About the Authors

Yemin Yu

Roles Formal analysis, Investigation, Methodology, Software, Validation, Writing – original draft, Writing – review & editing

‡ Work primarily done during an internship at Microsoft Research.

Affiliation Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong

Emre Hayir

Roles Data curation, Formal analysis, Investigation, Methodology, Software, Writing – review & editing

Affiliation Microsoft Research, Cambridge, Boston, Massachusetts, United States of America

Neil Tenenholtz

Roles Conceptualization, Supervision, Writing – review & editing

Affiliation Microsoft Research, Cambridge, Boston, Massachusetts, United States of America

Lester Mackey

Roles Conceptualization, Supervision, Writing – review & editing

Affiliation Microsoft Research, Cambridge, Boston, Massachusetts, United States of America

Ying Wei

Roles Project administration, Supervision, Writing – review & editing

Affiliation Department of Computer Science, Zhejiang University, Hangzhou, China

David Alvarez-Melis

Roles Conceptualization, Methodology, Supervision, Writing – review & editing

Affiliation Microsoft Research, Cambridge, Boston, Massachusetts, United States of America

Ava P. Amini

Roles Conceptualization, Methodology, Project administration, Supervision, Writing – review & editing

Affiliation Microsoft Research, Cambridge, Boston, Massachusetts, United States of America

Alex X. Lu

Roles Conceptualization, Data curation, Methodology, Project administration, Supervision, Writing – original draft, Writing – review & editing

lualex@microsoft.com

Affiliation Microsoft Research, Cambridge, Boston, Massachusetts, United States of America

Competing Interests

I have read the journal’s policy and the authors of this manuscript have the following competing interests: E.H, N.T, L.M, D.A.M, A.P.M, and A.X.L are employees of and hold equity in Microsoft.