# Optimization and Learning in Open Multi-Agent Systems

arXiv: https://arxiv.org/abs/2501.16847 · HTML: https://mlsanity.com/paper/2501.16847/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 70 references that are in the map.
- First posted on arXiv 28 Jan 2025.

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

- [Multi-Agent Online Optimization with Delays: Asynchronicity, Adaptivity, and Optimism](https://mlsanity.com/paper/2012.11579/) (2020)
- [Centrality measures for graphons: Accounting for uncertainty in networks](https://mlsanity.com/paper/1707.09350/) (2017)
- [Stability of Decentralized Gradient Descent in Open Multi-Agent Systems](https://mlsanity.com/paper/2009.05445/) (2020)
- [Payoff distribution in robust coalitional games on time-varying networks](https://mlsanity.com/paper/2009.03783/) (2020)
- [Dynamic Max-Consensus and Size Estimation of Anonymous Multi-Agent Networks](https://mlsanity.com/paper/2009.03858/) (2020)
- [Open Multi-Agent Systems: Gossiping with Random Arrivals and Departures](https://mlsanity.com/paper/1709.05142/) (2017)
- [MAX-consensus in open multi-agent systems with gossip interactions](https://mlsanity.com/paper/1709.05793/) (2017)
- [Stability of Open Multi-Agent Systems and Applications to Dynamic Consensus](https://mlsanity.com/paper/1906.00890/) (2019)
- [Lower bound performances for average consensus in open multi-agent systems (extended version)](https://mlsanity.com/paper/1909.02475/) (2019)
- [Fundamental Performance Limitations for Average Consensus in Open Multi-Agent Systems](https://mlsanity.com/paper/2004.06533/) (2020)
- [Optimization in Open Networks via Dual Averaging](https://mlsanity.com/paper/2105.13348/) (2021)
- [Robust Online Learning over Networks](https://mlsanity.com/paper/2309.00520/) (2023)
- [Learning in Time-Varying Monotone Network Games with Dynamic Populations](https://mlsanity.com/paper/2408.06253/) (2024)
- [Stability of Multi-Dimensional Switched Systems with an Application to Open Multi-Agent Systems](https://mlsanity.com/paper/2001.00435/) (2020)
- [Random coordinate descent algorithm for open multi-agent systems with complete topology and homogeneous agents](https://mlsanity.com/paper/2109.14510/) (2021)
- [Random Coordinate Descent for Resource Allocation in Open Multi-Agent Systems](https://mlsanity.com/paper/2205.10259/) (2022)
- [Resource allocation in open multi-agent systems: an online optimization analysis](https://mlsanity.com/paper/2207.09316/) (2022)
- [PrimeTime: A Finite-Time Consensus Protocol for Open Networks](https://mlsanity.com/paper/2304.09288/) (2023)
- [Average Consensus over Directed Networks in Open Multi-Agent Systems with Acknowledgement Feedback](https://mlsanity.com/paper/2409.08634/) (2024)

## Built on by (most cited first, 2 of 2)

- [Choose Your Battles: Distributed Learning Over Multiple Tug of War Games](https://mlsanity.com/paper/2509.20147/) (2025)
- [Bandit Learning in General Open Multi-agent Systems](https://mlsanity.com/paper/2605.06202/) (2026)

## Abstract (arXiv)

Modern artificial intelligence relies on networks of agents that collect data, process information, and exchange it with neighbors to collaboratively solve optimization and learning problems. This article introduces a novel distributed algorithm to address a broad class of these problems in "open networks", where the number of participating agents may vary due to several factors, such as autonomous decisions, heterogeneous resource availability, or DoS attacks. Extending the current literature, the convergence analysis of the proposed algorithm is based on the newly developed "Theory of Open Operators", which characterizes an operator as open when the set of components to be updated changes over time, yielding to time-varying operators acting on sequences of points of different dimensions and compositions. The mathematical tools and convergence results developed here provide a general framework for evaluating distributed algorithms in open networks, allowing to characterize their performance in terms of the punctual distance from the optimal solution, in contrast with regret-based metrics that assess cumulative performance over a finite-time horizon. As illustrative examples, the proposed algorithm is used to solve dynamic consensus or tracking problems on different metrics of interest, such as average, median, and min/max value, as well as classification problems with logistic loss functions.