Yanziyi(William) Zhang

Optimal Pilot Design

How should a decision maker experiment when the intervention used to learn also determines participants’ welfare? This paper studies a pilot that adaptively treats part of a finite population before committing to one treatment for everyone who remains. Treatment controls current payoffs and the speed of learning, while experimentation delays implementation and reduces its scale. Optimal pilot intensity is nondecreasing in confidence and the remaining population. The pilot stops at a confidence threshold that weakly falls as the population is depleted but converges to a strictly positive floor. Across histories with interior stopping, longer pilots end with weakly lower confidence and posterior expected per-capita implementation welfare: decisive histories stop early, while unresolved histories continue. Experimental treatment strictly exceeds its same-belief implementation benchmark and drops discontinuously at interior commitment. These results jointly characterise how to experiment, when to stop, and what to implement.

Optimal Learning with Uncertain Bias

While biased information sources differ in informativeness, people may be more or less confident about the sources’ slant. Learning choices are influenced by the trade-off between more informative and more confounded signals. This paper studies a dynamic information acquisition problem, where attention is distributed across sources with different precision and bias uncertainty. We characterise the optimal attention strategy. The set of consulted information sources gradually expands during the learning process. Precision alone determines the order in which sources enter the information diet, whereas bias uncertainty shapes the length of each learning stage. We further discuss how optimal learning adapts to changes in the information environment.

With Emiliano Sandri and Emma Tao

Learning with Paradigms: General Framework and Analysis of a simple case