Adaptive Sequential Experiments with Unknown Information Arrival Processes

48 Pages Posted: 26 Jul 2021 Last revised: 22 Dec 2022

See all articles by Yonatan Gur

Yonatan Gur

Stanford Graduate School of Business

Ahmadreza Momeni

Stanford University

Date Written: January 11, 2022


Sequential experiments that are deployed in a broad range of practices are characterized by an exploration–exploitation tradeoff that is well understood when in each time period feedback is received only on the action that was selected in that period. However, in many practical settings additional information may become available between decision epochs. We study the performance one may achieve when leveraging such auxiliary information, and the design of algorithms that effectively do so without prior knowledge of the information arrival process. Our formulation considers a broad class of distributions that are informative about mean rewards from actions, and allows auxiliary observations from these distributions to arrive according to an arbitrary and a priori unknown process. When it is known how to map auxiliary observations to mean reward estimates, we characterize the best achievable performance as a function of the information arrival process. In terms of achieving optimal performance, we establish that upper confidence bound and Thompson sampling algorithms possess natural robustness with respect to the information arrival process, which uncovers a novel property of these popular algorithms. When the mappings connecting auxiliary observations and rewards are a priori unknown, we characterize a necessary and sufficient condition under which auxiliary information allows performance improvement, and devise an adaptive policy (termed 2UCBs) that guarantees near optimality. We use data from a large media site to analyze the value that may be captured by leveraging auxiliary observations in the design of content recommendations. Our study highlights the importance of utilizing auxiliary information in the design of sequential experiments, and characterizes how salient features of the auxiliary information stream impact performance. Our study also emphasizes the risk in processing auxiliary information using non-adaptive approaches that are predicated on correct interpretation of this information, as opposed to deploying flexible, adaptive methods.

Keywords: Sequential experiments, online learning, multi-armed bandits, transfer learning, minimax complexity, adaptive algorithms, product recommendations

JEL Classification: C44, C45, C9

Suggested Citation

Gur, Yonatan and Momeni, Ahmadreza, Adaptive Sequential Experiments with Unknown Information Arrival Processes (January 11, 2022). Manufacturing & Service Operations Management, 24 (5), 2666-2684, Available at SSRN: or

Yonatan Gur (Contact Author)

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Ahmadreza Momeni

Stanford University ( email )

Stanford, CA 94305
United States

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