# Efficient Distributed Online Prediction and Stochastic Optimization with Approximate Distributed Averaging

arXiv: https://arxiv.org/abs/1403.0603 · HTML: https://mlsanity.com/paper/1403.0603/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2014.

## Built on by (most cited first, 3 of 3)

- [Consensus Control for Decentralized Deep Learning](https://mlsanity.com/paper/2102.04828/) (2021)
- [Asynchronous Training Schemes in Distributed Learning with Time Delay](https://mlsanity.com/paper/2208.13154/) (2022)
- [Decentralized optimization with non-identical sampling in presence of stragglers](https://mlsanity.com/paper/2108.11071/) (2021)

## Abstract (arXiv)

We study distributed methods for online prediction and stochastic optimization. Our approach is iterative: in each round nodes first perform local computations and then communicate in order to aggregate information and synchronize their decision variables. Synchronization is accomplished through the use of a distributed averaging protocol. When an exact distributed averaging protocol is used, it is known that the optimal regret bound of O(√m) can be achieved using the distributed mini-batch algorithm of Dekel et al. (2012), where m is the total number of samples processed across the network. We focus on methods using approximate distributed averaging protocols and show that the optimal regret bound can also be achieved in this setting. In particular, we propose a gossip-based optimization method which achieves the optimal regret bound. The amount of communication required depends on the network topology through the second largest eigenvalue of the transition matrix of a random walk on the network. In the setting of stochastic optimization, the proposed gossip-based approach achieves nearly-linear scaling: the optimization error is guaranteed to be no more than ε after O(frac1n ε2) rounds, each of which involves O(log n) gossip iterations, when nodes communicate over a well-connected graph. This scaling law is also observed in numerical experiments on a cluster.