The Annals of Statistics
- Ann. Statist.
- Volume 22, Number 3 (1994), 1212-1221.
Two-Armed Dirichlet Bandits with Discounting
Sequential selections are to be made from two independent stochastic processes, or "arms." At each stage we choose which arm to observe based on past selections and observations. The observations on arm $i$ are conditionally i.i.d. given their marginal distribution $P_i$ which has a Dirichlet process prior with parameter $\alpha_i, i = 1, 2$. Future observations are discounted: at stage $m$, the payoff is $a_m$ times the observation $Z_m$ at that stage. The discount sequence $A_n = (a_1, a_2,\cdots, a_n, 0,0,\cdots)$ is a nonincreasing sequence of nonnegative numbers, where the "horizon" $n$ is finite. The objective is to maximize the total expected payoff $E(\sum^n_1a_iZ_i)$. It is shown that optimal strategies continue with an arm when it yields a sufficiently large observation, one larger than a "break-even observation." This generalizes results of Clayton and Berry, who considered two arms with one arm known and assumed $a_m = 1 \forall m \leq n$.
Ann. Statist., Volume 22, Number 3 (1994), 1212-1221.
First available in Project Euclid: 11 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62L05: Sequential design
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures
Chattopadhyay, Manas K. Two-Armed Dirichlet Bandits with Discounting. Ann. Statist. 22 (1994), no. 3, 1212--1221. doi:10.1214/aos/1176325626. https://projecteuclid.org/euclid.aos/1176325626