# Towards Sharp Analysis for Distributed Learning with Random Features

## TL;DR

This paper advances the theoretical understanding of distributed learning with random features by extending optimal rates to non-attainable cases, reducing feature requirements, and improving partition scalability, supported by experiments.

## Contribution

It introduces refined analysis techniques for non-attainable cases, data-dependent feature generation, and enhanced partitioning strategies in distributed learning with random features.

## Key findings

- Extended optimal rates to non-attainable cases
- Reduced number of random features needed
- Improved scalability with additional unlabeled data

## Abstract

In recent studies, the generalization properties for distributed learning and random features assumed the existence of the target concept over the hypothesis space. However, this strict condition is not applicable to the more common non-attainable case. In this paper, using refined proof techniques, we first extend the optimal rates for distributed learning with random features to the non-attainable case. Then, we reduce the number of required random features via data-dependent generating strategy, and improve the allowed number of partitions with additional unlabeled data. Theoretical analysis shows these techniques remarkably reduce computational cost while preserving the optimal generalization accuracy under standard assumptions. Finally, we conduct several experiments on both simulated and real-world datasets, and the empirical results validate our theoretical findings.