Fair Exploration via Axiomatic Bargaining

Jackie Baek () and Vivek F. Farias ()
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Jackie Baek: Stern School of Business, New York University, New York, New York 10012
Vivek F. Farias: Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142

Management Science, 2024, vol. 70, issue 12, 8922-8939

Abstract: Exploration is often necessary in online learning to maximize long-term rewards, but it comes at the cost of short-term “regret.” We study how this cost of exploration is shared across multiple groups. For example, in a clinical trial setting, patients who are assigned a suboptimal treatment effectively incur the cost of exploration. When patients are associated with natural groups on the basis of, say, race or age, it is natural to ask whether the cost of exploration borne by any single group is “fair.” So motivated, we introduce the “grouped” bandit model. We leverage the theory of axiomatic bargaining, and the Nash bargaining solution in particular, to formalize what might constitute a fair division of the cost of exploration across groups. On one hand, we show that any regret-optimal policy strikingly results in the least fair outcome: such policies will perversely leverage the most “disadvantaged” groups when they can. More constructively, we derive policies that are optimally fair and simultaneously enjoy a small “price of fairness.” We illustrate the relative merits of our algorithmic framework with a case study on contextual bandits for warfarin dosing where we are concerned with the cost of exploration across multiple races and age groups.

Keywords: bandits; fairness; exploration; Nash bargaining solution (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:70:y:2024:i:12:p:8922-8939

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