Generalizing the theory of cooperative inference

TL;DR

This paper extends the theory of cooperative inference by relaxing assumptions, demonstrating convergence, robustness, and effectiveness, and exploring geometric and optimal transport connections.

Contribution

It introduces generalized conditions for cooperative inference, including convergence for any discrete distribution and robustness through equivalence classes.

Findings

Demonstrates convergence for all discrete joint distributions.

Establishes robustness via equivalence classes and stability under perturbation.

Provides bounds based on structural properties of joint distributions.

Abstract

Cooperation information sharing is important to theories of human learning and has potential implications for machine learning. Prior work derived conditions for achieving optimal Cooperative Inference given strong, relatively restrictive assumptions. We relax these assumptions by demonstrating convergence for any discrete joint distribution, robustness through equivalence classes and stability under perturbation, and effectiveness by deriving bounds from structural properties of the original joint distribution. We provide geometric interpretations, connections to and implications for optimal transport, and connections to importance sampling, and conclude by outlining open questions and challenges to realizing the promise of Cooperative Inference.