Join ordering is the NP-hard problem of selecting the most efficient sequence in which to evaluate joins (conjunctive, binary operators) in a database query. As the performance of query execution critically depends on this choice, join ordering lies at the core of query optimization. Traditional approaches cast this problem as a discrete combinatorial search over binary trees guided by a cost model, but they often suffer from high computational complexity and limited scalability. We show that, when the cost model is differentiable, the query plans can be continuously relaxed into a soft adjacency matrix representing a superposition of plans. This continuous relaxation, together with a Gumbel-Softmax parameterization of the adjacency matrix and differentiable constraints enforcing plan validity, enables gradient-based search for plans within this relaxed space. Using a learned Graph Neural Network as the cost model, we demonstrate that this gradient-based approach can find comparable and even lower-cost plans compared to traditional discrete local search methods on two different graph datasets. Furthermore, we empirically show that the runtime of this approach scales linearly with query size, in contrast to quadratic or exponential runtimes of classical approaches. We believe this first step towards gradient-based join ordering can lead to more effective and efficient query optimizers in the future.

Active Learning (AL) deals with identifying the most informative samples for labeling to reduce data annotation costs for supervised learning tasks. AL research suffers from the fact that lifts from literature generalize poorly and that only a small number of repetitions of experiments are conducted. To overcome these obstacles, we propose CDALBench, the first active learning benchmark which includes tasks in computer vision, natural language processing and tabular learning. Furthermore, by providing an efficient, greedy oracle, CDALBench can be evaluated with 50 runs for each experiment. We show, that both the cross-domain character and a large amount of repetitions are crucial for sophisticated evaluation of AL research. Concretely, we show that the superiority of specific methods varies over the different domains, making it important to evaluate Active Learning with a cross-domain benchmark. Additionally, we show that having a large amount of runs is crucial. With only conducting three runs as often done in the literature, the superiority of specific methods can strongly vary with the specific runs. This effect is so strong, that, depending on the seed, even a well-established method's performance can be significantly better and significantly worse than random for the same dataset.

Core-Set This method is based on the finding that the decision boundaries of convolutional neural networks are based on a small set of samples.

And how to best employ AL on my dataset?

This paper revisits the LLM cache bandit problem, with a special focus on addressing the query heterogeneity for cost-effective LLM inference. Previous works often assume uniform query sizes. Heterogeneous query sizes introduce a combinatorial structure for cache selection, making the cache replacement process more computationally and statistically challenging. We treat optimal cache selection as a knapsack problem and employ an accumulation-based strategy to effectively balance computational overhead and cache updates. In theoretical analysis, we prove that the regret of our algorithm achieves an $O(\sqrt{MNT})$ bound, improving the coefficient of $\sqrt{MN}$ compared to the $O(MN\sqrt{T})$ result in Berkeley, where $N$ is the total number of queries and $M$ is the cache size. Additionally, we also provide a problem-dependent bound, which was absent in previous works. The experiment rely on real-world data show that our algorithm reduces the total cost by approximately 12\%.

Example 1 Figure 1 shows a graph mapping. Edge mappings can be trivially inferred. Hence, the claim is proved. These four cases cover all possible situations and hence, the triangle inequality is established. From the triangle inequality, we can infer the lower bounds listed in lines 2 and 4 of Alg. 2. Hence, if Alg. 3 presents the pseudocode.