Support Sufficiency as Action-Sufficient Compression: A Rate-Regret Framework for Decision-Making
A preprint submitted to the Journal of Mathematical Psychology proposes a formal model called 'support sufficiency' that defines how decision-making systems should compress information to retain only what is needed for optimal action. The framework uses rate-distortion theory, recasting the problem as a rate-regret tradeoff where distortion is measured by consequence-sensitive policy regret rather than reconstruction error. The work aims to clarify why simpler arbitration schemes—such as those relying solely on content or scalar confidence—can fail when their information partitions cut across action boundaries.
Researcher Mark Walsh has submitted a 22-page preprint to arXiv formalizing the concept of 'support sufficiency' as action-sufficient compression in decision-making systems. The paper defines a support state H, a finite action set, and a consequence geometry specifying payoff structure, then identifies the coarsest lossless compression as the quotient of support space by policy equivalence—merging states only when they demand the same optimal action. Approximate sufficiency is defined through bounded expected policy regret, yielding a rate-regret problem analogous to classical rate-distortion theory, with the optimal stochastic action channel taking a Gibbs distribution form. The framework explicitly distinguishes action adequacy from reconstruction fidelity, information-bottleneck prediction, and rational inattention, positioning itself as a unifying interpretive lens for robust single-cycle arbitration. The authors argue that robust decision-making does not require preserving all information in a support state, only the distinctions that the consequence geometry renders action-relevant. The paper is primarily theoretical and interpretive in scope, with the finite single-cycle setting as its formal domain.
What's missing
As a theoretical preprint, the paper does not include empirical validation or computational experiments demonstrating the framework's performance on real or simulated decision problems. It is also unclear how the single-cycle formulation extends to sequential or multi-cycle decision settings, and whether the Gibbs-form optimal channel is tractable to compute for large or continuous support spaces. The paper has not yet undergone peer review.
What different sources said
- arXiv cs.AICenter
Support sufficiency as action-sufficient compression: a single-cycle rate-regret formulation
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