We revisit the proof by Qin et al. (2014) of bounded regret of the C 2 UCB contextual combinatorial bandit. We demonstrate an error in the proof of volumetric expansion of the moment matrix, used in upper bounding a function of context vector norms. We prove a relaxed inequality that yields the originally-stated regret bound.

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Effective physical database design tuning requires selection of several physical design structures (PDS), such as indices and materialised views, whose combination influences overall system performance in a non-linear manner. While the simplicity of combining the results of iterative searches for individual PDSs may be appealing, such a greedy approach may yield vastly suboptimal results compared to an integrated search. We propose a new self-driving approach (HMAB) based on hierarchical multi-armed bandit learners, which can work in an integrated space of multiple PDS while avoiding the full cost of combinatorial search. HMAB eschews the optimiser cost misestimates by direct performance observations through a strategic exploration, while carefully leveraging its knowledge to prune the less useful exploration paths. As an added advantage, HMAB comes with a provable guarantee on its expected performance. To the best of our knowledge, this is the first learned system to tune both indices and materialised views in an integrated manner. We find that our solution enjoys superior empirical performance relative to state-of-the-art commercial physical database design tools that search over the integrated space of materialised views and indices. Specifically, HMAB achieves up to 96% performance gain over a state-of-the-art commercial physical database design tool when running industrial benchmarks.

Automating physical database design has remained a long-term interest in database research due to substantial performance gains afforded by optimised structures. Despite significant progress, a majority of today's commercial solutions are highly manual, requiring offline invocation by database administrators (DBAs) who are expected to identify and supply representative training workloads. Even the latest advancements like query stores provide only limited support for dynamic environments. This status quo is untenable: identifying representative static workloads is no longer realistic; and physical design tools remain susceptible to the query optimiser's cost misestimates (stemming from unrealistic assumptions such as attribute value independence and uniformity of data distribution).We propose a self-driving approach to online index selection that eschews the DBA and query optimiser, and instead learns the benefits of viable structures through strategic exploration and direct performance observation. We view the problem as one of sequential decision making under uncertainty, specifically within the bandit learning setting. Multi-armed bandits balance exploration and exploitation to provably guarantee average performance that converges to a fixed policy that is optimal with perfect hindsight. Our comprehensive empirical results demonstrate up to 75% speed-up on shifting and ad-hoc workloads and 28% speed-up on static workloads compared against a state-ofthe-art commercial tuning tool.

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