# On Decentralized Tracking with ADMM for Problems with Time-Varying Curvature

## TL;DR

This paper investigates the effectiveness of ADMM in decentralized tracking of solutions to stochastic, time-varying optimization problems, accommodating occasional loss of strong convexity and gradient Lipschitz continuity, with performance measured in mean square deviation.

## Contribution

It provides a theoretical analysis of ADMM's tracking performance under stochastic, non-strongly convex conditions in a decentralized setting.

## Key findings

- ADMM can effectively track solutions despite stochastic and non-strongly convex objectives.
- Performance is characterized in terms of mean square deviation error.
- The analysis extends understanding of decentralized optimization under realistic, time-varying conditions.

## Abstract

We analyze the performance of the alternating direction method of multipliers (ADMM) to track, in a decentralized manner, a solution of a stochastic sequence of optimization problems parametrized by a discrete time Markov process. The main advantage of considering a stochastic model is that we allow the objective functions to occasionally lose strong convexity and/or Lipschitz continuity of their gradients. Due to the stochastic nature of our model, the tracking statement is given in a mean square deviation error.