Electronic Journal of Statistics

Learning vs earning trade-off with missing or censored observations: The two-armed Bayesian nonparametric beta-Stacy bandit problem

Stefano Peluso, Antonietta Mira, and Pietro Muliere

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Existing Bayesian nonparametric methodologies for bandit problems focus on exact observations, leaving a gap in those bandit applications where censored observations are crucial. We address this gap by extending a Bayesian nonparametric two-armed bandit problem to right-censored data, where each arm is generated from a beta-Stacy process as defined by Walker and Muliere (1997). We first show some properties of the expected advantage of choosing one arm over the other, namely the monotonicity in the arm response and, limited to the case of continuous state space, the continuity in the right-censored arm response. We partially characterize optimal strategies by proving the existence of stay-with-a-winner and stay-with-a-winner/switch-on-a-loser break-even points, under non-restrictive conditions that include the special cases of the simple homogeneous process and the Dirichlet process. Numerical estimations and simulations for a variety of discrete and continuous state space settings are presented to illustrate the performance and flexibility of our framework.

Article information

Electron. J. Statist., Volume 11, Number 2 (2017), 3368-3406.

Received: December 2016
First available in Project Euclid: 6 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62N01: Censored data models

Creative Commons Attribution 4.0 International License.


Peluso, Stefano; Mira, Antonietta; Muliere, Pietro. Learning vs earning trade-off with missing or censored observations: The two-armed Bayesian nonparametric beta-Stacy bandit problem. Electron. J. Statist. 11 (2017), no. 2, 3368--3406. doi:10.1214/17-EJS1342. https://projecteuclid.org/euclid.ejs/1507255609

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