Robust Experimentation in the Continuous Time Bandit Problem
This work addresses robust experimentation strategies for decision-makers facing uncertainty in economic or AI contexts, but it is incremental as it builds on existing bandit and ambiguity models.
The paper tackles the problem of decision-making under ambiguity in a continuous-time two-armed bandit setting, showing that ambiguity aversion increases the threshold for exploring the ambiguous arm and that providing unambiguous information further raises this threshold, leading to more conservative exploration.
We study the experimentation dynamics of a decision maker (DM) in a two-armed bandit setup (Bolton and Harris (1999)), where the agent holds ambiguous beliefs regarding the distribution of the return process of one arm and is certain about the other one. The DM entertains Multiplier preferences a la Hansen and Sargent (2001), thus we frame the decision making environment as a two-player differential game against nature in continuous time. We characterize the DM value function and her optimal experimentation strategy that turns out to follow a cut-off rule with respect to her belief process. The belief threshold for exploring the ambiguous arm is found in closed form and is shown to be increasing with respect to the ambiguity aversion index. We then study the effect of provision of an unambiguous information source about the ambiguous arm. Interestingly, we show that the exploration threshold rises unambiguously as a result of this new information source, thereby leading to more conservatism. This analysis also sheds light on the efficient time to reach for an expert opinion.