using generalized additive models; second, for each series, the aggregation algorithm 'polynomially weighted average forecaster with multiple learning rates', introduced by Gaillard, Stoltz and van Erven in 2014, finds an optimal linear combination of the benchmarks; finally, the forecasts are projected onto a coherent subspace to ensure that the final forecasts satisfy the hierarchical constraints. By minimizing a regret criterion, we show that the aggregation and projection steps improve the root mean square error of the forecasts. Our approach is tested on household electricity consumption data; experimental results suggest that successive aggregation and projection steps improve the benchmark forecasts at different levels of household aggregation

Reimagining Demand-Side Management with Mean Field Learning

Integrating renewable energy into the power grid while balancing supply and demand is a complex issue, given its intermittent nature. Demand side management (DSM) offers solutions to this challenge. We propose a new method for DSM, in particular the problem of controlling a large population of electrical devices to follow a desired consumption signal. We model it as a finite horizon Markovian mean field control problem. We develop a new algorithm, MD-MFC, which provides theoretical guarantees for convex and Lipschitz objective functions. What distinguishes MD-MFC from the existing load control literature is its effectiveness in directly solving the target tracking problem without resorting to regularization techniques on the main problem. A non-standard Bregman divergence on a mirror descent scheme allows dynamic programming to be used to obtain simple closed-form solutions. In addition, we show that general mean-field game algorithms can be applied to this problem, which expands the possibilities for addressing load control problems. We illustrate our claims with experiments on a realistic data set

Efficient Model-Based Concave Utility Reinforcement Learning through Greedy Mirror Descent

Many machine learning tasks can be solved by minimizing a convex function of an occupancy measure over the policies that generate them. These include reinforcement learning, imitation learning, among others. This more general paradigm is called the Concave Utility Reinforcement Learning problem (CURL). Since CURL invalidates classical Bellman equations, it requires new algorithms. We introduce MD-CURL, a new algorithm for CURL in a finite horizon Markov decision process. MD-CURL is inspired by mirror descent and uses a non-standard regularization to achieve convergence guarantees and a simple closed-form solution, eliminating the need for computationally expensive projection steps typically found in mirror descent approaches. We then extend CURL to an online learning scenario and present Greedy MD-CURL, a new method adapting MD-CURL to an online, episode-based setting with partially unknown dynamics. Like MD-CURL, the online version Greedy MD-CURL benefits from low computational complexity, while guaranteeing sub-linear or even logarithmic regret, depending on the level of information available on the underlying dynamics