BRiG-AFA: Bellman Risk-to-Go Learning for Non-Myopic Active Feature Acquisition

2026-08-03

AI Summary

This work addresses the challenge of dynamically selecting the most informative unobserved features for each test sample under a limited acquisition budget to optimize predictive performance. The authors propose a supervised, non-myopic active feature acquisition (AFA) method that, for the first time, directly applies the Bellman equation to regress terminal classification risk. The approach constructs its objective by backward-fitting candidate conditional risks at each budget step, eliminating the need for reinforcement learning or generative modeling. Relying solely on supervised learning and greedy inference, the method is straightforward to deploy. Experiments demonstrate significant improvements: on Fashion-MNIST, it achieves a 10.20 ± 0.74 percentage point accuracy gain with four feature acquisitions, and across budgets {2, 4, 8, 12, 16}, it yields an average pairwise gain of 3.50 ± 0.37 percentage points over strong baselines.

Abstract

Active feature acquisition (AFA) asks which unobserved feature to measure next for each test instance under a budget. Greedy rules are easy to train but can overlook context features whose value is realized only through later acquisitions, while reinforcement-learning and generative approaches introduce difficult optimization or conditional-density estimation. We introduce \method, a deployable, supervised alternative that learns a separate candidate-conditioned risk-to-go function for every remaining budget. Starting from the one-step terminal classification risk, the functions are fitted backward with Bellman targets; inference greedily minimizes the learned terminal risk using only observed values, the mask, candidate identity, and remaining budget. A controlled non-myopic benchmark shows the expected mechanism: at budgets two and three, \method improves accuracy over its one-step ablation by $4.84\pm2.17$ and $4.39\pm1.10$ percentage points (mean $\pm$ standard error over five seeds). On Fashion-MNIST with 20 candidate pixels, it improves accuracy at every nontrivial reported budget on average, including $10.20\pm0.74$ points at four acquisitions; its mean paired gain across budgets $\{2,4,8,12,16\}$ is $3.50\pm0.37$ points. A three-seed MiniBooNE study is mixed at small budgets but positive at 8 and 16 acquisitions, identifying a current boundary rather than supporting a universal claim. These results establish a reproducible mechanism-level case for direct Bellman risk regression and delimit the experiments still needed for state-of-the-art comparison.

Problem

• Active Feature Acquisition
• Non-Myopic Decision Making
• Budgeted Learning
• Feature Selection
• Sequential Decision Making

Innovation

• Bellman risk-to-go
• non-myopic active feature acquisition
• supervised risk regression
• budget-aware learning
• feature acquisition policy