# Fast Convergence Rates for Distributed Non-Bayesian Learning

arXiv: https://arxiv.org/abs/1508.05161 · HTML: https://mlsanity.com/paper/1508.05161/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Aug 2015.

## Built on by (most cited first, 26 of 26)

- [Improving the Transient Times for Distributed Stochastic Gradient Methods](https://mlsanity.com/paper/2105.04851/) (2021)
- [Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks](https://mlsanity.com/paper/2106.07243/) (2021)
- [Communication-efficient Distributed Cooperative Learning with Compressed Beliefs](https://mlsanity.com/paper/2102.07767/) (2021)
- [Learning from Heterogeneous Data Based on Social Interactions over Graphs](https://mlsanity.com/paper/2112.09483/) (2021)
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- [Submodular Information Selection for Hypothesis Testing with Misclassification Penalties](https://mlsanity.com/paper/2405.10930/) (2024)
- [FLECS-CGD: A Federated Learning Second-Order Framework via Compression and Sketching with Compressed Gradient Differences](https://mlsanity.com/paper/2210.09626/) (2022)
- [Distributed Bayesian Learning of Dynamic States](https://mlsanity.com/paper/2212.02565/) (2022)
- [Locally Differentially Private Gradient Tracking for Distributed Online Learning over Directed Graphs](https://mlsanity.com/paper/2310.16105/) (2023)
- [Provably Accelerated Decentralized Gradient Method Over Unbalanced Directed Graphs](https://mlsanity.com/paper/2107.12065/) (2021)
- [On the Fusion Strategies for Federated Decision Making](https://mlsanity.com/paper/2303.06109/) (2023)
- [Non-Asymptotic Performance of Social Machine Learning Under Limited Data](https://mlsanity.com/paper/2306.09397/) (2023)
- [Causal Influences over Social Learning Networks](https://mlsanity.com/paper/2307.09575/) (2023)
- [Distributed Variational Inference for Online Supervised Learning](https://mlsanity.com/paper/2309.02606/) (2023)
- [Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities](https://mlsanity.com/paper/2312.01227/) (2023)
- [Causal Influence in Federated Edge Inference](https://mlsanity.com/paper/2405.01260/) (2024)
- [An Optimal Transport Approach for Network Regression](https://mlsanity.com/paper/2406.12204/) (2024)
- [An Asynchronous Decentralized Algorithm for Wasserstein Barycenter Problem](https://mlsanity.com/paper/2304.11653/) (2023)
- [Differentially Private Distributed Estimation and Learning](https://mlsanity.com/paper/2306.15865/) (2023)
- [Distributed Fractional Bayesian Learning for Adaptive Optimization](https://mlsanity.com/paper/2404.11354/) (2024)
- [Learning Multimodal Confidence for Intention Recognition in Human-Robot Interaction](https://mlsanity.com/paper/2405.14116/) (2024)
- [Classification with a Network of Partially Informative Agents: Enabling Wise Crowds from Individually Myopic Classifiers](https://mlsanity.com/paper/2409.19947/) (2024)
- [Robust Information Selection for Hypothesis Testing with Misclassification Penalties](https://mlsanity.com/paper/2502.14738/) (2025)
- [Doubly Adaptive Social Learning](https://mlsanity.com/paper/2504.17370/) (2025)
- [Adaptive Learning for IRS-Assisted Wireless Networks: Securing Opportunistic Communications Against Byzantine Eavesdroppers](https://mlsanity.com/paper/2508.08206/) (2025)
- [A Hybrid Stochastic Gradient Tracking Method for Distributed Online Optimization Over Time-Varying Directed Networks](https://mlsanity.com/paper/2508.20645/) (2025)

## Abstract (arXiv)

We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a distributed algorithm and establish consistency, as well as a non-asymptotic, explicit and geometric convergence rate for the concentration of the beliefs around the set of optimal hypotheses. Additionally, if the agents interact over static networks, we provide an improved learning protocol with better scalability with respect to the number of nodes in the network.