# Communication-Efficient Accurate Statistical Estimation

## TL;DR

This paper introduces CEASE, a set of communication-efficient iterative algorithms for distributed statistical estimation that achieve rapid convergence and statistical efficiency with minimal communication, suitable for large-scale data scenarios.

## Contribution

The paper proposes novel CEASE algorithms that adapt to loss function similarities, converge quickly without good initialization, and achieve statistical efficiency in finite steps.

## Key findings

- Algorithms converge rapidly with linear rates.
- Statistical efficiency achieved in finite steps.
- Validated through extensive experiments on synthetic and real data.

## Abstract

When the data are stored in a distributed manner, direct application of traditional statistical inference procedures is often prohibitive due to communication cost and privacy concerns. This paper develops and investigates two Communication-Efficient Accurate Statistical Estimators (CEASE), implemented through iterative algorithms for distributed optimization. In each iteration, node machines carry out computation in parallel and communicate with the central processor, which then broadcasts aggregated information to node machines for new updates. The algorithms adapt to the similarity among loss functions on node machines, and converge rapidly when each node machine has large enough sample size. Moreover, they do not require good initialization and enjoy linear converge guarantees under general conditions. The contraction rate of optimization errors is presented explicitly, with dependence on the local sample size unveiled. In addition, the improved statistical accuracy per iteration is derived. By regarding the proposed method as a multi-step statistical estimator, we show that statistical efficiency can be achieved in finite steps in typical statistical applications. In addition, we give the conditions under which the one-step CEASE estimator is statistically efficient. Extensive numerical experiments on both synthetic and real data validate the theoretical results and demonstrate the superior performance of our algorithms.