Near-Optimal Active Learning of Halfspaces via Query Synthesis in the Noisy Setting

TL;DR

This paper introduces a dimension coupling framework for active learning of linear classifiers via query synthesis, achieving near-optimal query complexity and linear scalability in noisy settings, with significant improvements over prior methods.

Contribution

The paper presents a novel dimension coupling framework that reduces high-dimensional active learning to low-dimensional problems, providing theoretical guarantees and practical efficiency.

Findings

DC framework is resilient to noise.

Query complexity is near optimal, within a constant factor.

DC outperforms prior methods in query efficiency and speed.

Abstract

In this paper, we consider the problem of actively learning a linear classifier through query synthesis where the learner can construct artificial queries in order to estimate the true decision boundaries. This problem has recently gained a lot of interest in automated science and adversarial reverse engineering for which only heuristic algorithms are known. In such applications, queries can be constructed de novo to elicit information (e.g., automated science) or to evade detection with minimal cost (e.g., adversarial reverse engineering). We develop a general framework, called dimension coupling (DC), that 1) reduces a d-dimensional learning problem to d-1 low dimensional sub-problems, 2) solves each sub-problem efficiently, 3) appropriately aggregates the results and outputs a linear classifier, and 4) provides a theoretical guarantee for all possible schemes of aggregation. The proposed method is proved resilient to noise. We show that the DC framework avoids the curse of dimensionality: its computational complexity scales linearly with the dimension. Moreover, we show that the query complexity of DC is near optimal (within a constant factor of the optimum algorithm). To further support our theoretical analysis, we compare the performance of DC with the existing work. We observe that DC consistently outperforms the prior arts in terms of query complexity while often running orders of magnitude faster.