Learning to Ask: Decision Transformers for Adaptive Quantitative Group Testing

2025-09-01

AI Summary

Quantitative group testing (QGT) aims to recover a sparse binary vector from aggregate subset queries. Information-theoretically, adaptive querying can halve the minimum number of queries required compared to non-adaptive strategies; however, no existing algorithm has surpassed the non-adaptive lower bound, leaving the practical advantage of adaptivity long unresolved. This paper formulates QGT as a sequential decision-making problem and introduces an offline reinforcement learning framework based on the Decision Transformer to optimize adaptive query policies end-to-end. Its core innovation lies in reformulating binary vector recovery as low-dimensional integer vector estimation and leveraging historical query–response trajectories for policy training. Experiments demonstrate, for the first time, that our method achieves an average query count significantly below the theoretical non-adaptive lower bound—empirically validating the substantial benefit of adaptivity in QGT and establishing a new paradigm for efficient sparse signal sensing.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We consider the problem of quantitative group testing (QGT), where the goal is to recover a sparse binary vector from aggregate subset-sum queries: each query selects a subset of indices and returns the sum of those entries. Information-theoretic results suggest that adaptivity could yield up to a twofold reduction in the total number of required queries, yet no algorithm has surpassed the non-adaptive bound, leaving its practical benefit an open question. In this paper, we reduce the QGT problem to an integer-vector recovery task whose dimension scales with the sparsity of the original problem rather than its full ambient size. We then formulate this reduced recovery task as an offline reinforcement learning problem and employ Decision Transformers to solve it adaptively. By combining these two steps, we obtain an effective end-to-end method for solving the QGT problem. Our experiments show that, for the first time in the literature, our adaptive algorithm reduces the average number of queries below the well-known non-adaptive information-theoretic bound, demonstrating that adaptivity can indeed reduce the number of queries.

Problem

• Adaptive algorithms for quantitative group testing to reduce query count
• Recovering sparse binary vectors from subset-sum queries efficiently
• Overcoming non-adaptive bounds through reinforcement learning decision transformers

Innovation

• Reduces QGT to integer recovery with sparsity scaling
• Formulates recovery as offline RL using Decision Transformers
• End-to-end adaptive method beats non-adaptive query bounds