A Lagrangian Duality Approach to Active Learning

TL;DR

This paper introduces ALLY, a novel active learning method that uses a primal-dual optimization framework to select the most informative samples based on dual variables, improving model performance efficiently.

Contribution

The paper proposes a Lagrangian duality-based active learning approach that effectively identifies informative samples through dual variables, enhancing data selection strategies.

Findings

ALLY outperforms traditional methods in classification and regression tasks.

Dual variables serve as effective proxies for sample informativeness.

The approach can generate maximally-informative synthetic samples.

Abstract

We consider the pool-based active learning problem, where only a subset of the training data is labeled, and the goal is to query a batch of unlabeled samples to be labeled so as to maximally improve model performance. We formulate the problem using constrained learning, where a set of constraints bounds the performance of the model on labeled samples. Considering a primal-dual approach, we optimize the primal variables, corresponding to the model parameters, as well as the dual variables, corresponding to the constraints. As each dual variable indicates how significantly the perturbation of the respective constraint affects the optimal value of the objective function, we use it as a proxy of the informativeness of the corresponding training sample. Our approach, which we refer to as Active Learning via Lagrangian dualitY, or ALLY, leverages this fact to select a diverse set of unlabeled samples with the highest estimated dual variables as our query set. We demonstrate the benefits of our approach in a variety of classification and regression tasks and discuss its limitations depending on the capacity of the model used and the degree of redundancy in the dataset. We also examine the impact of the distribution shift induced by active sampling and show that ALLY can be used in a generative mode to create novel, maximally-informative samples.