# Distributed Approximation of Functions over Fast Fading Channels with Applications to Distributed Learning and the Max-Consensus Problem

## TL;DR

This paper develops a framework for distributed function approximation over fast fading channels with noise, providing probabilistic error bounds applicable to various distributions, with direct applications in distributed learning and network consensus.

## Contribution

It introduces explicit probabilistic bounds for function approximation errors over fading channels considering sub-gaussian noise, extending prior work to more realistic channel models.

## Key findings

- Derived bounds on the number of channel uses needed for a given accuracy.
- Applicable to non-Gaussian fading and noise distributions.
- Immediate applications in distributed machine learning and network consensus.

## Abstract

In this work, we consider the problem of distributed approximation of functions over multiple-access channels with additive noise. In contrast to previous works, we take fast fading into account and give explicit probability bounds for the approximation error allowing us to derive bounds on the number of channel uses that are needed to approximate a function up to a given approximation accuracy. Neither the fading nor the noise process is limited to Gaussian distributions. Instead, we consider sub-gaussian random variables which include Gaussian as well as many other distributions of practical relevance. The results are motivated by and have immediate applications to a) computing predictors in models for distributed machine learning and b) the max-consensus problem in ultra-dense networks.