# Learn-and-Adapt Stochastic Dual Gradients for Network Resource Allocation

## TL;DR

This paper introduces LA-SDG, a novel learn-and-adapt stochastic dual gradient method that improves network resource allocation by effectively learning Lagrange multipliers from data, achieving better cost-delay tradeoffs.

## Contribution

The paper develops LA-SDG, a new method that learns optimal Lagrange multipliers from data and adapts resource allocation, requiring minimal additional computation over existing methods.

## Key findings

- LA-SDG outperforms existing schemes in cost-delay tradeoff.
- LA-SDG requires only one extra gradient evaluation.
- Theoretical and empirical results confirm LA-SDG's effectiveness.

## Abstract

Network resource allocation shows revived popularity in the era of data deluge and information explosion. Existing stochastic optimization approaches fall short in attaining a desirable cost-delay tradeoff. Recognizing the central role of Lagrange multipliers in network resource allocation, a novel learn-and-adapt stochastic dual gradient (LA-SDG) method is developed in this paper to learn the sample-optimal Lagrange multiplier from historical data, and accordingly adapt the upcoming resource allocation strategy. Remarkably, LA-SDG only requires just an extra sample (gradient) evaluation relative to the celebrated stochastic dual gradient (SDG) method. LA-SDG can be interpreted as a foresighted learning scheme with an eye on the future, or, a modified heavy-ball iteration from an optimization viewpoint. It is established - both theoretically and empirically - that LA-SDG markedly improves the cost-delay tradeoff over state-of-the-art allocation schemes.