Batched Bandit Problems

26 Pages Posted: 31 Oct 2015

See all articles by Vianney Perchet

Vianney Perchet

Université Paris VII Denis Diderot

Philippe Rigollet

Massachusetts Institute of Technology (MIT)

Sylvain Chassang

New York University (NYU) - Department of Economics

Erik Snowberg

California Institute of Technology - Division of the Humanities and Social Sciences; National Bureau of Economic Research (NBER)

Date Written: October 29, 2015

Abstract

Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. Our results show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits.

Keywords: Multi-armed bandit problems, regret bounds, batches, multi-phase allocation, grouped clinical trials, sample size determination, switching cost

Suggested Citation

Perchet, Vianney and Rigollet, Philippe and Chassang, Sylvain and Snowberg, Erik, Batched Bandit Problems (October 29, 2015). Princeton University William S. Dietrich II Economic Theory Center Research Paper No. 074_2015. Available at SSRN: https://ssrn.com/abstract=2683578 or http://dx.doi.org/10.2139/ssrn.2683578

Vianney Perchet

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Philippe Rigollet

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Sylvain Chassang (Contact Author)

New York University (NYU) - Department of Economics ( email )

19 West 4th Street
New York, NY 10012
United States

Erik Snowberg

California Institute of Technology - Division of the Humanities and Social Sciences ( email )

1200 East California Blvd.
Pasadena, CA 91125
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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