Optimal and Adaptive Non-Stationary Dueling Bandits Under a Generalized Borda Criterion

Core Concepts

Establishing optimal and adaptive regret bounds for non-stationary dueling bandits under the Borda criterion.

Abstract

This content delves into the optimization of algorithms for non-stationary dueling bandits, focusing on the Borda criterion. It introduces a novel framework of generalized Borda scores, unifying Condorcet and Borda regret minimization tasks. The analysis highlights key insights into tracking changes in winner arms adaptively without prior knowledge of non-stationarity. Various algorithmic designs are discussed to achieve optimal dynamic regret bounds.
Structure:

Introduction to Dueling Bandits (K-armed problem with relative feedback).
Setup - Non-stationary Dueling Bandits.
Dynamic Regret Lower Bounds (Borda and Condorcet criteria).
Dynamic Regret Upper Bounds (Borda and Condorcet formulations).
A New Unified View of Condorcet and Borda Regret (Generalized Borda scores).
Algorithmic Design - Base Algorithm and Meta-Algorithm for non-stationary settings.
Novelties in Condorcet Regret Analysis (Recasting as Generalized Borda Regret).
Conclusion and Future Questions.

Stats

Saha and Gupta (2022) provided an algorithm achieving nearly optimal Condorcet dynamic regret of ˜O(√KLT), requiring knowledge of the total number of changes L.
Buening and Saha (2023) proposed a notion of significant Condorcet winner switches, achieving an adaptive dynamic regret bound of ˜O(Kp˜LT) under certain conditions.
Suk and Agarwal (2023) showed that tighter measures of non-stationarity can be learned adaptively outside SST∩STI assumptions in dueling bandits.

Quotes

"Surprisingly, our techniques for non-stationary Borda dueling bandits also yield improved rates within the Condorcet winner setting."
"Our focus in this work is on the more challenging non-stationary dueling bandits where preferences may change over time."
"We introduce a new unified framework, that of generalized Borda scores, for dueling bandits which generalizes both the Condorcet and Borda problems."

Key Insights Distilled From

Optimal and Adaptive Non-Stationary Dueling Bandits Under a Generalized Borda Criterion

by Joe Suk,Arpi... at arxiv.org 03-20-2024

https://arxiv.org/pdf/2403.12950.pdf

Deeper Inquiries

Can we learn other notions of significant CW switches in the Condorcet dueling bandit problem

In the context of the Condorcet dueling bandit problem, it has been shown that learning other notions of significant Condorcet winner (CW) switches is indeed possible. The key lies in defining a new measure of non-stationarity that captures changes in winner arms which are detrimental to performance. This tighter notion, termed approximate CW changes, allows for adaptive learning without requiring knowledge of the underlying non-stationarity.
By introducing this concept and establishing conditions like the General Identifiability Condition (GIC), it becomes feasible to track and learn from significant winner switches beyond traditional assumptions like SST∩STI. Through innovative algorithmic design and analysis techniques, such as recasting Condorcet regret as a Borda-like regret quantity within a generalized Borda framework, it becomes possible to achieve optimal regret rates even outside strict preference model assumptions.

Is it possible to attain adaptive and optimal Borda dynamic regret in terms of significant winner switches

The goal of attaining adaptive and optimal Borda dynamic regret in terms of significant winner switches has been successfully achieved through novel approaches presented in recent research. By introducing a new unified view through the generalized Borda score framework, algorithms have been developed to minimize dynamic regret under changing preferences without foreknowledge of non-stationarity levels.
Key advancements include designing base algorithms with soft elimination strategies combined with time-varying exploration schedules. These methodologies allow for accurate estimation of generalized Borda scores while adapting learning rates dynamically based on evolving scenarios. Additionally, meta-algorithms like METABOSSE enable hierarchical scheduling and management across multiple instances for efficient detection and response to unknown shifts in preferences.

How can tracking changing von-Neumann winners in non-stationary dueling bandits be approached

Tracking changing von-Neumann winners in non-stationary dueling bandits presents an intriguing challenge yet to be fully explored. While existing research has focused on Condorcet and Borda formulations with their respective objectives and measures of non-stationarity, extending these insights to capture dynamics related to von-Neumann winners could open up new avenues for study.
Approaching this task may involve developing specialized frameworks or algorithms tailored towards detecting shifts specifically relevant to von-Neumann criteria. By leveraging principles from existing work on tracking changes in winner arms along with innovative adaptations suited for von-Neumann concepts, researchers can potentially address this aspect comprehensively within the broader context of non-stationary dueling bandits.