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 integration in MLOps pipelines deploying trustworthy machine learning models in critical sectors like energy. 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.

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 a new convex training program for ReLU shallow neural networks which allows us to cast the problem as an exact, tractable reformulation of its order-1 Wasserstein distributionally robust equivalent. Our training procedure is conservative by design, has low stochasticity, is solvable with open-source solvers, and is scalable to large industrial deployments. We provide out-of-sample performance guarantees and show that hard convex physical constraints can be enforced in the training program. WaDiRo-SCNN aims to make neural networks safer for critical applications, such as in the energy sector. Finally, we numerically demonstrate the performance of our model on a synthetic experiment and a real-world power system application, i.e., the prediction of non-residential buildings' hourly energy consumption. The experimental results are convincing and showcase the strengths of the proposed model.

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's 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. 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 Lov\'asz 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.