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

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 boldsymbolπ0 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 tildemathcal Oleft(frackappatildeDeltad2(log(T)right), where tildeDelta is the constraint-aware sub-optimality gap subject to policy π0, with variance-aware multiplicative term kappa that we carefully handle using heteroskedastic regression. We further show Dri-MED enjoys tildeO(d) expected constraint violations. Our numerical results suggest that Dri-MED significantly outperforms conservative baselines that ignores the drift and preference structure.