Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability

• 成果类型: Article
• 署名作者: Fryer, Roland; Harms, Philipp
• 署名单位: Harvard University; National Bureau of Economic Research; University of Freiburg
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2017.0863
• 发表日期: 2018
• 页码: 399-427
• 关键词: Strategic experimentation; diffusion-processes; multiarmed bandits; index policies; EXISTENCE

摘要

We present a two-armed bandit model of decision making under uncertainty where the expected return to investing in the risky arm increases when choosing that arm and decreases when choosing the safe arm. These dynamics are natural in applications such as human capital development, job search, and occupational choice. Using new insights from stochastic control, along with a monotonicity condition on the payoff dynamics, we show that optimal strategies in our model are stopping rules that can be characterized by an index which formally coincides with Gittins' index. Our result implies the indexability of a new class of restless bandit models.