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

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-andadapt 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 LASDG markedly improves the cost-delay tradeoff over state-of-theart allocation schemes.