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

TL;DR

This paper introduces a framework for adaptive combinatorial experimental design that balances regret minimization and statistical inference, using Pareto optimality to guide decision-making in multi-armed bandit problems.

Contribution

It formalizes the Pareto optimality concept for CMAB, proposes two algorithms with theoretical guarantees, and analyzes the impact of feedback richness on the Pareto frontier.

Findings

Both algorithms are Pareto optimal with finite-time guarantees.

Richer feedback improves the Pareto frontier and estimation accuracy.

The framework advances adaptive experimentation in multi-objective decision-making.

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 accuracy under our proposed methods. Taken together, these findings establish a principled framework for adaptive combinatorial experimentation in multi-objective decision-making.