Pierre-Yves Massé

Pierre-Yves Massé, Maylis Duru, Benoit Couraud et al.

While Renewable Energy Communities (RECs) and Collective Self-Consumption (CSC) schemes have emerged as promising tools to accelerate renewable energy adoption and support the net-zero transition, their full potential can only be realised when complemented by demand-side flexibility that aligns consumption with renewable generation. Water storage heaters can function as distributed thermal storage, absorbing excess renewable energy at the community level. This work quantifies both the benefits of water storage heaters flexibility for energy consumers in a CSC community in France (such as energy bill reduction, increase of self-consumption), and the challenges related to the implementation and user acceptance. At the first stage, an annual simulation analysis is performed on a community of 41 households and a large solar PV plant, comparing a scenario without a CSC community, a scenario with a standard CSC community, and a scenario with a CSC community with flexibility from water storage heaters, which showed that an average benefit of 70euro/year per household can be achieved due to flexibility and an increase of 6% and 22% of solar PV community self-consumption and self-production respectively. In the second stage, we present the results of the real-world deployment in the community, analysing its technical performance and user reception, and examine the main factors shaping user engagement and satisfaction.

Pierre-Yves Massé, Yann Ollivier

We prove local convergence of several notable gradient descent algorithms used in machine learning, for which standard stochastic gradient descent theory does not apply directly. This includes, first, online algorithms for recurrent models and dynamical systems, such as \emph{Real-time recurrent learning} (RTRL) and its computationally lighter approximations NoBackTrack and UORO; second, several adaptive algorithms such as RMSProp, online natural gradient, and Adam with $β^2\to 1$.Despite local convergence being a relatively weak requirement for a new optimization algorithm, no local analysis was available for these algorithms, as far as we knew. Analysis of these algorithms does not immediately follow from standard stochastic gradient (SGD) theory. In fact, Adam has been proved to lack local convergence in some simple situations \citep{j.2018on}. For recurrent models, online algorithms modify the parameter while the model is running, which further complicates the analysis with respect to simple SGD.Local convergence for these various algorithms results from a single, more general set of assumptions, in the setup of learning dynamical systems online. Thus, these results can cover other variants of the algorithms considered.We adopt an "ergodic" rather than probabilistic viewpoint, working with empirical time averages instead of probability distributions. This is more data-agnostic and creates differences with respect to standard SGD theory, especially for the range of possible learning rates. For instance, with cycling or per-epoch reshuffling over a finite dataset instead of pure i.i.d.\ sampling with replacement, empirical averages of gradients converge at rate $1/T$ instead of $1/\sqrt{T}$ (cycling acts as a variance reduction method), theoretically allowing for larger learning rates than in SGD.

Pierre-Yves Massé, Yann Ollivier

The practical performance of online stochastic gradient descent algorithms is highly dependent on the chosen step size, which must be tediously hand-tuned in many applications. The same is true for more advanced variants of stochastic gradients, such as SAGA, SVRG, or AdaGrad. Here we propose to adapt the step size by performing a gradient descent on the step size itself, viewing the whole performance of the learning trajectory as a function of step size. Importantly, this adaptation can be computed online at little cost, without having to iterate backward passes over the full data.