On the capacity of information processing systems

TL;DR

This paper analyzes the capacity of systems with multiple experts to accurately identify hidden labels of jobs, optimizing resource allocation to ensure stability and minimal error in label recovery.

Contribution

It introduces an adaptive inspection policy that is asymptotically optimal for stabilizing the system and accurately recovering labels with minimal resources.

Findings

The proposed policy achieves asymptotic optimality as error probability approaches zero.

The analysis applies to applications like crowd-sourcing and diagnostics.

The system's capacity depends on the number of experts and inspection architecture.

Abstract

We propose and analyze a family of information processing systems, where a finite set of experts or servers are employed to extract information about a stream of incoming jobs. Each job is associated with a hidden label drawn from some prior distribution. An inspection by an expert produces a noisy outcome that depends both on the job's hidden label and the type of the expert, and occupies the expert for a finite time duration. A decision maker's task is to dynamically assign inspections so that the resulting outcomes can be used to accurately recover the labels of all jobs, while keeping the system stable. Among our chief motivations are applications in crowd-sourcing, diagnostics, and experiment designs, where one wishes to efficiently learn the nature of a large number of items, using a finite pool of computational resources or human agents. We focus on the capacity of such an information processing system. Given a level of accuracy guarantee, we ask how many experts are needed in order to stabilize the system, and through what inspection architecture. Our main result provides an adaptive inspection policy that is asymptotically optimal in the following sense: the ratio between the required number of experts under our policy and the theoretical optimal converges to one, as the probability of error in label recovery tends to zero.