Bertrand Travacca

Bertrand Travacca, Greg Rybka, Kenji Shiraishi

We build upon previous work out of UC Berkeley's energy, controls, and applications laboratory (eCal) that developed a model for price prediction of the energy day-ahead market (DAM) and a stochastic load scheduling for distributed energy resources (DER) with DAM based objective\cite{Travacca}. In similar fashion to the work of Travacca et al., in this project we take the standpoint of a DER aggregator pooling a large number of electricity consumers - each of which have an electric vehicle and solar PV panels - to bid their pooled energy resources into the electricity markets. The primary contribution of this project is the optimization of an aggregated load schedule for participation in the California Independent System Operator (CAISO) real time (15-minute) electricity market. The goal of the aggregator is to optimally manage its pool of resources, particularly the flexible resources, in order to minimize its cost in the real time market. We achieves this through the use of a model predictive control scheme. A critical difference between the prior work in \cite{Travacca} is that the structure of the optimization problem is drastically different. Based upon our review of the current and public literature, no similar approaches exist. The main objective of this project were building methods. Nevertheless, to illustrate a simulation with 100 prosumers was realized. The results should therefore be taken with a grain of salt. We find that the Real Time operation does not substantially decrease or increase the total cost the aggregator faces in the RT market, but this is probably due to parameters that need further tuning and data, that need better processing.

Laurent El Ghaoui, Fangda Gu, Bertrand Travacca et al.

Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only implicitly defined. The implicit framework greatly simplifies the notation of deep learning, and opens up many new possibilities, in terms of novel architectures and algorithms, robustness analysis and design, interpretability, sparsity, and network architecture optimization.

Abhishek Halder, Kenneth F. Caluya, Bertrand Travacca et al.

We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN). The ordinary and stochastic differential equations associated with the HNN were introduced in the literature as analog optimizers, and were reported to exhibit good performance in numerical experiments. In this work, we point out that the deterministic HNN can be transcribed into Amari's natural gradient descent, and thereby uncover the explicit relation between the underlying Riemannian metric and the activation functions. By exploiting an equivalence between the natural gradient descent and the mirror descent, we show how the choice of activation function governs the geometry of the HNN dynamics. For the stochastic HNN, we show that the so-called "diffusion machine", while not a gradient flow itself, induces a gradient flow when lifted in the space of probability measures. We characterize this infinite dimensional flow as the gradient descent of certain free energy with respect to a Wasserstein metric that depends on the geodesic distance on the ground manifold. Furthermore, we demonstrate how this gradient flow interpretation can be used for fast computation via recently developed proximal algorithms.