# Learning to Ask: Decision Transformers for Adaptive Quantitative Group Testing

arXiv: https://arxiv.org/abs/2509.01723 · HTML: https://mlsanity.com/paper/2509.01723/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [Multi-Game Decision Transformers](https://mlsanity.com/paper/2205.15241/) (2022)
- [Prompting Decision Transformer for Few-Shot Policy Generalization](https://mlsanity.com/paper/2206.13499/) (2022)
- [Support Recovery in Universal One-bit Compressed Sensing](https://mlsanity.com/paper/2107.09091/) (2021)
- [Optimal Nested Test Plan for Combinatorial Quantitative Group Testing](https://mlsanity.com/paper/1407.2283/) (2014)
- [Approximate Message Passing with Rigorous Guarantees for Pooled Data and Quantitative Group Testing](https://mlsanity.com/paper/2309.15507/) (2023)
- [Improved Support Recovery in Universal One-bit Compressed Sensing](https://mlsanity.com/paper/2210.16657/) (2022)

## Abstract (arXiv)

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.