Stochastic Averaging for Constrained Optimization with Application to Online Resource Allocation

TL;DR

This paper introduces a novel online learning-based method for stochastic constrained optimization in resource allocation, achieving fast convergence, low delay, and queue stability in stochastic networks.

Contribution

It develops a learn-and-adapt procedure that combines stochastic approximation and statistical learning for efficient online resource allocation.

Findings

Improves delay and convergence performance over existing schemes.

Achieves queue stability in stochastic network optimization.

Provides low-complexity online updates with near-optimal learning errors.

Abstract

Existing approaches to resource allocation for nowadays stochastic networks are challenged to meet fast convergence and tolerable delay requirements. The present paper leverages online learning advances to facilitate stochastic resource allocation tasks. By recognizing the central role of Lagrange multipliers, the underlying constrained optimization problem is formulated as a machine learning task involving both training and operational modes, with the goal of learning the sought multipliers in a fast and efficient manner. To this end, an order-optimal offline learning approach is developed first for batch training, and it is then generalized to the online setting with a procedure termed learn-and-adapt. The novel resource allocation protocol permeates benefits of stochastic approximation and statistical learning to obtain low-complexity online updates with learning errors close to the statistical accuracy limits, while still preserving adaptation performance, which in the stochastic network optimization context guarantees queue stability. Analysis and simulated tests demonstrate that the proposed data-driven approach improves the delay and convergence performance of existing resource allocation schemes.