We study zeroth-order optimisation under context distributional uncertainty, a setting commonly tackled using Bayesian optimisation (BO). A prevailing strategy to make BO more robust to the complex and noisy nature of data is to employ an ensemble as the surrogate model, thereby mitigating the weaknesses of any single model. In this study, we propose a novel algorithm for Ensemble Distributionally Robust Bayesian Optimisation that remains computationally tractable while managing continuous context. We obtain theoretical sublinear regret bounds, improving current state-of-the-art results. We show that our method's empirical behaviour aligns with its theoretical guarantees.

We consider a contextual bandit problem with S contexts and K actions. In each round t = 1,2,... the learner observes a random context and chooses an action based on its past experience. The learner then observes a random reward whose mean is a function of the context and the action for the round. Under the assumption that the contexts can be lumped into r min{S,K}groups such that the mean reward for the various actions is the same for any two contexts that are in the same group, we give an algorithm that outputs an ε-optimal policy after using at most eO(r(S+K)/ε2) samples with high probability and provide a matching Ω(r(S + K)/ε2) lower bound. In the regret minimization setting, we give an algorithm whose cumulative regret up to time T is bounded by eO( p r3(S+K)T). To the best of our knowledge, we are the first to show the near-optimal sample complexity in the PAC setting and eO( p poly(r)(S+K)T)minimax regret in the online setting for this problem. We also show our algorithms can be applied to more general low-rank bandits and get improved regret bounds in some scenarios.

Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning. To overcome this challenge, robust satisficing (RS) seeks a robust solution to an unspecified distributional shift while achieving a utility above a desired threshold. This paper focuses on the problem of RS in contextual Bayesian optimization when there is a discrepancy between the true and reference distributions of the context. We propose a novel robust Bayesian satisficing algorithm called RoBOS for noisy black-box optimization.

Consider a recommendation platform that interacts with a finite set of users in an online fashion. Users arrive at the platform and receive a recommendation.

Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning.

We consider the problem of designing contextual bandit algorithms in the "cross-learning" setting of Balseiro et al., where the learner observes the loss for the action

We consider the problem of designing contextual bandit algorithms in the "cross-learning" setting of Balseiro et al., where the learner observes the loss for the action

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