[2602.24231] Adaptive Combinatorial Experimental Design: Pareto Optimality for Decision-Making and Inference

Computer Science > Machine Learning arXiv:2602.24231 (cs) [Submitted on 27 Feb 2026] Title:Adaptive Combinatorial Experimental Design: Pareto Optimality for Decision-Making and Inference Authors:Hongrui Xie, Junyu Cao, Kan Xu View a PDF of the paper titled Adaptive Combinatorial Experimental Design: Pareto Optimality for Decision-Making and Inference, by Hongrui Xie and Junyu Cao and Kan Xu View PDF HTML (experimental) Abstract:In this paper, we provide the first investigation into adaptive combinatorial experimental design, focusing on the trade-off between regret minimization and statistical power in combinatorial multi-armed bandits (CMAB). While minimizing regret requires repeated exploitation of high-reward arms, accurate inference on reward gaps requires sufficient exploration of suboptimal actions. We formalize this trade-off through the concept of Pareto optimality and establish equivalent conditions for Pareto-efficient learning in CMAB. We consider two relevant cases under different information structures, i.e., full-bandit feedback and semi-bandit feedback, and propose two algorithms MixCombKL and MixCombUCB respectively for these two cases. We provide theoretical guarantees showing that both algorithms are Pareto optimal, achieving finite-time guarantees on both regret and estimation error of arm gaps. Our results further reveal that richer feedback significantly tightens the attainable Pareto frontier, with the primary gains arising from improved estimation ac...