Bandits for Efficient Experimentation: Adapting to Control Group, Preferences, and Context Drifts

Abstract:We consider a variant of the linear contextual stochastic multi-armed bandits, where the learner must provide recommendations to a group of users, each having its personalized preference vector, and in the presence of context distributions that are drifting over time. Under practitioner-friendly assumptions, we reduce this setting to linear bandit with stationary mean but heteroskedastic and non-stationary noise. We further study the case when the learner must ensure the mean reward of each decision must exceed that of a baseline strategy $\boldsymbol{\pi}_0$ at each decision step. We introduce Dri-MED, an algorithm inspired from the linear version of the MED strategy, and carefully adapted to handle the non-stationary heteroskedastic noise. We show that the instance-dependent regret scales as $\tilde{\mathcal O}\left(\frac{\kappa}{\tilde{\Delta}}d^2(\log(T)\right)$, where $\tilde{\Delta}$ is the constraint-aware sub-optimality gap subject to policy $\pi_0$, with variance-aware multiplicative term $\kappa$ that we carefully handle using heteroskedastic regression. We further show Dri-MED enjoys $\tilde{\mathcal{O}}(d)$ expected constraint violations. Our numerical results suggest that Dri-MED significantly outperforms conservative baselines that ignores the drift and preference structure.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)

arXiv:2606.09802 [cs.LG]

(or arXiv:2606.09802v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.09802 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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