Economics research seminar: Audrey Hu, City University of Hong Kong

Research topic: Optimal Allocation Strategies in a Discrete-Time Two-Armed Bandit Problem (by Audrey Hu and Liang Zou)

Presenter

Audrey Hu, City University of Hong Kong

Topic

Optimal Allocation Strategies in a Discrete-Time Two-Armed Bandit Problem (by Audrey Hu and Liang Zou)

abstract

This study addresses a theoretic-bandit problem involving a "safe" and a "risky" arm across countable periods. The agent, with one time unit per period, strategically allocates time between these two arms aiming at achieving a "breakthrough." The risky arm's type is unknown, which can be "good" or "bad," and breakthrough depends on proving it to be good. Breakthrough probability is an exponential function of the allocated time, given the risky arm is good. Departing from the "either-or" binary choices in previous studies, we explore smooth allocation strategies in the [0,1] range. A methodological contribution of this study lies in a problem transformation that enhances tractability, going beyond the standard Bellman-equation approach for bandit problems. The re-formulation of the problem allows us to obtain clear analytical solutions and comparative statics results. In general, we find that the optimal allocation plan significantly differs from binary strategies, and stopping after any finite periods of unsuccessful trials is suboptimal.

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