Security-Constrained Optimal Power Flow (SCOPF) plays a crucial role in power grid stability but becomes increasingly complex as systems grow. This paper introduces PDL-SCOPF, a self-supervised end-to-end primal-dual learning framework for producing near-optimal solutions to large-scale SCOPF problems in milliseconds. Indeed, PDL-SCOPF remedies the limitations of supervised counterparts that rely on training instances with their optimal solutions, which becomes impractical for large-scale SCOPF problems. PDL-SCOPF mimics an Augmented Lagrangian Method (ALM) for training primal and dual networks that learn the primal solutions and the Lagrangian multipliers, respectively, to the unconstrained optimizations. In addition, PDL-SCOPF incorporates a repair layer to ensure the feasibility of the power balance in the nominal case, and a binary search layer to compute, using the Automatic Primary Response (APR), the generator dispatches in the contingencies. The resulting differentiable program can then be trained end-to-end using the objective function of the SCOPF and the power balance constraints of the contingencies. Experimental results demonstrate that the PDL-SCOPF delivers accurate feasible solutions with minimal optimality gaps. The framework underlying PDL-SCOPF aims at bridging the gap between traditional optimization methods and machine learning, highlighting the potential of self-supervised end-to-end primal-dual learning for large-scale optimization tasks.

Reliability Assessment Commitment (RAC) Optimization is increasingly important in grid operations due to larger shares of renewable generations in the generation mix and increased prediction errors. Independent System Operators (ISOs) also aim at using finer time granularities, longer time horizons, and possibly stochastic formulations for additional economic and reliability benefits. The goal of this paper is to address the computational challenges arising in extending the scope of RAC formulations. It presents RACLearn that (1) uses a Graph Neural Network (GNN) based architecture to predict generator commitments and active line constraints, (2) associates a confidence value to each commitment prediction, (3) selects a subset of the high-confidence predictions, which are (4) repaired for feasibility, and (5) seeds a state-of-the-art optimization algorithm with feasible predictions and active constraints. Experimental results on exact RAC formulations used by the Midcontinent Independent System Operator (MISO) and an actual transmission network (8965 transmission lines, 6708 buses, 1890 generators, and 6262 load units) show that the RACLearn framework can speed up RAC optimization by factors ranging from 2 to 4 with negligible loss in solution quality.

This paper reconsiders end-to-end learning approaches to the Optimal Power Flow (OPF). Existing methods, which learn the input/output mapping of the OPF, suffer from scalability issues due to the high dimensionality of the output space. This paper first shows that the space of optimal solutions can be significantly compressed using principal component analysis (PCA). It then proposes Compact Learning, a new method that learns in a subspace of the principal components before translating the vectors into the original output space. This compression reduces the number of trainable parameters substantially, improving scalability and effectiveness. Compact Learning is evaluated on a variety of test cases from the PGLib with up to 30,000 buses. The paper also shows that the output of Compact Learning can be used to warm-start an exact AC solver to restore feasibility, while bringing significant speed-ups.

This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must balance optimality and feasibility conditions. Supervised learning methods often approach this challenge by training the model on a large collection of pre-solved instances. This paper takes a different route and proposes the idea of Primal-Dual Learning (PDL), a self-supervised training method that does not require a set of pre-solved instances or an optimization solver for training and inference. Instead, PDL mimics the trajectory of an Augmented Lagrangian Method (ALM) and jointly trains primal and dual neural networks. Being a primal-dual method, PDL uses instance-specific penalties of the constraint terms in the loss function used to train the primal network. Experiments show that, on a set of nonlinear optimization benchmarks, PDL typically exhibits negligible constraint violations and minor optimality gaps, and is remarkably close to the ALM optimization. PDL also demonstrated improved or similar performance in terms of the optimality gaps, constraint violations, and training times compared to existing approaches.

Estimating the data density is one of the challenging problems in deep learning. In this paper, we present a simple yet effective method for estimating the data density using a deep neural network and the Donsker-Varadhan variational lower bound on the KL divergence. We show that the optimal critic function associated with the Donsker-Varadhan representation on the KL divergence between the data and the uniform distribution can estimate the data density. We also present the deep neural network-based modeling and its stochastic learning. The experimental results and possible applications of the proposed method demonstrate that it is competitive with the previous methods and has a lot of possibilities in applied to various applications.

Building a scalable machine learning system for unsupervised anomaly detection via representation learning is highly desirable. One of the prevalent methods is using a reconstruction error from variational autoencoder (VAE) via maximizing the evidence lower bound. We revisit VAE from the perspective of information theory to provide some theoretical foundations on using the reconstruction error, and finally arrive at a simpler and more effective model for anomaly detection. In addition, to enhance the effectiveness of detecting anomalies, we incorporate a practical model uncertainty measure into the metric. We show empirically the competitive performance of our approach on benchmark datasets.