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Decision making under uncertainty: a quasimetric approach.

Steve N'Guyen¹, Clément Moulin-Frier¹, Jacques Droulez¹

¹Laboratoire de Physiologie de la Perception et de l'Action, UMR 7152 Collège de France - CNRS, Paris, France.

|December 31, 2013

Summary

We introduce a novel geometric approach for discrete decision-making problems under uncertainty. This method uses a goal-independent quasimetric structure to analyze costs and probabilities, offering a new perspective beyond traditional methods.

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Area of Science:

Decision Sciences
Artificial Intelligence
Operations Research

Background:

Discrete decision-making under uncertainty is prevalent across engineering, economics, and AI.
Existing methods rely on trial-and-error learning or probabilistic models of consequences.
These approaches often require extensive data or complex probability distributions.

Purpose of the Study:

To propose a novel geometric approach for discrete decision-making problems with positive costs under uncertainty.
To introduce a goal-independent quasimetric structure on the state space.
To compare the precision and computation time of this new method against classical approaches.

Main Methods:

Defining a quasimetric structure on the state space, independent of specific goals.
Incorporating both cost functions and transition probabilities into this geometric structure.
Empirical comparison of the proposed method's performance (precision, computation time) with existing techniques.

Main Results:

The proposed geometric approach provides a new framework for analyzing decision problems.
Preliminary comparisons suggest potential advantages in precision or computational efficiency.
The quasimetric structure offers a novel way to represent decision spaces.

Conclusions:

This geometric perspective offers a promising alternative to traditional methods for decision-making under uncertainty.
The quasimetric approach may enhance the understanding and solution of complex decision problems.
Further research is warranted to explore the full potential and applicability of this method.