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A No Free Lunch Theorem for Human-AI Collaboration

Kenny Peng, Nikhil Garg, Jon Kleinberg

TL;DR

This work investigates the challenge of complementarity in binary classification settings where the goal is to maximize 0-1 accuracy, and shows a "No Free Lunch"-style result given two or more agents who can make calibrated probabilistic predictions.

Abstract

The gold standard in human-AI collaboration is complementarity -- when combined performance exceeds both the human and algorithm alone. We investigate this challenge in binary classification settings where the goal is to maximize 0-1 accuracy. Given two or more agents who can make calibrated probabilistic predictions, we show a "No Free Lunch"-style result. Any deterministic collaboration strategy (a function mapping calibrated probabilities into binary classifications) that does not essentially always defer to the same agent will sometimes perform worse than the least accurate agent. In other words, complementarity cannot be achieved "for free." The result does suggest one model of collaboration with guarantees, where one agent identifies "obvious" errors of the other agent. We also use the result to understand the necessary conditions enabling the success of other collaboration techniques, providing guidance to human-AI collaboration.

A No Free Lunch Theorem for Human-AI Collaboration

TL;DR

This work investigates the challenge of complementarity in binary classification settings where the goal is to maximize 0-1 accuracy, and shows a "No Free Lunch"-style result given two or more agents who can make calibrated probabilistic predictions.

Abstract

The gold standard in human-AI collaboration is complementarity -- when combined performance exceeds both the human and algorithm alone. We investigate this challenge in binary classification settings where the goal is to maximize 0-1 accuracy. Given two or more agents who can make calibrated probabilistic predictions, we show a "No Free Lunch"-style result. Any deterministic collaboration strategy (a function mapping calibrated probabilities into binary classifications) that does not essentially always defer to the same agent will sometimes perform worse than the least accurate agent. In other words, complementarity cannot be achieved "for free." The result does suggest one model of collaboration with guarantees, where one agent identifies "obvious" errors of the other agent. We also use the result to understand the necessary conditions enabling the success of other collaboration techniques, providing guidance to human-AI collaboration.

Paper Structure

This paper contains 15 sections, 7 theorems, 26 equations, 1 figure.

Table of Contents

  1. Introduction
  2. A No Free Lunch Theorem
  3. Implications for Human-AI Collaboration
  4. Successful Collaborations
  5. Leveraging Independence: Condorcet's Jury Theorem, Wisdom of Crowds, Random Forests.
  6. Leveraging Learning: Experts, Boosting.
  7. Human-AI Collaboration
  8. Proof of \ref{['thm:main']}
  9. Preliminaries
  10. Correctness and Agreement.
  11. Combining collaboration settings.
  12. Building Calibrated Predictors from Partitions.
  13. Main Proof
  14. Conclusion
  15. Open Problems.

Key Result

Theorem 1

Every reliable collaboration strategy is non-collaborative.

Figures (1)

  • Figure 1: An illustration of a collaboration setting constructed in the proof of \ref{['prop:part1']}: the input space $\mathcal{X} = \{0, 1, 2, \cdots, n\}$ and the partition $\mathcal{A}_i$ (comprised of $\{0, i\}$ and the remaining singleton sets $\{j\}$ for $i\notin \{0, i\}$). In this setting, agent $i$ is always correct for the inputs $x\notin \{0,i\}$, since $P_i(x)$ is exactly $\Pr[Y=1|X=x]$ on these points. The full collaboration setting used in \ref{['prop:part1']} consists of combining $n$ such settings---one for each agent $k\in [n]$. Each such setting $S_k$ is constructed such that the collaboration strategy $\mathcal{C}$ performs strictly worse than agent $k$ and no better than the remaining agents.

Theorems & Definitions (15)

  • Theorem 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Definition 5
  • Proposition 6
  • proof
  • Theorem 1
  • ...and 5 more