MALADY: Multiclass Active Learning with Auction Dynamics on Graphs

TL;DR

MALADY tackles the problem of data-efficient multiclass classification under limited labeling by integrating auction dynamics on similarity graphs with a graph-based SSL framework. It introduces a novel acquisition function derived from dual variables of modified assignment problems, ensuring uncertainty sampling near decision boundaries and incorporating exact class-size constraints. The approach is instantiated through a constrained energy minimization that reduces to a sequence of auction-based optimizations, enabling effective active learning with few labels across diverse datasets. The method demonstrates strong performance advantages over multiple baselines, highlighting its potential for data-efficient deployment in domains like healthcare, remote sensing, and NLP.

Abstract

Active learning enhances the performance of machine learning methods, particularly in semi-supervised cases, by judiciously selecting a limited number of unlabeled data points for labeling, with the goal of improving the performance of an underlying classifier. In this work, we introduce the Multiclass Active Learning with Auction Dynamics on Graphs (MALADY) framework which leverages the auction dynamics algorithm on similarity graphs for efficient active learning. In particular, we generalize the auction dynamics algorithm on similarity graphs for semi-supervised learning in [24] to incorporate a more general optimization functional. Moreover, we introduce a novel active learning acquisition function that uses the dual variable of the auction algorithm to measure the uncertainty in the classifier to prioritize queries near the decision boundaries between different classes. Lastly, using experiments on classification tasks, we evaluate the performance of our proposed method and show that it exceeds that of comparison algorithms.

Figures (11)

• Figure 1: The flowchart of the sequential active learning process. The process starts by training the underlying classifier using the initial labeled set $\mathcal{L}$. A query point $\mathcal{Q}\in\mathcal{U}$ is then selected based on the current acquisition function values. This query point is also labeled according to an oracle (human in the loop or a domain expert), and subsequently, the point is added to the current labeled data $\mathcal{L}$. This process continues until the desired number of points is reached in the labeled set $\mathcal{L}$.
• Figure 2: Auction Dynamics Semi-supervised learning (SSL) framework
• Figure 3: (a) Ground truth with six initial points, (b) Acquisition function value for our proposed acquisition function (\ref{['eqn:acquisition function']}) at Iteration 100, (c) Acquisition function value of uncertainty sampling settles_active_2012 with Laplace learning zhu2003semi at Iteration 100. Brighter regions of the plot indicate larger acquisition function values, and labeled points are marked in red circles; the query point for the current iteration is marked as a red star with a black outline. Notice that our acquisition function (b) focuses on all decision boundaries between oppositely labeled clusters, whereas standard uncertainty sampling (c) only focuses on a subset of these boundaries.
• Figure 4: The flowchart of our MALADY. Green box: Similarity graph construction using a chosen similarity function (section \ref{['Graph_Construction']}); Blue box: Active learning process using proposed acquisition function (section \ref{['acq function']}); Grey box: Auction dynamics method for semi-supervised inference (section \ref{['ssl']}). The result is the partition of the vertex set; Red box: When $|\mathcal{L}| = T$, the accuracy of the proposed method is computed.
• Figure 5: MALADY: Multiclass Active Learning with Auction DYnamics on Graphs