用行动必要压缩重新定义支持状态的充分性,提升决策鲁棒性。
Support sufficiency as action-sufficient compression: a single-cycle rate-regret formulation
- 将支持状态压缩为仅保留影响行动选择的关键区分
- 在单周期设定下,最优压缩对应最小化期望政策后悔的率-后悔问题
- 适用于需高效决策但无需完整信息的系统,如机器人控制
稳健决策需要信息压缩。一个具有丰富支持状态的系统通常无法在行动时刻保留其完整结构,必须仅保留对当前后果几何下行动、验证、放弃或延迟所需的区分。本文将支持充分性形式化为行动必要压缩。设 $H$ 为全支持状态,$/mathcal{A}$ 为有限行动集,$Z$ 为指定收益结构的后果几何。固定 $Z$ 时,最粗略的精确行动必要压缩是支持空间对策略等价关系的商。当两个支持状态所需最优行动相同时,可精确合并。这解释了为何仅依赖内容或标量置信度的仲裁方法在诱导划分跨越行动边界时会失效。近似充分性则通过有界期望政策后悔定义。在有限单周期设定下,这转化为以 $H$ 为信源、$/mathcal{A}$ 为重建字母表、失真由后果敏感后悔决定的率-后悔问题。最优随机行动信道继承标准率-失真 Gibbs 形式,此处应用于支持状态并采用后悔失真。贡献在于区分行动充分性与重建保真度、信息瓶颈预测及理性忽视。稳健单周期仲裁无需保留全部支持,但必须保留后果几何所决定的行动相关区分。
原文摘要 · Abstract (English)
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. In the finite single-cycle setting, this yields a rate-regret problem with source $H$, reproduction alphabet $\mathcal{A}$, and distortion given by consequence-sensitive regret. The optimal stochastic action channel inherits the standard rate-distortion Gibbs form, applied here to support states with regret distortion. The contribution is interpretive: action adequacy is distinguished from reconstruction fidelity, information-bottleneck prediction, and rational inattention. Robust single-cycle arbitration does not require preserving all support, but it does require preserving the distinctions that consequence geometry makes action-relevant.
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