Noisy Optimization Complexity Under Locality Assumption

International audienceIn spite of various recent publications on the subject, there are still gaps between upper and lower bounds in evolutionary optimization for noisy objective function. In this paper we reduce the gap, and get tight bounds within logarithmic factors in the case of small noise and no long-distance influence on the objective function

Conv-NILM-Net, a causal and multi-appliance model for energy source separation

Non-Intrusive Load Monitoring (NILM) seeks to save energy by estimating individual appliance power usage from a single aggregate measurement. Deep neural networks have become increasingly popular in attempting to solve NILM problems. However most used models are used for Load Identification rather than online Source Separation. Among source separation models, most use a single-task learning approach in which a neural network is trained exclusively for each appliance. This strategy is computationally expensive and ignores the fact that multiple appliances can be active simultaneously and dependencies between them. The rest of models are not causal, which is important for real-time application. Inspired by Convtas-Net, a model for speech separation, we propose Conv-NILM-net, a fully convolutional framework for end-to-end NILM. Conv-NILM-net is a causal model for multi appliance source separation. Our model is tested on two real datasets REDD and UK-DALE and clearly outperforms the state of the art while keeping a significantly smaller size than the competing models.Comment: Published in ECMLPKDD 2022, MLBEM worksho

Variance Reduction in Population-Based Optimization: Application to Unit Commitment

forthcomingInternational audienceWe consider noisy optimization and some traditional variance reduction techniques aimed at improving the convergence rate, namely (i) common random numbers (CRN), which is relevant for population-based noisy optimization and (ii) stratified sampling, which is relevant for most noisy optimization problems. We present artificial models of noise for which common random numbers are very efficient, and artificial models of noise for which common random numbers are detrimental. We then experiment on a desperately expensive unit commitment problem. As expected, stratified sampling is never detrimental. Nonetheless, in practice, common random numbers provided, by far, most of the improvement

L'hybridation de méthodes d'optimisation dynamique

This thesis is dedicated to sequential decision making (also known as multistage optimization) in uncertain complex environments. Studied algorithms are essentially applied to electricity production ("Unit Commitment" problems) and energy stock management (hydropower), in front of stochastic demand and water inflows. The manuscript is divided in 7 chapters and 4 parts: Part I, "General Introduction", Part II, "Background Review", Part III, "Contributions" and Part IV, "General Conclusion". This first chapter (Part I) introduces the context and motivation of our work, namely energy stock management. "Unit Commitment" (UC) problems are a classical example of "Sequential Decision Making" problem (SDM) applied to energy stock management. They are the central application of our work and in this chapter we explain main challenges arising with them (e.g. stochasticity, constraints, curse of dimensionality, ...). Classical frameworks for SDM problems are also introduced and common mistakes arising with them are be discussed. We also emphasize the consequences of these - too often neglected - mistakes and the importance of not underestimating their effects. Along this chapter, fundamental definitions commonly used with SDM problems are described. An overview of our main contributions concludes this first chapter. The second chapter (Part II) is a background review of the most classical algorithms used to solve SDM problems. Since the applications we try to solve are stochastic, we there focus on resolution methods for stochastic problems. We begin our study with classical Dynamic Programming methods to solve "Markov Decision Processes" (a special kind of SDM problems with Markovian random processes). We then introduce "Direct Policy Search", a widely used method in the Reinforcement Learning community. A distinction is be made between "Value Based" and "Policy Based" exploration methods. The third chapter (Part II) extends the previous one by covering the most classical algorithms used to solve UC's subtleties. It contains a state of the art of algorithms commonly used for energy stock management, mainly "Model Predictive Control", "Stochastic Dynamic Programming" and "Stochastic Dual Dynamic Programming". We briefly overview distinctive features and limitations of these methods. The fourth chapter (Part III) presents our main contribution: a new algorithm named "Direct Value Search" (DVS), designed to solve large scale unit commitment problems. We describe how it outperforms classical methods presented in the third chapter. We show that DVS is an "anytime" algorithm (users immediately get approximate results) which can handle large state spaces and large action spaces with non convexity constraints, and without assumption on the random process. Moreover, we explain how DVS can reduce modelling errors and can tackle challenges described in the first chapter, working on the "real" detailed problem without "cast" into a simplified model. Noisy optimisation is a key component of DVS algorithm; the fifth chapter (Part III) is dedicated to it. In this chapter, some theoretical convergence rate are studied and new convergence bounds are proved - under some assumptions and for given families of objective functions. Some variance reduction techniques aimed at improving the convergence rate of graybox noisy optimization problems are studied too in the last part of this chapter. Chapter sixth (Part III) is devoted to non-quasi-convex optimization. We prove that a variant of evolution strategy can reach a log-linear convergence rate with non-quasi-convex objective functions. Finally, the seventh chapter (Part IV) concludes and suggests some directions for future work.Dans ce manuscrit de thèse, mes travaux portent sur la combinaison de méthodes pour la prise de décision séquentielle (plusieurs étapes de décision corrélées) dans des environnements complexes et incertains. Les méthodes mises au point sont essentiellement appliquées à des problèmes de gestion et de production d'électricité tels que l'optimisation de la gestion des stocks d'énergie dans un parc de production pour anticiper au mieux la fluctuation de la consommation des clients.Le manuscrit comporte 7 chapitres regroupés en 4 parties : Partie I, « Introduction générale », Partie II, « État de l'art », Partie III, « Contributions » et Partie IV, « Conclusion générale ».Le premier chapitre (Partie I) introduit le contexte et les motivations de mes travaux, à savoir la résolution de problèmes d' « Unit commitment », c'est à dire l'optimisation des stratégies de gestion de stocks d'énergie dans les parcs de production d'énergie. Les particularités et les difficultés sous-jacentes à ces problèmes sont décrites ainsi que le cadre de travail et les notations utilisées dans la suite du manuscrit.Le second chapitre (Partie II) dresse un état de l'art des méthodes les plus classiques utilisées pour la résolution de problèmes de prise de décision séquentielle dans des environnements incertains. Ce chapitre introduit des concepts nécessaires à la bonne compréhension des chapitres suivants (notamment le chapitre 4). Les méthodes de programmation dynamique classiques et les méthodes de recherche de politique directe y sont présentées.Le 3e chapitre (Partie II) prolonge le précédent en dressant un état de l'art des principales méthodes d’optimisation spécifiquement adaptées à la gestion des parcs de production d'énergie et à leurs subtilités. Ce chapitre présente entre autre les méthodes MPC (Model Predictive Control), SDP (Stochastic Dynamic Programming) et SDDP (Stochastic Dual Dynamic Programming) avec pour chacune leurs particularités, leurs avantages et leurs limites. Ce chapitre complète le précédent en introduisant d'autres concepts nécessaires à la bonne compréhension de la suite du manuscrit.Le 4e chapitre (Partie III) contient la principale contribution de ma thèse : un nouvel algorithme appelé « Direct Value Search » (DVS) créé pour résoudre des problèmes de prise de décision séquentielle de grande échelle en milieu incertain avec une application directe aux problèmes d' « Unit commitment ». Ce chapitre décrit en quoi ce nouvel algorithme dépasse les méthodes classiques présentées dans le 3e chapitre. Cet algorithme innove notamment par sa capacité à traiter des grands espaces d'actions contraints dans un cadre non-linéaire, avec un grand nombre de variables d'état et sans hypothèse particulière quant aux aléas du système optimisé (c'est à dire applicable sur des problèmes où les aléas ne sont pas nécessairement Markovien).Le 5e chapitre (Partie III) est consacré à un concept clé de DVS : l'optimisation bruitée. Ce chapitre expose une nouvelle borne théorique sur la vitesse de convergence des algorithmes d'optimisation appliqués à des problèmes bruités vérifiant certaines hypothèses données. Des méthodes de réduction de variance sont également étudiées et appliquées à DVS pour accélérer sensiblement sa vitesse de convergence.Le 6e chapitre (Partie III) décrit un résultat mathématique sur la vitesse de convergence linéaire d’un algorithme évolutionnaire appliqué à une famille de fonctions non quasi-convexes. Dans ce chapitres, il est prouvé que sous certaines hypothèses peu restrictives sur la famille de fonctions considérée, l'algorithme présenté atteint une vitesse de convergence linéaire.Le 7e chapitre (Partie IV) conclut ce manuscrit en résumant mes contributions et en dressant quelques pistes de recherche intéressantes à explorer

Noisy Optimization Complexity Under Locality Assumption

International audienceIn spite of various recent publications on the subject, there are still gaps between upper and lower bounds in evolutionary optimization for noisy objective function. In this paper we reduce the gap, and get tight bounds within logarithmic factors in the case of small noise and no long-distance influence on the objective function

Optimization of Energy Policies Using Direct Value Search

National audienceDirect Policy Search is a widely used tool for reinforcement learning; however, it is usually not suitable for handling high-dimensional constrained action spaces such as those arising in power system control (unit commitmen problems). We propose Direct Value Search, an hybridization of DPS with Bellman decomposition techniques. We prove runtime properties, and apply the results to an energy management problem

Direct model predictive control

International audienceDue to simplicity and convenience, Model Predictive Control, which consists in optimizing future decisions based on a pessimistic deterministic forecast of the random processes, is one of the main tools for stochastic control. Yet, it suffers from a large computation time, unless the tactical horizon (i.e. the number of future time steps included in the optimization) is strongly reduced, and lack of real stochasticity handling. We here propose a combination between Model Predictive Control and Direct Policy Search

Conv-NILM-Net, a causal and multi-appliance model for energy source separation

International audienceNon-Intrusive Load Monitoring (NILM) seeks to save energy by estimating individual appliance power usage from a single aggregate measurement. Deep neural networks have become increasingly popular in attempting to solve NILM problems. However most used models are used for Load Identification rather than online Source Separation. Among source separation models, most use a single-task learning approach in which a neural network is trained exclusively for each appliance. This strategy is computationally expensive and ignores the fact that multiple appliances can be active simultaneously and dependencies between them. The rest of models are not causal, which is important for real-time application. Inspired by Convtas-Net, a model for speech separation, we propose Conv-NILM-net, a fully convolutional framework for end-to-end NILM. Conv-NILM-net is a causal model for multi appliance source separation. Our model is tested on two real datasets REDD and UK-DALE and clearly outperforms the state of the art while keeping a significantly smaller size than the competing models

Evolutionary Cutting Planes

forthcomingInternational audienceThe Cutting Plane method is a simple and efficient method for optimizing convex functions in which subgradients are available. This paper proposes several methods for parallelizing it, in particular using a typically evolutionary method, and compares them experimentally in a well-conditioned and ill-conditioned settings