Tractable Agreement Protocols

Abstract: As ML models become increasingly powerful, it is an attractive proposition to use them in important decision making pipelines, in collaboration with human decision makers. But how should a human being and a machine learning model collaborate to reach decisions that are better than either of them could achieve on their own? If the human and the ML model were perfect Bayesians, operating in a setting with a commonly known and correctly specified prior, Aumann’s classical agreement theorem would give us one answer: they could engage in conversation about the task at hand, and their conversation would be guaranteed to converge to (accuracy-improving) agreement. This classical result however would require making many implausible assumptions, both about the knowledge and computational power of both parties. We show how to recover similar (and more general) results using only computationally and statistically tractable assumptions, which substantially relax full Bayesian rationality. We further give weak-learning conditions under which this collaboration will result in “information aggregation” — i.e. predictions that are as accurate as could have been made by a model that had access to -both- party’s observations, even though neither party in the interaction actually has access to these pooled observations.