# Information Bottleneck under Perfect Privacy

arXiv: https://arxiv.org/abs/2608.11003 · HTML: https://mlsanity.com/paper/2608.11003/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [Splitting methods with variable metric for KL functions](https://mlsanity.com/paper/1405.1357/) (2014)
- [Learnability for the Information Bottleneck](https://mlsanity.com/paper/1907.07331/) (2019)
- [Bottlenecks CLUB: Unifying Information-Theoretic Trade-offs Among Complexity, Leakage, and Utility](https://mlsanity.com/paper/2207.04895/) (2022)
- [Online Proximal-ADMM For Time-varying Constrained Convex Optimization](https://mlsanity.com/paper/2005.03267/) (2020)
- [Bottleneck Problems: Information and Estimation-Theoretic View](https://mlsanity.com/paper/2011.06208/) (2020)
- [Information Extraction Under Privacy Constraints](https://mlsanity.com/paper/1511.02381/) (2015)
- [Multi-Block Nonconvex Nonsmooth Proximal ADMM: Convergence and Rates under Kurdyka-Lojasiewicz Property](https://mlsanity.com/paper/2009.04014/) (2020)
- [A Linearly Convergent Douglas-Rachford Splitting Solver for Markovian Information-Theoretic Optimization Problems](https://mlsanity.com/paper/2203.07527/) (2022)
- [Proximal ADMM for Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2205.01951/) (2022)
- [A Provably Convergent Information Bottleneck Solution via ADMM](https://mlsanity.com/paper/2102.04729/) (2021)
- [Perturbed Proximal Gradient ADMM for Nonconvex Composite Optimization](https://mlsanity.com/paper/2504.12759/) (2025)

## Abstract (arXiv)

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.