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A system that forms a rich support state cannot usually preserve its full structure at the point of action. It must retain only those distinctions needed to act, verify, abstain, or defer under the current consequence geometry. This paper formalizes support sufficiency as action-sufficient compression. Let $H$ denote a full support state, $\\mathcal{A}$ a finite action set, and $Z$ a consequence geometry specifying payoff structure. For fixed $Z$, the coarsest exactly action-sufficient compression is the quotient of support space by policy equivalence. Two support states may be merged exactly when they require the same optimal action. This clarifies why content-only and scalar-confidence-only arbitration fail whenever their induced partitions cross action boundaries. Approximate sufficiency is then defined by bounded expected policy regret. In the finite single-cycle setting, this yields a ra","title":"Support sufficiency as action-sufficient compression: a single-cycle rate-regret formulation","url":"https://arxiv.org/abs/2606.09858","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.09858v1 Announce Type: cross \nAbstract: Robust decision-making requires compression. A system that forms a rich support state cannot usually preserve its full structure at the point of action. It must retain only those distinctions needed to act, verify, abstain, or defer under the current consequence geometry. This paper formalizes support sufficiency as action-sufficient compression. Let $H$ denote a full support state, $\\mathcal{A}$ a finite action set, and $Z$ a consequence geometry specifying payoff structure. For fixed $Z$, the coarsest exactly action-sufficient compression is the quotient of support space by policy equivalence. Two support states may be merged exactly when they require the same optimal action. This clarifies why content-only and scalar-confidence-only arbitration fail whenever their induced partitions cross action boundaries. Approximate sufficiency is then defined by bounded expected policy regret. 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