# Adaptive Decentralized Composite Optimization via Three-Operator Splitting

arXiv: https://arxiv.org/abs/2602.17545 · HTML: https://mlsanity.com/paper/2602.17545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [AdaGrad stepsizes: Sharp convergence over nonconvex landscapes](https://mlsanity.com/paper/1806.01811/) (2018)
- [On the Convergence of Stochastic Gradient Descent with Adaptive Stepsizes](https://mlsanity.com/paper/1805.08114/) (2018)
- [Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization](https://mlsanity.com/paper/1709.08765/) (2017)
- [Adaptive Gradient Descent without Descent](https://mlsanity.com/paper/1910.09529/) (2019)
- [A Three-Operator Splitting Scheme and its Optimization Applications](https://mlsanity.com/paper/1504.01032/) (2015)
- [DADAM: A Consensus-based Distributed Adaptive Gradient Method for Online Optimization](https://mlsanity.com/paper/1901.09109/) (2019)
- [A general framework for decentralized optimization with first-order methods](https://mlsanity.com/paper/2009.05837/) (2020)
- [Adaptive Proximal Gradient Method for Convex Optimization](https://mlsanity.com/paper/2308.02261/) (2023)
- [Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient](https://mlsanity.com/paper/2301.04431/) (2023)
- [On the Convergence of Decentralized Adaptive Gradient Methods](https://mlsanity.com/paper/2109.03194/) (2021)
- [AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization](https://mlsanity.com/paper/2401.08024/) (2024)
- [A first-order primal-dual algorithm with linesearch](https://mlsanity.com/paper/1608.08883/) (2016)
- [Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization](https://mlsanity.com/paper/2302.03238/) (2023)
- [Problem-Parameter-Free Decentralized Nonconvex Stochastic Optimization](https://mlsanity.com/paper/2402.08821/) (2024)
- [Towards Parameter-free Distributed Optimization: a Port-Hamiltonian Approach](https://mlsanity.com/paper/2404.13529/) (2024)
- [A Parameter-free Decentralized Algorithm for Composite Convex Optimization](https://mlsanity.com/paper/2508.01466/) (2025)
- [An Accelerated Primal Dual Algorithm with Backtracking for Decentralized Constrained Optimization](https://mlsanity.com/paper/2512.07085/) (2025)

## Abstract (arXiv)

The paper studies decentralized optimization over networks, where agents minimize a sum of it locally smooth (strongly) convex losses and plus a nonsmooth convex extended value term. We propose decentralized methods wherein agents it adaptively adjust their stepsize via local backtracking procedures coupled with lightweight min-consensus protocols. Our design stems from a three-operator splitting factorization applied to an equivalent reformulation of the problem. The reformulation is endowed with a new BCV preconditioning metric (Bertsekas-O'Connor-Vandenberghe), which enables efficient decentralized implementation and local stepsize adjustments. We establish robust convergence guarantees. Under mere convexity, the proposed methods converge with a sublinear rate. Under strong convexity of the sum-function, and assuming the nonsmooth component is partly smooth, we further prove linear convergence. Numerical experiments corroborate the theory and highlight the effectiveness of the proposed adaptive stepsize strategy.