Robust Linear Dueling Bandits with Post-serving Context under Unknown Delays and Adversarial Corruptions

TL;DR

This paper introduces a robust algorithm for linear dueling bandits in volatile environments with delays and adversarial corruptions, achieving near-optimal regret bounds under challenging conditions.

Contribution

It proposes erm, an algorithm that predicts post-serving contexts and adaptively mitigates delays and corruptions, with theoretical guarantees on regret.

Findings

Achieves a regret bound of  ( ( ext{T}) + ext{C} + ext{D}))

The algorithm is delay-regime-agnostic and handles unknown stochastic or adversarial delays and corruptions.

Lower bounds nearly match upper bounds, confirming near-optimality in adversarial delay settings.

Abstract

We study linear dueling bandits in volatile environments characterized by the simultaneous presence of post-serving contexts, delayed feedback, and adversarial corruption. Feedback is subject to unknown stochastic or adversarial delays and a cumulative corruption budget $\mathcal{C}$. To address these challenges, we propose \term, which integrates a learned approximator that predicts post-serving contexts from pre-serving information. It further employs an adaptive weighting strategy that clips feature vectors to mitigate the impact of corrupted and delayed observations simultaneously. Under standard regularity conditions and a parametric post-serving mapping, we rigorously establish that our algorithm is delay-regime-agnostic, achieving a regret upper bound of $\widetilde{\mathcal{O}}(d(\sqrt{T} + \mathcal{C} + \mathcal{D}))$, where $d$ is the total feature dimension and $\mathcal{D}$ encapsulates the delay complexity. Crucially, our analysis reveals an additive cost structure between corruption and delay, avoiding the multiplicative degradation typical of prior works. We further establish lower bounds that nearly match our upper bounds up to a $\sqrt{d}$ factor for adversarial delays in the absence of post-serving contexts.