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

arXiv: https://arxiv.org/abs/2608.02305 · HTML: https://mlsanity.com/paper/2608.02305/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 12 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [Learning to Maximize Mutual Information for Dynamic Feature Selection](https://mlsanity.com/paper/2301.00557/) (2023)
- [Active Feature Acquisition with Generative Surrogate Models](https://mlsanity.com/paper/2010.02433/) (2020)
- [Estimating Conditional Mutual Information for Dynamic Feature Selection](https://mlsanity.com/paper/2306.03301/) (2023)
- [Opportunistic Learning: Budgeted Cost-Sensitive Learning from Data Streams](https://mlsanity.com/paper/1901.00243/) (2019)
- [Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisition](https://mlsanity.com/paper/2302.13960/) (2023)
- [Evaluation of Active Feature Acquisition Methods for Time-varying Feature Settings](https://mlsanity.com/paper/2312.01530/) (2023)
- [Stochastic Encodings for Active Feature Acquisition](https://mlsanity.com/paper/2508.01957/) (2025)
- [Learning to Acquire Information](https://mlsanity.com/paper/1704.06131/) (2017)

## Abstract (arXiv)

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±2.17 and 4.39±1.10 percentage points (mean ± 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±0.74 points at four acquisitions; its mean paired gain across budgets 2,4,8,12,16 is 3.50±0.37 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.