In many real-world dynamical systems, the effect of an input on an output is not immediate but occurs after a time-varying delay, influenced by both the input and the system's internal state. These delays are typically unobservable, making system modelling particularly challenging, as the temporal relationship between inputs and outputs is not directly accessible. While inferring such dynamic delays is crucial for accurate modelling, most existing approaches either assume fixed delays or disregard delay structure altogether. This often leads to misaligned input-output relationships, especially in nonlinear, state-dependent systems, ultimately degrading predictive performance. We propose DelayNetODE, a novel delay-aware neural architecture that infers dynamic, input-dependent delays in an unsupervised manner while modelling system behaviour in continuous time. The framework consists of three key components: (1) a graph-based encoder that estimates continuous-valued delays from local temporal features, (2) a soft attention mechanism that aligns past inputs based on inferred delays, and (3) a Neural Ordinary Differential Equation (Neural ODE) decoder that models the continuous-time evolution of the output conditioned on delay-adjusted inputs. We evaluate DeiayNetODE on both synthetic and real-world datasets with nonlinear, time-varying delays. Results show this approach consistently outperforms the state-of-the-art models in both prediction accuracy and delay estimation. By inferring delays in an unsupervised manner and aligning inputs accordingly, DelayNetODE provides a principled and explainable approach for capturing latent temporal dependencies and improving system modelling in complex dynamical settings.

Multi-armed bandits have long been known to enjoy optimal long-term performance, with sub-linear cumulative re-gret bounds standard. Recent developments take the performance of early rounds into consideration by ‘warm-starting’ bandits via incorporating pre-existing information into initialisation. Unfor-tunately, existing warm-start approaches are brittle to differences in the reward distributions between pretraining and deployment phases. This paper considers one such contextual bandit setting, where the same linear relationship relates contexts and rewards in pretraining and deployment phases, but only up to (unknown) constant scaling. A probabilistic model is proposed to capture this novel transfer learning problem, and a simple algorithm is derived as a maximum a posteriori point estimate. We present a regret bound for our method, with empirical evaluation across a range of datasets and against several cold- and warm-start baselines. A real-world motivated experiment on database index selection demonstrates nonlinear modelling via neural network feature embeddings.

Abstract Multi-armed bandits achieve excellent long-term performance in practice and sublinear cumulative regret in theory. However, a real-world limitation of bandit learning is poor performance in early rounds due to the need for exploration—a phenomenon known as the cold-start problem. While this limitation may be necessary in the general classical stochastic setting, in practice where “pre-training” data or knowledge is available, it is natural to attempt to “warm-start” bandit learners. This paper provides a theoretical treatment of warm-start contextual bandit learning, adopting Linear Thompson Sampling as a principled framework for flexibly transferring domain knowledge as might be captured by bandit learning in a prior related task, a supervised pre-trained Bayesian posterior, or domain expert knowledge. Under standard conditions, we prove a general regret bound. We then apply our warm-start algorithmic technique to other common bandit learners—the $$\epsilon $$ ϵ -greedy and upper-confidence bound contextual learners. An upper regret bound is then provided for LinUCB. Our suite of warm-start learners are evaluated in experiments with both artificial and real-world datasets, including a motivating task of tuning a commercial database. A comprehensive range of experimental results are presented, highlighting the effect of different hyperparameters and quantities of pre-training data.

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). 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. Furthermore, modern application environments like hybrid transactional and analytical processing (HTAP) systems render analytical modelling next to impossible. We propose a self-driving approach to online index selection that does not depend on 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 in analytical processing environments and 59% speed-up in HTAP environments. Lastly, our bandit framework outperforms a Monte Carlo tree search (MCTS)-based database optimiser, providing up to 24% speed-up.

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.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 simplified bandit framework outperforms deep reinforcement learning (RL) in terms of convergence speed and performance volatility. 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 and up to 58% speed-up against the deep RL alternatives.

Multi-armed bandits achieve excellent long-term performance in practice and sublinear cumulative regret in theory. However a real-world limitation of bandit learning is poor performance in early rounds due to the need for exploration– a phenomenon known as the cold-start problem. While this limitation may be necessary in the classical stochastic setting, in practice where “pre-training” data or knowledge is available, it is natural to attempt to “warm start” bandit learners. This paper provides a theoretical treatment of warm-start contextual bandit learning, adopting Linear Thompson Sampling as a principled framework for flexibly transferring domain knowledge as might be captured by bandit learning in a prior related task, a supervised pre-trained Bayesian posterior, or domain expert knowledge. Under standard conditions we prove a general regret bound. We then apply our warm-start algorithmic technique to other common bandit learners, the $\epsilon$-greedy and upper-confidence bound contextual learners. Our suite of warm-start learners are evaluated in experiments with both artificial and real-world datasets, including a motivating task of tuning a commercial database.