Paper #206

Title:

Minimax lower bounds for the two-armed bandit problem

Authors:

Sanjeev R. Kulkarni and Gábor Lugosi

Date:

February 1997

Abstract:

We obtain minimax lower bounds on the regret for the classical two--armed bandit problem. We provide a finite--sample minimax version of the well--known log $n$ asymptotic lower bound of Lai and Robbins. Also, in contrast to the log $n$ asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable configurations of the two arms. That is, we show that for {\sl every} allocation rule and for {\sl every} $n$, there is a configuration such that the regret at time $n$ is at least 1 -- $\epsilon$ times the regret of random guessing, where $\epsilon$ is any small positive constant.

Keywords:

Bandit problem, minimax lower bounds

JEL codes:

C12, C73

Area of Research:

Microeconomics

Published in:

IEEE Transactions on Automatic Control

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