Bounded rational decision-making from elementary computations that reduce uncertainty

Abstract

In its most basic form, decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can be reduced is limited by the amount of available computational resources. Here, we introduce the notion of elementary computation based on a fundamental principle for probability transfers that reduce uncertainty. Elementary computations can be considered as the inverse of Pigou-Dalton transfers applied to probability distributions, closely related to the concepts of majorization, T-transforms, and generalized entropies that induce a preorder on the space of probability distributions. As a consequence we can define resource cost functions that are order-preserving and therefore monotonic with respect to the uncertainty reduction. This leads to a comprehensive notion of decision-making processes with limited resources. Along the way, we prove several new results on majorization theory, as well as on entropy and divergence measures.

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Cited by in corpus (12)

• The Two Kinds of Free Energy and the Bayesian Revolution
• Specialization in Hierarchical Learning Systems
• Representing preorders with injective monotones
• An Information-theoretic On-line Learning Principle for Specialization in Hierarchical Decision-Making Systems
• Thermodynamic fluctuation theorems govern human sensorimotor learning
• Reinforcement Learning with Subspaces using Free Energy Paradigm
• Hierarchical Expert Networks for Meta-Learning
• Jarzyski's equality and Crooks' fluctuation theorem for general Markov chains with application to decision-making systems
• Majorization requires infinitely many second laws
• A theoretical framework to explain non-Nash equilibrium strategic behavior in experimental games
• Countability constraints in order-theoretic approaches to computability
• Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making