arXiv subjects

Julien Pallage

Publications and source records attributed to Julien Pallage.

5 recordsLinked to original sources

arXiv2026

An Accelerated Proximal Gradient Method for Bures-Wasserstein Space

We study composite optimization over the Bures--Wasserstein (BW) space of Gaussian measures. Our main observation is that a useful class of BW problems can be lifted into the Euclidean space of affine transport maps, such that the lifted problems can be solved efficiently using accelerated proximal gradient methods. For objectives whose smooth and nonsmooth components admit convex smooth and convex proximable affine lifts, respectively, our algorithm BW-FISTA achieves minimax-optimal objective gap $O(k^{-2})$ after $k$ iterations. We verify these regularity conditions for potential and interaction energies together with common spectral regularizers, and we treat stochastic gradients under a suitable noise model. As a principal application, we consider Gaussian variational inference with a log-concave, log-smooth target. Here, the resulting entropy term is handled by an efficient, exact proximal step, and we improve the previous rate of $O(k^{-1})$ to $O(k^{-2})$. We numerically verify this predicted boost with synthetic experiments.

math.OC↗

arXiv2025

Wasserstein Distributionally Robust Shallow Convex Neural Networks

In this work, we propose Wasserstein distributionally robust shallow convex neural networks (WaDiRo-SCNNs) to provide reliable nonlinear predictions when subject to adverse and corrupted datasets. Our approach is based on the reformulation of a new convex training program for ReLU-based shallow neural networks, which allows us to cast the problem into the order-1 Wasserstein distributionally robust optimization framework. Our training procedure is conservative, has low stochasticity, is solvable with open-source solvers, and is scalable to large industrial deployments. We provide out-of-sample performance guarantees, show that hard convex physical constraints can be enforced in the training program, and propose a mixed-integer convex post-training verification program to evaluate model stability. WaDiRo-SCNN aims to make neural networks safer for critical applications, such as in the energy sector. Finally, we numerically demonstrate our model's performance through both a synthetic experiment and a real-world power system application, viz., the prediction of hourly energy consumption in non-residential buildings within the context of virtual power plants, and evaluate its stability across standard regression benchmark datasets. The experimental results are convincing and showcase the strengths of the proposed model.

cs.LG↗

arXiv2025

Sliced-Wasserstein Distance-based Data Selection

We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying machine learning models in critical sectors, e.g., power systems, as it offers a conservative data selection and an optimal transport interpretation. To ensure the scalability of our method, we provide two efficient approximations. The first approximation processes reduced-cardinality representations of the datasets concurrently. The second makes use of a computationally light Euclidian distance approximation. Additionally, we open the first dataset showcasing localized critical peak rebate demand response in a northern climate. We present the filtering patterns of our method on synthetic datasets and numerically benchmark our method for training data selection. Finally, we employ our method as part of a first forecasting benchmark for our open-source dataset.

cs.LG↗

arXiv2024

Sliced-Wasserstein-based Anomaly Detection and Open Dataset for Localized Critical Peak Rebates

In this work, we present a new unsupervised anomaly (outlier) detection (AD) method using the sliced-Wasserstein metric. This filtering technique is conceptually interesting for MLOps pipelines deploying machine learning models in critical sectors, e.g., energy, as it offers a conservative data selection. Additionally, we open the first dataset showcasing localized critical peak rebate demand response in a northern climate. We demonstrate the capabilities of our method on synthetic datasets as well as standard AD datasets and use it in the making of a first benchmark for our open-source localized critical peak rebate dataset.

cs.LG↗

arXiv2024

Online Dynamic Submodular Optimization

We propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings. We consider the subset of problems in which the objective function is submodular. We propose the online submodular greedy algorithm (OSGA) which solves to optimality an approximation of the previous round loss function to avoid the NP-hardness of the original problem. We extend OSGA to a generic approximation function. We show that OSGA has a dynamic regret bound similar to the tightest bounds in online convex optimization with respect to the time horizon and the cumulative round optimum variation. For instances where no approximation exists or a computationally simpler implementation is desired, we design the online submodular projected gradient descent (OSPGD) by leveraging the Lovaśz extension. We obtain a regret bound that is akin to the conventional online gradient descent (OGD). Finally, we numerically test our algorithms in two power system applications: fast-timescale demand response and real-time distribution network reconfiguration.

math.OC↗