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Amortized Active Learning for Nonparametric Functions

Cen-You Li, Marc Toussaint, Barbara Rakitsch, Christoph Zimmer

TL;DR

This work tackles efficient active learning for nonparametric regression by introducing an amortized learning framework. A neural policy is trained offline on GP-simulated tasks to propose data labels, enabling zero-shot, real-time AL deployment without iterative GP updates or acquisition optimization. The authors formulate differentiable AL objectives under a GP prior, employ Fourier features to approximate GP samples, and demonstrate that nonmyopic amortized AL matches the accuracy of traditional GP AL while vastly reducing query time across multiple benchmarks and real datasets. The approach delivers practical speedups for low-data regression tasks and showcases robust generalization across 1D and 2D problems with real-world data.

Abstract

Active learning (AL) is a sequential learning scheme aiming to select the most informative data. AL reduces data consumption and avoids the cost of labeling large amounts of data. However, AL trains the model and solves an acquisition optimization for each selection. It becomes expensive when the model training or acquisition optimization is challenging. In this paper, we focus on active nonparametric function learning, where the gold standard Gaussian process (GP) approaches suffer from cubic time complexity. We propose an amortized AL method, where new data are suggested by a neural network which is trained up-front without any real data (Figure 1). Our method avoids repeated model training and requires no acquisition optimization during the AL deployment. We (i) utilize GPs as function priors to construct an AL simulator, (ii) train an AL policy that can zero-shot generalize from simulation to real learning problems of nonparametric functions and (iii) achieve real-time data selection and comparable learning performances to time-consuming baseline methods.

Amortized Active Learning for Nonparametric Functions

TL;DR

This work tackles efficient active learning for nonparametric regression by introducing an amortized learning framework. A neural policy is trained offline on GP-simulated tasks to propose data labels, enabling zero-shot, real-time AL deployment without iterative GP updates or acquisition optimization. The authors formulate differentiable AL objectives under a GP prior, employ Fourier features to approximate GP samples, and demonstrate that nonmyopic amortized AL matches the accuracy of traditional GP AL while vastly reducing query time across multiple benchmarks and real datasets. The approach delivers practical speedups for low-data regression tasks and showcases robust generalization across 1D and 2D problems with real-world data.

Abstract

Active learning (AL) is a sequential learning scheme aiming to select the most informative data. AL reduces data consumption and avoids the cost of labeling large amounts of data. However, AL trains the model and solves an acquisition optimization for each selection. It becomes expensive when the model training or acquisition optimization is challenging. In this paper, we focus on active nonparametric function learning, where the gold standard Gaussian process (GP) approaches suffer from cubic time complexity. We propose an amortized AL method, where new data are suggested by a neural network which is trained up-front without any real data (Figure 1). Our method avoids repeated model training and requires no acquisition optimization during the AL deployment. We (i) utilize GPs as function priors to construct an AL simulator, (ii) train an AL policy that can zero-shot generalize from simulation to real learning problems of nonparametric functions and (iii) achieve real-time data selection and comparable learning performances to time-consuming baseline methods.
Paper Structure (29 sections, 14 equations, 8 figures, 1 table, 4 algorithms)

This paper contains 29 sections, 14 equations, 8 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Contributions:
  3. Related works:
  4. Problem Statement
  5. Assumptions:
  6. AL with a priori trained policy $\phi$
  7. Training objectives:
  8. Simulated AL:
  9. NN structure:
  10. Complexity:
  11. Experiments
  12. NN training
  13. Benchmark tasks
  14. Sin function (1D):
  15. Branin function (2D):
  16. ...and 14 more sections

Figures (8)

  • Figure 1: The conventional AL of a GP regression relies on computationally expensive (orange) GP fitting and acquisition optimization. Our amortized AL approach meta trains a NN active learner up-front, purely from synthetic data, allowing a fast, easy and real-time applicable (green) AL deployment.
  • Figure 1: Classical AL
  • Figure 2: AL with NN Policy
  • Figure 2: A policy is trained with \ref{['alg-nonmyopic_al_training']} together with the entropy or regularized entropy objective. See \ref{['table-training_time']} for the training time. A myopic policy is trained with \ref{['alg-myopic_al_training']}, where detail is given in \ref{['sectionS3-losses_details']}. $N_{init}=1$. For 1D problems (Sin & airline passenger), $T=10$, which means a total of $11$ observations. For 2D problems, $T=20$, which means a total of $21$ observations. For each benchmark problem, a star is marked if RMSE of the method is significantly smaller than Random (Wilcoxon signed-rank test, p-value threshold $0.05$). The time only takes querying time into account. For GP AL method, GP predictive distributions are necessary for the acquisition function and thus the GP training time is part of the querying time (\ref{['figure1', 'alg-classical_al']}). Output labeling time is excluded.
  • Figure 3: Nonmyopic AL training
  • ...and 3 more figures