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Register a new userNo DBA? No regret! Multi-armed bandits for index tuning of analytical and HTAP workloads with provable guarantees
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Added by
Benjamin Rubinstein
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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 todays 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 optimisers cost misestimates. Furthermore, modern application environments such as hybrid transactional and analytical processing (HTAP) systems render analytical modelling next to impossible. 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 policies that are optimal with perfect hindsight. Our comprehensive empirical evaluation against a state-of-the-art commercial tuning tool demonstrates up to 75% speed-up on shifting and ad-hoc workloads and up to 28% speed-up on static workloads in analytical processing environments. In HTAP environments, our solution provides up to 59% speed-up on shifting and 51% speed-up on static workloads. Furthermore, our bandit framework outperforms deep reinforcement learning (RL) in terms of convergence speed and performance volatility (providing up to 58% speed-up).
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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 todays commercial solutions are highly manual, requiring offline invocation by database administrators (DBAs) who are expected to identify and supply representative training workloads. Unfortunately, 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 optimisers 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-of-the-art commercial tuning tool.
Filtering data based on predicates is one of the most fundamental operations for any modern data warehouse. Techniques to accelerate the execution of filter expressions include clustered indexes, specialized sort orders (e.g., Z-order), multi-dimensional indexes, and, for high selectivity queries, secondary indexes. However, these schemes are hard to tune and their performance is inconsistent. Recent work on learned multi-dimensional indexes has introduced the idea of automatically optimizing an index for a particular dataset and workload. However, the performance of that work suffers in the presence of correlated data and skewed query workloads, both of which are common in real applications. In this paper, we introduce Tsunami, which addresses these limitations to achieve up to 6X faster query performance and up to 8X smaller index size than existing learned multi-dimensional indexes, in addition to up to 11X faster query performance and 170X smaller index size than optimally-tuned traditional indexes.
Consider a player that in each round $t$ out of $T$ rounds chooses an action and observes the incurred cost after a delay of $d_{t}$ rounds. The cost functions and the delay sequence are chosen by an adversary. We show that even if the players algorithms lose their no regret property due to too large delays, the expected discounted ergodic distribution of play converges to the set of coarse correlated equilibrium (CCE) if the algorithms have no discounted-regret. For a zero-sum game, we show that no discounted-regret is sufficient for the discounted ergodic average of play to converge to the set of Nash equilibria. We prove that the FKM algorithm with $n$ dimensions achieves a regret of $Oleft(nT^{frac{3}{4}}+sqrt{n}T^{frac{1}{3}}D^{frac{1}{3}}right)$ and the EXP3 algorithm with $K$ arms achieves a regret of $Oleft(sqrt{ln Kleft(KT+Dright)}right)$ even when $D=sum_{t=1}^{T}d_{t}$ and $T$ are unknown. These bounds use a novel doubling trick that provably retains the regret bound for when $D$ and $T$ are known. Using these bounds, we show that EXP3 and FKM have no discounted-regret even for $d_{t}=Oleft(tlog tright)$. Therefore, the CCE of a finite or convex unknown game can be approximated even when only delayed bandit feedback is available via simulation.
We consider multi-objective optimization (MOO) of an unknown vector-valued function in the non-parametric Bayesian optimization (BO) setting, with the aim being to learn points on the Pareto front of the objectives. Most existing BO algorithms do not model the fact that the multiple objectives, or equivalently, tasks can share similarities, and even the few that do lack rigorous, finite-time regret guarantees that capture explicitly inter-task structure. In this work, we address this problem by modelling inter-task dependencies using a multi-task kernel and develop two novel BO algorithms based on random scalarizations of the objectives. Our algorithms employ vector-valued kernel regression as a stepping stone and belong to the upper confidence bound class of algorithms. Under a smoothness assumption that the unknown vector-valued function is an element of the reproducing kernel Hilbert space associated with the multi-task kernel, we derive worst-case regret bounds for our algorithms that explicitly capture the similarities between tasks. We numerically benchmark our algorithms on both synthetic and real-life MOO problems, and show the advantages offered by learning with multi-task kernels.
In a multi-armed bandit problem, an online algorithm chooses from a set of strategies in a sequence of trials so as to maximize the total payoff of the chosen strategies. While the performance of bandit algorithms with a small finite strategy set is quite well understood, bandit problems with large strategy sets are still a topic of very active investigation, motivated by practical applications such as online auctions and web advertisement. The goal of such research is to identify broad and natural classes of strategy sets and payoff functions which enable the design of efficient solutions. In this work we study a very general setting for the multi-armed bandit problem in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric. We refer to this problem as the Lipschitz MAB problem. We present a complete solution for the multi-armed problem in this setting. That is, for every metric space (L,X) we define an isometry invariant which bounds from below the performance of Lipschitz MAB algorithms for X, and we present an algorithm which comes arbitrarily close to meeting this bound. Furthermore, our technique gives even better results for benign payoff functions.
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