# Adaptive Matching for Expert Systems with Uncertain Task Types

## TL;DR

This paper introduces an adaptive matching model for expert systems with uncertain task types, optimizing task-expert assignments by considering feedback and externalities to improve throughput in online platforms.

## Contribution

It develops a novel backpressure algorithm that accounts for task externalities and feedback, outperforming greedy approaches in expert resource allocation.

## Key findings

- The proposed algorithm achieves maximum throughput in the model.
- Greedy matching approaches are suboptimal due to externalities.
- Simulation results validate the theoretical throughput gains.

## Abstract

A matching in a two-sided market often incurs an externality: a matched resource may become unavailable to the other side of the market, at least for a while. This is especially an issue in online platforms involving human experts as the expert resources are often scarce. The efficient utilization of experts in these platforms is made challenging by the fact that the information available about the parties involved is usually limited. To address this challenge, we develop a model of a task-expert matching system where a task is matched to an expert using not only the prior information about the task but also the feedback obtained from the past matches. In our model the tasks arrive online while the experts are fixed and constrained by a finite service capacity. For this model, we characterize the maximum task resolution throughput a platform can achieve. We show that the natural greedy approaches where each expert is assigned a task most suitable to her skill is suboptimal, as it does not internalize the above externality. We develop a throughput optimal backpressure algorithm which does so by accounting for the `congestion' among different task types. Finally, we validate our model and confirm our theoretical findings with data-driven simulations via logs of Math.StackExchange, a StackOverflow forum dedicated to mathematics.