On the Complexity of Learning to Cooperate with Populations of Socially Rational Agents

TL;DR

This paper investigates the difficulty of learning to cooperate with a population of adaptive, rational agents in repeated games, providing bounds on sample complexity and highlighting challenges beyond naive imitation approaches.

Contribution

It introduces formal bounds on the sample complexity for learning cooperation strategies with rational populations, revealing the problem's inherent complexity.

Findings

Assumptions of rationality and Pareto efficiency are insufficient for zero-shot cooperation.

Provides upper and lower bounds on the samples needed to learn cooperation strategies.

Shows that learning bounds can be significantly tighter than naive imitation-based methods.

Abstract

Artificially intelligent agents deployed in the real-world will require the ability to reliably \textit{cooperate} with humans (as well as other, heterogeneous AI agents). To provide formal guarantees of successful cooperation, we must make some assumptions about how partner agents could plausibly behave. Any realistic set of assumptions must account for the fact that other agents may be just as adaptable as our agent is. In this work, we consider the problem of cooperating with a \textit{population} of agents in a finitely-repeated, two player general-sum matrix game with private utilities. Two natural assumptions in such settings are that: 1) all agents in the population are individually rational learners, and 2) when any two members of the population are paired together, with high-probability they will achieve at least the same utility as they would under some Pareto efficient equilibrium strategy. Our results first show that these assumptions alone are insufficient to ensure \textit{zero-shot} cooperation with members of the target population. We therefore consider the problem of \textit{learning} a strategy for cooperating with such a population using prior observations its members interacting with one another. We provide upper and lower bounds on the number of samples needed to learn an effective cooperation strategy. Most importantly, we show that these bounds can be much stronger than those arising from a "naive'' reduction of the problem to one of imitation learning.