  Bayesian optimization (BO) has become popular for sequential optimization of
black-box functions. When BO is used to optimize a target function, we often
have access to previous evaluations of potentially related functions. This begs
the question as to whether we can leverage these previous experiences to
accelerate the current BO task through meta-learning (meta-BO), while ensuring
robustness against potentially harmful dissimilar tasks that could sabotage the
convergence of BO. This paper introduces two scalable and provably robust
meta-BO algorithms: robust meta-Gaussian process-upper confidence bound
(RM-GP-UCB) and RM-GP-Thompson sampling (RM-GP-TS). We prove that both
algorithms are asymptotically no-regret even when some or all previous tasks
are dissimilar to the current task, and show that RM-GP-UCB enjoys a better
theoretical robustness than RM-GP-TS. We also exploit the theoretical
guarantees to optimize the weights assigned to individual previous tasks
through regret minimization via online learning, which diminishes the impact of
dissimilar tasks and hence further enhances the robustness. Empirical
evaluations show that (a) RM-GP-UCB performs effectively and consistently
across various applications, and (b) RM-GP-TS, despite being less robust than
RM-GP-UCB both in theory and in practice, performs competitively in some
scenarios with less dissimilar tasks and is more computationally efficient.
