# Asynchronous Incremental Stochastic Dual Descent Algorithm for Network Resource Allocation

## TL;DR

This paper introduces an asynchronous incremental stochastic dual descent algorithm for network resource allocation, enabling efficient, distributed optimization in heterogeneous networks with delayed gradient updates.

## Contribution

It presents a novel asynchronous incremental dual descent algorithm that handles delayed stochastic gradients, suitable for energy-constrained and heterogeneous network environments.

## Key findings

- Proves dual convergence with constant and diminishing step sizes.
- Shows near-optimality of the resource allocation policy with constant step size.
- Demonstrates effectiveness through multi-cell coordinated beamforming application.

## Abstract

Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as energy and bandwidth are divided among nodes to satisfy certain long-term objectives. This paper proposes an asynchronous incremental dual decent resource allocation algorithm that utilizes delayed stochastic {gradients} for carrying out its updates. The proposed algorithm is well-suited to heterogeneous networks as it allows the computationally-challenged or energy-starved nodes to, at times, postpone the updates. The asymptotic analysis of the proposed algorithm is carried out, establishing dual convergence under both, constant and diminishing step sizes. It is also shown that with constant step size, the proposed resource allocation policy is asymptotically near-optimal. An application involving multi-cell coordinated beamforming is detailed, demonstrating the usefulness of the proposed algorithm.