# Nonasymptotic Convergence Rates for Cooperative Learning Over Time-Varying Directed Graphs

arXiv: https://arxiv.org/abs/1410.1977 · HTML: https://mlsanity.com/paper/1410.1977/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2014.

## Built on by (most cited first, 6 of 6)

- [Communication-efficient Distributed Cooperative Learning with Compressed Beliefs](https://mlsanity.com/paper/2102.07767/) (2021)
- [SureFED: Robust Federated Learning via Uncertainty-Aware Inward and Outward Inspection](https://mlsanity.com/paper/2308.02747/) (2023)
- [On Arbitrary Compression for Decentralized Consensus and Stochastic Optimization over Directed Networks](https://mlsanity.com/paper/2204.08160/) (2022)
- [Differentially Private Distributed Estimation and Learning](https://mlsanity.com/paper/2306.15865/) (2023)
- [Network Fault-tolerant and Byzantine-resilient Social Learning via Collaborative Hierarchical Non-Bayesian Learning](https://mlsanity.com/paper/2307.14952/) (2023)
- [Robust synchronization and policy adaptation for networked heterogeneous agents](https://mlsanity.com/paper/2409.03273/) (2024)

## Abstract (arXiv)

We study the problem of distributed hypothesis testing with a network of agents where some agents repeatedly gain access to information about the correct hypothesis. The group objective is to globally agree on a joint hypothesis that best describes the observed data at all the nodes. We assume that the agents can interact with their neighbors in an unknown sequence of time-varying directed graphs. Following the pioneering work of Jadbabaie, Molavi, Sandroni, and Tahbaz-Salehi, we propose local learning dynamics which combine Bayesian updates at each node with a local aggregation rule of private agent signals. We show that these learning dynamics drive all agents to the set of hypotheses which best explain the data collected at all nodes as long as the sequence of interconnection graphs is uniformly strongly connected. Our main result establishes a non-asymptotic, explicit, geometric convergence rate for the learning dynamic.