Learning to Ask: Decision Transformers for Adaptive Quantitative Group Testing

W e 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. W e then formulate this reduced recovery task as an offline reinforcement learning problem and employ Decision T ransformers 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. Quantitative Group T esting (QGT) is the problem of detecting k defective items within a collection of n items through a series of tests conducted on m distinct pools. Each test returns an integer indicating how many defective items are present in the pooled subset.