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One if by Land, Two if by Sea, Three if by Four Seas, and More to Come -- Values of Perception, Prediction, Communication, and Common Sense in Decision Making

Aolin Xu

TL;DR

The defined quantities suggest answers to practical questions arising in the design of autonomous decision-making systems, and provide insights to cognitive science and neural science, toward the understanding of how natural decision makers make use of information gained from different sources and operations.

Abstract

This work aims to rigorously define the values of perception, prediction, communication, and common sense in decision making. The defined quantities are decision-theoretic, but have information-theoretic analogues, e.g., they share some simple but key mathematical properties with Shannon entropy and mutual information, and can reduce to these quantities in particular settings. One interesting observation is that, the value of perception without prediction can be negative, while the value of perception together with prediction and the value of prediction alone are always nonnegative. The defined quantities suggest answers to practical questions arising in the design of autonomous decision-making systems. Example questions include: Do we need to observe and predict the behavior of a particular agent? How important is it? What is the best order to observe and predict the agents? The defined quantities may also provide insights to cognitive science and neural science, toward the understanding of how natural decision makers make use of information gained from different sources and operations.

One if by Land, Two if by Sea, Three if by Four Seas, and More to Come -- Values of Perception, Prediction, Communication, and Common Sense in Decision Making

TL;DR

The defined quantities suggest answers to practical questions arising in the design of autonomous decision-making systems, and provide insights to cognitive science and neural science, toward the understanding of how natural decision makers make use of information gained from different sources and operations.

Abstract

This work aims to rigorously define the values of perception, prediction, communication, and common sense in decision making. The defined quantities are decision-theoretic, but have information-theoretic analogues, e.g., they share some simple but key mathematical properties with Shannon entropy and mutual information, and can reduce to these quantities in particular settings. One interesting observation is that, the value of perception without prediction can be negative, while the value of perception together with prediction and the value of prediction alone are always nonnegative. The defined quantities suggest answers to practical questions arising in the design of autonomous decision-making systems. Example questions include: Do we need to observe and predict the behavior of a particular agent? How important is it? What is the best order to observe and predict the agents? The defined quantities may also provide insights to cognitive science and neural science, toward the understanding of how natural decision makers make use of information gained from different sources and operations.
Paper Structure (14 sections, 7 theorems, 27 equations, 2 figures)

This paper contains 14 sections, 7 theorems, 27 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related works
  4. Definitions of values of different operations
  5. A generic decision-making problem
  6. Value of common sense
  7. Value of perception
  8. Value of prediction
  9. Value of perception together with prediction
  10. Value of communication
  11. Information-theoretic realizations and interpretations
  12. Functional properties of defined values
  13. Extension to multi-agent settings and applications
  14. Conclusion

Key Result

Lemma 1

$\mathbb{E}[\ell(X,Y,u^*)]$ is concave in the joint distribution $P_{X,Y}$.

Figures (2)

  • Figure 1: Real-world example where the value of perception without prediction can be negative: observing a truck slowing down without considering a potentially cutting-in vehicle occluded by the truck may result in a dangerous lane change of ego vehicle.
  • Figure 2: Values of common sense, perception, prediction, and communication, as well as their information-theoretic analogues, are shown as colored regions. Interpretations of some combined regions are shown on the right.

Theorems & Definitions (13)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • Proposition 1
  • proof
  • Proposition 2
  • ...and 3 more