Learning When to Take Advice: A Statistical Test for Achieving A Correlated Equilibrium

TL;DR

This paper introduces a statistical test enabling agents in multiagent systems to determine when to follow mediator advice, ensuring convergence to a correlated equilibrium if the advice is beneficial, or safely reverting to their original strategies otherwise.

Contribution

The paper presents a novel algorithm that verifies the usefulness of mediator advice in multiagent learning, guaranteeing correct identification of beneficial advice in the limit.

Findings

Agents reach correlated equilibrium when advice is useful.

The test reliably distinguishes useful advice from non-useful advice.

Agents can safely revert to original strategies if advice is not beneficial.

Abstract

We study a multiagent learning problem where agents can either learn via repeated interactions, or can follow the advice of a mediator who suggests possible actions to take. We present an algorithmthat each agent can use so that, with high probability, they can verify whether or not the mediator's advice is useful. In particular, if the mediator's advice is useful then agents will reach a correlated equilibrium, but if the mediator's advice is not useful, then agents are not harmed by using our test, and can fall back to their original learning algorithm. We then generalize our algorithm and show that in the limit it always correctly verifies the mediator's advice.