On the Minimax Regret for Linear Bandits in a wide variety of Action Spaces

TL;DR

This paper establishes an optimal lower bound on the minimax regret for linear bandit problems across diverse convex action spaces, addressing a long-standing open problem in the field.

Contribution

It provides the first comprehensive lower bound characterization for linear bandits in various convex action spaces, advancing theoretical understanding.

Findings

Optimal regret lower bound derived for convex action spaces

Addresses open problem in linear bandit theory

Enhances understanding of regret minimization in complex action spaces

Abstract

As noted in the works of \cite{lattimore2020bandit}, it has been mentioned that it is an open problem to characterize the minimax regret of linear bandits in a wide variety of action spaces. In this article we present an optimal regret lower bound for a wide class of convex action spaces.