Rationalizing Boltzmann Rationality: An Axiomatic Characterization of Entropy-Regularized Policies

Silviu Pitis

Papers from arXiv.org

Abstract: The softmax policy $\pi(a \mid s) \propto \exp(\beta Q(s,a))$ is the default model of stochastic choice in reinforcement learning (RL). Various justifications based on robustness, exploration, and optimization have been offered in the RL literature, but none uniquely derives the softmax form from first principles. This leaves a basic tension unresolved: the entropy bonus in the soft Bellman equation violates the Independence axiom that underwrites the Markov decision process (MDP) reward structure. We dissolve this tension by distinguishing two kinds of randomness: chance and choice. By restricting von Neumann-Morgenstern (VNM) Independence to environmental lotteries over base prospects, we show that imposing independence of irrelevant alternatives (IIA) and monotonicity on the policy and value functions at choice nodes uniquely determines the Boltzmann policy, the entropy-regularized representation, and the soft Bellman equation. The choice between the soft and hard Bellman equations thus reduces to a design decision: whether the agent values its own ability to choose. We develop RL-specific consequences, including return monotonicity and convergence under generalized discounting, and synthesize the independent lines from economics and information theory that arrive at the same structure, offering a normative assessment of when IIA is appropriate for agent design.

Date: 2026-07
References: Add references at CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2607.17316 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2607.17316

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().