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Bucketized Active Sampling for Learning ACOPF

Michael Klamkin, Mathieu Tanneau, Terrence W. K. Mak, Pascal Van Hentenryck

TL;DR

Bucketized Active Sampling (BAS) addresses the practical problem of training fast ACOPF proxies under time constraints by partitioning the input space into buckets and using a bucket-validation set to guide sample generation. A DNN-based predictor is trained within a BAS loop that adaptively adjusts the learning rate via patience-based scheduling and allocates labeling resources across buckets using acquisition scores. The key contributions are the BAS framework, bucketized validation for bucket-wise sampling decisions, and a suite of acquisition metrics including gradient-based and uncertainty-based variants, evaluated on large ACOPF benchmarks where BAS consistently achieves faster convergence and higher data efficiency than traditional active-learning baselines. The results demonstrate that distributing new samples across feasible, sensitive regions reduces wasted effort on infeasible inputs, enabling Just-in-Time learning for dynamically changing power grids and forecast scenarios.

Abstract

This paper considers optimization proxies for Optimal Power Flow (OPF), i.e., machine-learning models that approximate the input/output relationship of OPF. Recent work has focused on showing that such proxies can be of high fidelity. However, their training requires significant data, each instance necessitating the (offline) solving of an OPF. To meet the requirements of market-clearing applications, this paper proposes Bucketized Active Sampling (BAS), a novel active learning framework that aims at training the best possible OPF proxy within a time limit. BAS partitions the input domain into buckets and uses an acquisition function to determine where to sample next. By applying the same partitioning to the validation set, BAS leverages labeled validation samples in the selection of unlabeled samples. BAS also relies on an adaptive learning rate that increases and decreases over time. Experimental results demonstrate the benefits of BAS.

Bucketized Active Sampling for Learning ACOPF

TL;DR

Bucketized Active Sampling (BAS) addresses the practical problem of training fast ACOPF proxies under time constraints by partitioning the input space into buckets and using a bucket-validation set to guide sample generation. A DNN-based predictor is trained within a BAS loop that adaptively adjusts the learning rate via patience-based scheduling and allocates labeling resources across buckets using acquisition scores. The key contributions are the BAS framework, bucketized validation for bucket-wise sampling decisions, and a suite of acquisition metrics including gradient-based and uncertainty-based variants, evaluated on large ACOPF benchmarks where BAS consistently achieves faster convergence and higher data efficiency than traditional active-learning baselines. The results demonstrate that distributing new samples across feasible, sensitive regions reduces wasted effort on infeasible inputs, enabling Just-in-Time learning for dynamically changing power grids and forecast scenarios.

Abstract

This paper considers optimization proxies for Optimal Power Flow (OPF), i.e., machine-learning models that approximate the input/output relationship of OPF. Recent work has focused on showing that such proxies can be of high fidelity. However, their training requires significant data, each instance necessitating the (offline) solving of an OPF. To meet the requirements of market-clearing applications, this paper proposes Bucketized Active Sampling (BAS), a novel active learning framework that aims at training the best possible OPF proxy within a time limit. BAS partitions the input domain into buckets and uses an acquisition function to determine where to sample next. By applying the same partitioning to the validation set, BAS leverages labeled validation samples in the selection of unlabeled samples. BAS also relies on an adaptive learning rate that increases and decreases over time. Experimental results demonstrate the benefits of BAS.
Paper Structure (18 sections, 7 equations, 3 figures, 2 tables, 4 algorithms)

This paper contains 18 sections, 7 equations, 3 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. AC Optimal Power Flow
  4. Dataset Generation for OPF proxies
  5. Active Sampling
  6. Related Work
  7. Active Learning for ACOPF
  8. Active Learning: DNN Model
  9. The Active Learning Scheme for BAS
  10. Bucketized Active Sampling
  11. Patience-based Scheduling
  12. Experimental Evaluation
  13. Benchmarks
  14. Bucket-Validation Set Construction
  15. Learning Models
  16. ...and 3 more sections

Figures (3)

  • Figure 1: Illustration of traditional active sampling (top) and the proposed bucketized active sampling (bottom) methodologies. The sampling distribution $\mathfrak{D}_{U}$ is a uniform distribution over the two-dimensional set $[0,1]^2$ (denoted by the square box). Legend: $\bullet$ denotes an unlabeled data point; $\boldsymbol{\star}$ denotes a labeled data point in the bucket validation set; $\boldsymbol{\star}$ denotes a labeled data point that is added to the training set after active sampling.
  • Figure 2: Mean L1 Loss on testing set, averaged across 50 trials.
  • Figure 3: Mean training set distributions at termination.