When Humans and Machines Make Joint Decisions: A Non-Symmetric Bandit Model

How can humans and machines learn to make joint decisions? This has become an important question in domains such as medicine, law and finance. We approach the question from a theoretical perspective and formalize our intuitions about human-machine decision making in a non-symmetric bandit model. In doing so, we follow the example of a doctor who is assisted by a computer program. We show that in our model, exploration is generally hard. In particular, unless one is willing to make assumptions about how human and machine interact, the machine cannot explore efficiently. We highlight one such assumption, policy space independence, which resolves the coordination problem and allows both players to explore independently. Our results shed light on the fundamental difficulties faced by the interaction of humans and machines. We also discuss practical implications for the design of algorithmic decision systems.

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