2021/02/09 by Teng-Hui Huang, Huang, Teng-Hui, Aly El Gamal +1
Computer Science · #Advanced Neural Network Applications #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning and ELM #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2102.04729
openalex publication_date 2021/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Information bottleneck (IB) method enables optimizing over the trade-off between compression of data and prediction accuracy of learned representations, and has successfully and robustly been applied to both supervised and unsupervised representation learning problems. However, IB has several limitations. First, the IB problem is hard to optimize. The IB Lagrangian LIB:=I(X;Z)-βI(Y;Z) is non-convex and existing solutions guarantee only local convergence. As a result, the obtained solutions depend on initialization. Second, the evaluation of a solution is also a challenging task. Conventionally, it resorts to characterizing the information plane, that is, plotting I(Y;Z) versus I(X;Z) for all solutions obtained from different initial points. Furthermore, the IB Lagrangian has phase transitions while varying the multiplier β. At phase transitions, both I(X;Z) and I(Y;Z) increase abruptly and the rate of convergence becomes significantly slow for existing solutions. Recent works with IB adopt variational surrogate bounds to the IB Lagrangian. Although allowing efficient optimization, how close are these surrogates to the IB Lagrangian is not clear. In this work, we solve the IB Lagrangian using augmented Lagrangian methods. With augmented variables, we show that the IB objective can be solved with the alternating direction method of multipliers (ADMM). Different from prior works, we prove that the proposed algorithm is consistently convergent, regardless of the value of β. Empirically, our gradient-descent-based method results in information plane points that are comparable to those obtained through the conventional Blahut-Arimoto-based solvers and is convergent for a wider range of the penalty coefficient than previous ADMM solvers.