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 accuracy under our proposed methods. Taken together, these findings establish a principled framework for adaptive combinatorial experimentation in multi-objective decision-making.
Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement
Sun Yat-sen University（中山大学）；Singapore Management University（新加坡管理大学）；Eindhoven University of Technology（埃因霍温理工大学）；National University of Singapore（新加坡国立大学）
On Pareto Optimality for Parametric Choice Bandits
Department of Management Science and Engineering, Tsinghua University, Beijing, China（清华大学管理科学与工程系，北京，中国）；Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore（新加坡国立大学工业系统工程与管理系，新加坡）
Locally Pareto-Optimal Interpretations for Black-Box Machine Learning Models
University of California at Berkeley（加州大学伯克利分校）；Indian Institute of Technology Bombay（印度班加罗尔理工学院）；Chalmers University of Technology and University of Gothenburg（查尔姆斯理工大学和哥德堡大学）
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Optimizing $CO_{2}$ Capture in Pressure Swing Adsorption Units: A Deep Neural Network Approach with Optimality Evaluation and Operating Maps for Decision-Making
Norwegian University of Science and Technology（挪威科技大学）
