Learning to Emulate an Expert Projective Cone Scheduler

TL;DR

This paper introduces an online, data-driven algorithm that learns to emulate an expert projective cone scheduler, providing theoretical guarantees on convergence and practical applicability for queueing systems.

Contribution

It presents a novel online algorithm using multiplicative weights to automatically design projective cone schedulers from expert observations, with proven convergence bounds.

Findings

The learned policy's average loss converges to zero at a rate of O(ln(T)√(ln(n)/T)).

The algorithm effectively emulates the expert scheduler in numerical experiments.

It can incorporate additional data to refine the scheduling policy over time.

Abstract

Projective cone scheduling defines a large class of rate-stabilizing policies for queueing models relevant to several applications. While there exists considerable theory on the properties of projective cone schedulers, there is little practical guidance on choosing the parameters that define them. In this paper, we propose an algorithm for designing an automated projective cone scheduling system based on observations of an expert projective cone scheduler. We show that the estimated scheduling policy is able to emulate the expert in the sense that the average loss realized by the learned policy will converge to zero. Specifically, for a system with $n$ queues observed over a time horizon $T$, the average loss for the algorithm is $O(\ln(T)\sqrt{\ln(n)/T})$. This upper bound holds regardless of the statistical characteristics of the system. The algorithm uses the multiplicative weights update method and can be applied online so that additional observations of the expert scheduler can be used to improve an existing estimate of the policy. This provides a data-driven method for designing a scheduling policy based on observations of a human expert. We demonstrate the efficacy of the algorithm with a simple numerical example and discuss several extensions.