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American mathematician From Wikipedia, the free encyclopedia
Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician. He did research in topology, measure theory, statistics, and a variety of other fields.
 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (May 2022) |
Herbert Ellis Robbins | |
|---|---|
Herbert Robbins visiting Purdue in 1966 | |
| Born | January 12, 1915 New Castle, Pennsylvania, US |
| Died | February 12, 2001 (aged 86) Princeton, New Jersey, US |
| Alma mater | Harvard University |
| Scientific career | |
| Institutions | |
| Thesis | On the Classification of the Maps of a 2-Complex into a Space (1938) |
| Doctoral advisor | Hassler Whitney |
| Doctoral students | |
He was the co-author, with Richard Courant, of What is Mathematics?. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture (since proved) that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem (of optimal stopping).
Robbins was born in New Castle, Pennsylvania.
As an undergraduate, Robbins attended Harvard University, where Marston Morse influenced him to become interested in mathematics. Robbins received a doctorate from Harvard in 1938 under the supervision of Hassler Whitney and was an instructor at New York University from 1939 to 1941. After World War II, Robbins taught at the University of North Carolina at Chapel Hill from 1946 to 1952, where he was one of the original members of the department of mathematical statistics, then spent a year at the Institute for Advanced Study. In 1953, he became a professor of mathematical statistics at Columbia University. He retired from full-time activity at Columbia in 1985 and was then a professor at Rutgers University until his retirement in 1997. He has 567 descendants listed at the Mathematics Genealogy Project.
In 1955, Robbins introduced empirical Bayes methods at the Third Berkeley Symposium on Mathematical Statistics and Probability. Robbins was also one of the inventors of the first stochastic approximation algorithm, the Robbins–Monro method, and worked on the theory of power-one tests and optimal stopping. In 1985, in the paper "Asymptotically efficient adaptive allocation rules", with TL Lai, he constructed uniformly convergent population selection policies for the multi-armed bandit problem that possess the fastest rate of convergence to the population with highest mean, for the case that the population reward distributions are the one-parameter exponential family. These policies were simplified in the 1995 paper "Sequential choice from several populations", with Michael Katehakis.
He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences and was past president of the Institute of Mathematical Statistics.
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