Derivative Free Optimization (DFO) is attractive when the objective function's derivatives are not available and evaluations are costly. Moreover, if the function evaluations are noisy, then approximating gradients by finite differences is difficult. This paper gives quantitative lower bounds on the performance of DFO with noisy function evaluations, exposing a fundamental and unavoidable gap between optimization performance based on noisy evaluations versus noisy gradients. This challenges the conventional wisdom that the method of finite differences is comparable to a stochastic gradient. However, there are situations in which DFO is unavoidable, and for such situations we propose a new DFO algorithm that is proved to be near optimal for the class of strongly convex objective functions. A distinctive feature of the algorithm is that it only uses Boolean-valued function comparisons, rather than evaluations.

Given a set $V$ of $n$ elements we wish to linearly order them using pairwise preference labels which may be non-transitive (due to irrationality or arbitrary noise). The goal is to linearly order the elements while disagreeing with as few pairwise preference labels as possible. Our performance is measured by two parameters: The number of disagreements (loss) and the query complexity (number of pairwise preference labels). Our algorithm adaptively queries at most $O(n\poly(\log n,\eps {-1}))$ preference labels for a regret of $\eps$ times the optimal loss. This is strictly better, and often significantly better than what non-adaptive sampling could achieve.

Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, do two elements $u$ and $v$ belong to the same cluster?''. The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we provide a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and give strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix, which is used by an automated process to cluster similar points together. To improve accuracy of clustering, a fruitful approach in recent years has been to ask a domain expert or crowd to obtain labeled data interactively.

We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many queries are necessary and sufficient in order for the learner to accurately estimate the target, while simultaneously concealing the target from the adversary? Our main result is a query complexity lower bound that is tight up to the first order. We show that if the learner wants to estimate the target within an error of $\epsilon$, while ensuring that no adversary estimator can achieve a constant additive error with probability greater than $1/L$, then the query complexity is on the order of $L\log(1/\epsilon)$ as $\epsilon \to 0$. Our result demonstrates that increased privacy, as captured by $L$, comes at the expense of a \emph{multiplicative} increase in query complexity.

Knowledge graphs have been shown to play an important role in recent knowledge mining and discovery, for example in the field of life sciences or bioinformatics. Although a lot of research has been done on the field of query optimization, query transformation and of course in storing and retrieving large scale knowledge graphs the field of algorithmic optimization is still a major challenge and a vital factor in using graph databases. Few researchers have addressed the problem of optimizing algorithms on large scale labeled property graphs. Here, we present two optimization approaches and compare them with a naive approach of directly querying the graph database. The aim of our work is to determine limiting factors of graph databases like Neo4j and we describe a novel solution to tackle these challenges. For this, we suggest a classification schema to differ between the complexity of a problem on a graph database. We evaluate our optimization approaches on a test system containing a knowledge graph derived biomedical publication data enriched with text mining data. This dense graph has more than 71M nodes and 850M relationships. The results are very encouraging and - depending on the problem - we were able to show a speedup of a factor between 44 and 3839.

Logic-based systems for query answering over knowledge graphs return only answers that rely on information explicitly represented in the graph. To improve recall, recent works have proposed the use of embeddings to predict additional information like missing links, or labels. These embeddings enable scoring entities in the graph as the answer a query, without being fully dependent on the graph structure. In its simplest case, answering a query in such a setting requires predicting a link between two entities. However, link prediction is not sufficient to address complex queries that involve multiple entities and variables. To solve this task, we propose to apply a message passing mechanism to a graph representation of the query, where nodes correspond to variables and entities. This results in an embedding of the query, such that answering entities are close to it in the embedding space. The general formulation of our method allows it to encode a more diverse set of query types in comparison to previous work. We evaluate our method by answering queries that rely on edges not seen during training, obtaining competitive performance. In contrast with previous work, we show that our method can generalize from training for the single-hop, link prediction task, to answering queries with more complex structures. A qualitative analysis reveals that the learned embeddings successfully capture the notion of different entity types.

The goal of query performance prediction (QPP) is to automatically estimate the effectiveness of a search result for any given query, without relevance judgements. Post-retrieval features have been shown to be more effective for this task while being more expensive to compute than pre-retrieval features. Combining multiple post-retrieval features is even more effective, but state-of-the-art QPP methods are impossible to interpret because of the black-box nature of the employed machine learning models. However, interpretation is useful for understanding the predictive model and providing more answers about its behavior. Moreover, combining many post-retrieval features is not applicable to real-world cases, since the query running time is of utter importance. In this paper, we investigate a new framework for feature selection in which the trained model explains well the prediction. We introduce a step-wise (forward and backward) model selection approach where different subsets of query features are used to fit different models from which the system selects the best one. We evaluate our approach on four TREC collections using standard QPP features. We also develop two QPP features to address the issue of query-drift in the query feedback setting. We found that: (1) our model based on a limited number of selected features is as good as more complex models for QPP and better than non-selective models; (2) our model is more efficient than complex models during inference time since it requires fewer features; (3) the predictive model is readable and understandable; and (4) one of our new QPP features is consistently selected across different collections, proving its usefulness.

The excessively increased volume of data in modern data management systems demands an improved system performance, frequently provided by data distribution, system scalability and performance optimization techniques. Optimized horizontal data partitioning has a significant influence of distributed data management systems. An optimally partitioned schema found in the early phase of logical database design without loading of real data in the system and its adaptation to changes of business environment are very important for a successful implementation, system scalability and performance improvement. In this paper we present a novel approach for finding an optimal horizontally partitioned schema that manifests a minimal total execution cost of a given database workload. Our approach is based on a formal model that enables abstraction of the predicates in the workload queries, and are subsequently used to define all relational fragments. This approach has predictive features acquired by simulation of horizontal partitioning, without loading any data into the partitions, but instead, altering the statistics in the database catalogs. We define an optimization problem and employ a genetic algorithm (GA) to find an approximately optimal horizontally partitioned schema. The solutions to the optimization problem are evaluated using PostgreSQL's query optimizer. The initial experimental evaluation of our approach confirms its efficiency and correctness, and the numbers imply that the approach is effective in reducing the workload execution cost.

Join query optimization is a complex task and is central to the performance of query processing. In fact it belongs to the class of NP-hard problems. Traditional query optimizers use dynamic programming (DP) methods combined with a set of rules and restrictions to avoid exhaustive enumeration of all possible join orders. However, DP methods are very resource intensive. Moreover, given simplifying assumptions of attribute independence, traditional query optimizers rely on erroneous cost estimations, which can lead to suboptimal query plans. Recent success of deep reinforcement learning (DRL) creates new opportunities for the field of query optimization to tackle the above-mentioned problems. In this paper, we present our DRL-based Fully Observed Optimizer (FOOP) which is a generic query optimization framework that enables plugging in different machine learning algorithms. The main idea of FOOP is to use a data-adaptive learning query optimizer that avoids exhaustive enumerations of join orders and is thus significantly faster than traditional approaches based on dynamic programming. In particular, we evaluate various DRL-algorithms and show that Proximal Policy Optimization significantly outperforms Q-learning based algorithms. Finally we demonstrate how ensemble learning techniques combined with DRL can further improve the query optimizer.

We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many queries are necessary and sufficient in order for the learner to accurately estimate the target, while simultaneously concealing the target from the adversary? Our main result is a query complexity lower bound that is tight up to the first order. We show that if the learner wants to estimate the target within an error of $\varepsilon$, while ensuring that no adversary estimator can achieve a constant additive error with probability greater than $1/L$, then the query complexity is on the order of $L\log(1/\varepsilon)$, as $\varepsilon \to 0$. Our result demonstrates that increased privacy, as captured by $L$, comes at the expense of a {multiplicative} increase in query complexity. Our proof method builds on Fano's inequality and a family of proportional-sampling estimators. As an illustration of the method's wider applicability, we generalize the complexity lower bound to settings involving high-dimensional linear query learning and partial adversary observation.