在完全隐私保护下优化信息瓶颈，实现高保真与敏感信息零关联。
Information Bottleneck under Perfect Privacy
- 基于ADMM算法设计新方法，显式处理隐私约束下的信息压缩。
- 证明全局收敛性并给出收敛速率理论分析，支持不精确更新。
- 适合研究隐私保护机器学习的学者，尤其关注数据去敏技术者。
本文研究完全隐私条件下的信息瓶颈问题，重点关注主动率区域——此时表示率约束起决定性作用，直接限制可实现效用。目标是构建一个保留有用信息但与敏感变量统计独立的表示。这种严格独立性要求引入了经典率-相关性权衡之外的新约束，必须显式纳入优化过程。为此，我们开发了一种基于交替方向乘子法（ADMM）的方法，专门针对该问题结构。在适当正则条件下，建立了生成序列的全局收敛性，通过Kurdyka-Łojasiewicz指数刻画其收敛速率，并将分析扩展至不精确块更新情形。
原文摘要 · Abstract (English)
In this work, we study the information bottleneck under perfect privacy, with particular emphasis on the active-rate regime, where the representation-rate constraint is binding and directly limits the achievable utility. The goal is to construct a representation that preserves utility-relevant information while remaining statistically independent of a sensitive variable. This exact independence requirement introduces an additional constraint beyond the classical rate-relevance tradeoff and must be explicitly incorporated into the optimization. To this end, we develop an alternating direction method of multipliers (ADMM)-based method tailored to the resulting problem structure. Under suitable regularity conditions, we establish global convergence of the generated sequence, characterize its convergence rate through the Kurdyka-Lojasiewicz exponent, and extend the analysis to inexact block updates.
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