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Composite Optimization with Error Feedback: the Dual Averaging Approach

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Composite OptimizationDistributed OptimizationCommunication CompressionError FeedbackDual Averaging
Abstract:

Communication efficiency is a central challenge in distributed machine learning training, and message compression is a widely used solution. However, standard Error Feedback (EF) methods (Seide et al., 2014), though effective for smooth unconstrained optimization with compression (Karimireddy et al., 2019), fail in the broader and practically important setting of composite optimization, which captures, e.g., objectives consisting of a smooth loss combined with a non-smooth regularizer or constraints. The theoretical foundation and behavior of EF in the context of the general composite setting remain largely unexplored. In this work, we consider composite optimization with EF. We point out that the basic EF mechanism and its analysis no longer stand when a composite part is involved. We argue that this is because of a fundamental limitation in the method and its analysis technique. We propose a novel method that combines Dual Averaging with EControl (Gao et al., 2024), a state-of-the-art variant of the EF mechanism, and achieves for the first time a strong convergence analysis for composite optimization with error feedback. Along with our new algorithm, we also provide a new and novel analysis template for inexact dual averaging method, which might be of independent interest. We also provide experimental results to complement our theoretical findings.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes a dual averaging method combined with EControl for composite optimization under communication compression. It sits in the 'Composite and Constrained Optimization' leaf, which contains only two papers total (including this one). This represents a sparse research direction within the broader taxonomy of 30 papers. The sibling paper addresses accelerated primal-dual methods, suggesting this leaf focuses specifically on handling non-smooth regularizers and constraints—a problem structure less explored than the dominant smooth unconstrained objectives addressed in most error feedback literature.

The taxonomy reveals that neighboring branches focus on federated learning with compression (9 papers across three leaves), core error feedback theory (5 papers), and acceleration techniques (3 papers). The paper's leaf sits under 'Specialized Problem Settings and Extensions,' which also includes bilevel optimization, online learning, and domain-specific applications. While federated and decentralized branches address architectural concerns, and acceleration branches pursue faster convergence, this work diverges by tackling structural properties of the objective function itself—specifically composite structures combining smooth and non-smooth components that arise in regularized learning.

Among 29 candidates examined, the first contribution (dual averaging with EControl) shows one refutable candidate from 9 examined, suggesting some prior work exists in this direction but coverage remains limited. The second contribution (analysis template for inexact dual averaging) examined 10 candidates with none refutable, indicating potential novelty in the theoretical framework. The third contribution (identifying fundamental limitations in classical error feedback) also examined 10 candidates without refutation. The statistics suggest that while the algorithmic combination has some precedent, the analytical techniques and problem diagnosis appear less explored within the examined literature.

Based on the limited search scope of 29 semantically similar papers, the work appears to address a genuine gap where compression meets structured optimization. The sparse population of its taxonomy leaf and the contribution-level statistics suggest novelty in both problem formulation and analysis, though the search does not cover the entire field exhaustively. The positioning within specialized extensions rather than core theory or federated applications reflects its focus on broadening applicability beyond standard smooth objectives.

Taxonomy

Core-task Taxonomy Papers
30
3
Claimed Contributions
29
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: composite optimization with error feedback under communication compression. This field addresses the challenge of training machine learning models across distributed nodes while minimizing communication overhead through gradient compression, with error feedback mechanisms ensuring convergence despite information loss. The taxonomy reveals several major branches: foundational work on error feedback theory and mechanisms establishes convergence guarantees and design principles (e.g., Error Feedback Framework[1], EF21[15]); federated learning applications adapt these ideas to client-server architectures with heterogeneous data; decentralized and peer-to-peer methods explore fully distributed topologies without central coordination; acceleration techniques combine compression with momentum or variance reduction for faster convergence; and specialized extensions tackle constrained, composite, or nonconvex problems. These branches reflect a progression from theoretical foundations toward practical deployment scenarios, with cross-cutting concerns around biased versus unbiased compressors and the interplay between compression rates and convergence speed. Recent work shows particularly active development in acceleration methods that blend error feedback with adaptive or momentum-based updates (Accelerated Compression Feedback[6], Efficient-Adam[18]), and in handling complex problem structures beyond smooth unconstrained optimization. The original paper, Dual Averaging Error Feedback[0], sits within the specialized problem settings branch focusing on composite and constrained optimization, closely neighboring Accelerated Primal-Dual Inexact[20]. While many existing methods target standard smooth objectives, Dual Averaging Error Feedback[0] emphasizes dual averaging schemes that naturally accommodate non-smooth regularizers and constraints—a direction less explored than the dominant federated or acceleration branches. This positions the work as addressing a gap where compression meets structured optimization, complementing broader efforts in federated settings (Federated Biased Compression[2]) and theoretical refinements (Error Feedback Fixes SignSGD[3]) by extending applicability to regularized and constrained scenarios common in practice.

Claimed Contributions

Novel dual averaging method with EControl for composite optimization

The authors introduce a new algorithm that integrates dual averaging with the EControl error feedback mechanism to handle composite optimization problems (smooth loss plus non-smooth regularizer or constraints). This is the first method to achieve convergence rates for composite optimization with error feedback that match the best rates in the unconstrained setting.

9 retrieved papers
Can Refute
Novel analysis template for inexact dual averaging

The authors develop a new analytical framework for analyzing inexact dual averaging methods, where gradient estimates may be approximate or noisy. This template extends beyond the specific application to error feedback and may be useful for other optimization problems involving inexact updates.

10 retrieved papers
Identification of fundamental limitation in classical error feedback for composite problems

The authors identify and explain why the classical error feedback mechanism and its virtual iteration analysis fail in composite optimization settings. They show that the proximal step in composite updates destroys the additive structure that makes virtual iterate analysis effective in the unconstrained case.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Novel dual averaging method with EControl for composite optimization

The authors introduce a new algorithm that integrates dual averaging with the EControl error feedback mechanism to handle composite optimization problems (smooth loss plus non-smooth regularizer or constraints). This is the first method to achieve convergence rates for composite optimization with error feedback that match the best rates in the unconstrained setting.

Contribution

Novel analysis template for inexact dual averaging

The authors develop a new analytical framework for analyzing inexact dual averaging methods, where gradient estimates may be approximate or noisy. This template extends beyond the specific application to error feedback and may be useful for other optimization problems involving inexact updates.

Contribution

Identification of fundamental limitation in classical error feedback for composite problems

The authors identify and explain why the classical error feedback mechanism and its virtual iteration analysis fail in composite optimization settings. They show that the proximal step in composite updates destroys the additive structure that makes virtual iterate analysis effective in the unconstrained case.

Table of Contents