Linear Partial Monitoring for Sequential Decision-Making: Algorithms, Regret Bounds and Applications

TL;DR

This paper surveys and extends the linear partial monitoring framework, demonstrating that a single algorithm, IDS, achieves near-optimal regret bounds across various decision-making scenarios, including contextual and kernelized settings.

Contribution

It introduces a unified analysis of stochastic partial monitoring and shows that IDS is nearly optimal in all finite-action games within this framework.

Findings

IDS achieves near-optimal worst-case regret bounds.

The framework generalizes linear bandits to partial monitoring.

Extensions to contextual and kernelized models are provided.

Abstract

Partial monitoring is an expressive framework for sequential decision-making with an abundance of applications, including graph-structured and dueling bandits, dynamic pricing and transductive feedback models. We survey and extend recent results on the linear formulation of partial monitoring that naturally generalizes the standard linear bandit setting. The main result is that a single algorithm, information-directed sampling (IDS), is (nearly) worst-case rate optimal in all finite-action games. We present a simple and unified analysis of stochastic partial monitoring, and further extend the model to the contextual and kernelized setting.