# mathsfVISTA: Decentralized Machine Learning in Adversary Dominated Environments

arXiv: https://arxiv.org/abs/2605.07841 · HTML: https://mlsanity.com/paper/2605.07841/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 91 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [FLTrust: Byzantine-robust Federated Learning via Trust Bootstrapping](https://mlsanity.com/paper/2012.13995/) (2020)
- [The Hidden Vulnerability of Distributed Learning in Byzantium](https://mlsanity.com/paper/1802.07927/) (2018)
- [Momentum-Based Variance Reduction in Non-Convex SGD](https://mlsanity.com/paper/1905.10018/) (2019)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Adaptive Gradient Methods with Dynamic Bound of Learning Rate](https://mlsanity.com/paper/1902.09843/) (2019)
- [AdaGrad stepsizes: Sharp convergence over nonconvex landscapes](https://mlsanity.com/paper/1806.01811/) (2018)
- [Learning from History for Byzantine Robust Optimization](https://mlsanity.com/paper/2012.10333/) (2020)
- [Learning-Rate-Free Learning by D-Adaptation](https://mlsanity.com/paper/2301.07733/) (2023)
- [Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks](https://mlsanity.com/paper/1806.06763/) (2018)
- [Byzantine Stochastic Gradient Descent](https://mlsanity.com/paper/1803.08917/) (2018)
- [Exponential Moving Average of Weights in Deep Learning: Dynamics and Benefits](https://mlsanity.com/paper/2411.18704/) (2024)
- [Lagrange Coded Computing: Optimal Design for Resiliency, Security and Privacy](https://mlsanity.com/paper/1806.00939/) (2018)
- [Byzantine Machine Learning Made Easy by Resilient Averaging of Momentums](https://mlsanity.com/paper/2205.12173/) (2022)
- [Byzantine-Resilient Non-Convex Stochastic Gradient Descent](https://mlsanity.com/paper/2012.14368/) (2020)
- [Fast Convergence of Stochastic Gradient Descent under a Strong Growth Condition](https://mlsanity.com/paper/1308.6370/) (2013)
- [Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)](https://mlsanity.com/paper/2008.00742/) (2020)
- [DETOX: A Redundancy-based Framework for Faster and More Robust Gradient Aggregation](https://mlsanity.com/paper/1907.12205/) (2019)
- [Polynomial Codes: an Optimal Design for High-Dimensional Coded Matrix Multiplication](https://mlsanity.com/paper/1705.10464/) (2017)
- [Byzantine-Robust Federated Learning with Optimal Statistical Rates and Privacy Guarantees](https://mlsanity.com/paper/2205.11765/) (2022)
- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [VeriML: Enabling Integrity Assurances and Fair Payments for Machine Learning as a Service](https://mlsanity.com/paper/1909.06961/) (2019)
- [Robust Distributed Learning: Tight Error Bounds and Breakdown Point under Data Heterogeneity](https://mlsanity.com/paper/2309.13591/) (2023)

## Built on by (most cited first, 1 of 1)

- [Crypto x AI, AI x Crypto: A Survey](https://mlsanity.com/paper/2606.13892/) (2026)

## Abstract (arXiv)

Decentralized machine learning often relies on outsourcing computations, such as gradient evaluations, to untrusted worker nodes. Existing robust aggregation methods can mitigate malicious behavior under honest-majority assumptions, but may fail when adversaries control a majority of the workers. We study this adversary-dominated setting through an incentive-oriented framework in which reports are accepted and rewarded only when they are mutually consistent up to a threshold. This turns the adversary from a pure saboteur into a rational agent that trades off increasing estimation error against the risk of rejection and loss of reward. We consider iterative optimization under this model. Unlike one-shot computation, iterative learning requires long-horizon decisions: permissive acceptance rules enable faster early progress but admit more adversarial corruption, while strict rules improve estimation accuracy but cause frequent rejections. We propose mathsfVISTA, an adaptive algorithm that tunes the acceptance threshold using the optimization history. Numerical results show that mathsfVISTA improves convergence over static thresholds. We also provide a rigorous convergence analysis showing that, with suitable incentive-aware adaptation, adversary-dominated decentralized learning can retain the asymptotic convergence behavior of standard SGD without relying on an honest majority.