Multi-Objective Parametric Query Optimization

Classical query optimization compares query plans according to one cost metric and associates each plan with a constant cost value. In this paper, we introduce the Multi-Objective Parametric Query Optimization (MPQ) problem where query plans are compared according to multiple cost metrics and the cost of a given plan according to a given metric is modeled as a function that depends on multiple parameters. The cost metrics may for instance include execution time or monetary fees; a parameter may represent the selectivity of a query predicate that is unspecified at optimization time. MPQ generalizes parametric query optimization (which allows multiple parameters but only one cost metric) and multi-objective query optimization (which allows multiple cost metrics but no parameters). We formally analyze the novel MPQ problem and show why existing algorithms are inapplicable. We present a generic algorithm for MPQ and a specialized version for MPQ with piecewise-linear plan cost functions. We prove that both algorithms find all relevant query plans and experimentally evaluate the performance of our second algorithm in a Cloud computing scenario

Optimal web-scale tiering as a flow problem

We present a fast online solver for large scale parametric max-flow problems as they occur in portfolio optimization, inventory management, computer vision, and logistics. Our algorithm solves an integer linear program in an online fashion. It exploits total unimodularity of the constraint matrix and a Lagrangian relaxation to solve the problem as a convex online game. The algorithm generates approximate solutions of max-flow problems by performing stochastic gradient descent on a set of flows. We apply the algorithm to optimize tier arrangement of over 84 million web pages on a layered set of caches to serve an incoming query stream optimally

Speculative Approximations for Terascale Analytics

Model calibration is a major challenge faced by the plethora of statistical analytics packages that are increasingly used in Big Data applications. Identifying the optimal model parameters is a time-consuming process that has to be executed from scratch for every dataset/model combination even by experienced data scientists. We argue that the incapacity to evaluate multiple parameter configurations simultaneously and the lack of support to quickly identify sub-optimal configurations are the principal causes. In this paper, we develop two database-inspired techniques for efficient model calibration. Speculative parameter testing applies advanced parallel multi-query processing methods to evaluate several configurations concurrently. The number of configurations is determined adaptively at runtime, while the configurations themselves are extracted from a distribution that is continuously learned following a Bayesian process. Online aggregation is applied to identify sub-optimal configurations early in the processing by incrementally sampling the training dataset and estimating the objective function corresponding to each configuration. We design concurrent online aggregation estimators and define halting conditions to accurately and timely stop the execution. We apply the proposed techniques to distributed gradient descent optimization -- batch and incremental -- for support vector machines and logistic regression models. We implement the resulting solutions in GLADE PF-OLA -- a state-of-the-art Big Data analytics system -- and evaluate their performance over terascale-size synthetic and real datasets. The results confirm that as many as 32 configurations can be evaluated concurrently almost as fast as one, while sub-optimal configurations are detected accurately in as little as a $1/20^{\text{th}}$ fraction of the time