# Quantized Distributed Online Projection-free Convex Optimization

## TL;DR

This paper introduces a quantized distributed online optimization algorithm for convex problems over multi-agent networks, balancing communication efficiency and convergence performance through a novel quantization approach.

## Contribution

It develops a new quantized algorithm for distributed online convex optimization that reduces communication costs while maintaining theoretical convergence guarantees.

## Key findings

- Achieves dynamic regret bounds under different quantizer settings.
- Demonstrates trade-off between quantization level and convergence performance.
- Validates results with simulations on distributed linear regression.

## Abstract

This paper considers online distributed convex constrained optimization over a time-varying multi-agent network. Agents in this network cooperate to minimize the global objective function through information exchange with their neighbors and local computation. Since the capacity or bandwidth of communication channels often is limited, a random quantizer is introduced to reduce the transmission bits. Through incorporating this quantizer, we develop a quantized distributed online projection-free optimization algorithm, which can achieve the saving of communication resources and computational costs. For different parameter settings of the quantizer, we establish the corresponding dynamic regret upper bounds of the proposed algorithm and reveal the trade-off between the convergence performance and the quantization effect. Finally, the theoretical results are illustrated by the simulation of distributed online linear regression problem.