Optimal Cooperative Inference

TL;DR

This paper develops a formal framework for cooperative inference, introducing new indices to measure its effectiveness and establishing conditions for optimal cooperation, with implications for machine and human learning.

Contribution

It presents a novel theoretical framework for cooperative inference, including indices, a relation to Teaching Dimension, and conditions for optimal cooperation.

Findings

Introduces indices for measuring cooperative information transmission

Relates indices to Teaching Dimension in deterministic cases

Proves conditions for achieving optimal cooperative inference

Abstract

Cooperative transmission of data fosters rapid accumulation of knowledge by efficiently combining experiences across learners. Although well studied in human learning and increasingly in machine learning, we lack formal frameworks through which we may reason about the benefits and limitations of cooperative inference. We present such a framework. We introduce novel indices for measuring the effectiveness of probabilistic and cooperative information transmission. We relate our indices to the well-known Teaching Dimension in deterministic settings. We prove conditions under which optimal cooperative inference can be achieved, including a representation theorem that constrains the form of inductive biases for learners optimized for cooperative inference. We conclude by demonstrating how these principles may inform the design of machine learning algorithms and discuss implications for human and machine learning.