Interactive Scalar Quantization for Distributed Resource Allocation

TL;DR

This paper proposes an interactive scalar quantization scheme for distributed resource allocation, demonstrating that small delays can significantly reduce communication rates while maintaining near-optimal performance.

Contribution

It introduces a dynamic programming-based optimal quantization policy and simpler policies for efficient rate-delay trade-offs in distributed resource allocation.

Findings

Small delay increases lead to significant rate savings.

Optimal policy closely approximated by simpler policies with lower complexity.

Interactive quantization reduces communication overhead in distributed systems.

Abstract

In many resource allocation problems, a centralized controller needs to award some resource to a user selected from a collection of distributed users with the goal of maximizing the utility the user would receive from the resource. This can be modeled as the controller computing an extremum of the distributed users' utilities. The overhead rate necessary to enable the controller to reproduce the users' local state can be prohibitively high. An approach to reduce this overhead is interactive communication wherein rate savings are achieved by tolerating an increase in delay. In this paper, we consider the design of a simple achievable scheme based on successive refinements of scalar quantization at each user. The optimal quantization policy is computed via a dynamic program and we demonstrate that tolerating a small increase in delay can yield significant rate savings. We then consider two simpler quantization policies to investigate the scaling properties of the rate-delay trade-offs. Using a combination of these simpler policies, the performance of the optimal policy can be closely approximated with lower computational costs.