Is it possible to maximize a monotone submodular function faster than the widely used lazy greedy algorithm (also known as accelerated greedy), both in theory and practice? In this paper, we develop the first linear-time algorithm for maximizing a general monotone submodular function subject to a cardinality constraint. We show that our randomized algorithm, STOCHASTIC-GREEDY, can achieve a (1 − 1/e − ε) approximation guarantee, in expectation, to the optimum solution in time linear in the size of the data and independent of the cardinality constraint. We empirically demonstrate the effectiveness of our algorithm on submodular functions arising in data summarization, including training large-scale kernel methods, exemplar-based clustering, and sensor placement. We observe that STOCHASTIC-GREEDY practically achieves the same utility value as lazy greedy but runs much faster. More surprisingly, we observe that in many practical scenarios STOCHASTIC-GREEDY does not evaluate the whole fraction of data points even once and still achieves indistinguishable results compared to lazy greedy.

Temporal uncertainty in large-scale logistics forces one to trade off between lost efficiency through built-in slack and costly replanning when deadlines are missed. Due to the difficulty of reasoning about such likelihoods and consequences, a computational framework is needed to quantify and bound the risk of violating scheduling requirements. This work addresses the chance-constrained scheduling problem, where actions' durations are modeled probabilistically. Our solution method uses conflict-directed risk allocation to efficiently compute a scheduling policy. The key insight, compared to previous work in probabilistic scheduling, is to decouple the reasoning about temporal and risk constraints. This decomposes the problem into a separate master and subproblem, which can be iteratively solved much quicker. Through a set of simulated car-sharing scenarios, it is empirically shown that conflict-directed risk allocation computes solutions nearly an order of magnitude faster than prior art, which considers all constraints in a single lump-sum optimization.

The power output of photovoltaic systems (PVS) increases with the use of effective and efficient solar tracking techniques. However, current techniques suffer from several drawbacks in their tracking policy: (i) they usually do not consider the forecasted or prevailing weather conditions; even when they do, they (ii) rely on complex closed-loop controllers and sophisticated instruments; and (iii) typically, they do not take the energy consumption of the trackers into account. In this paper, we propose a policy iteration method (along with specialized variants), which is able to calculate near-optimal trajectories for effective and efficient day-ahead solar tracking, based on weather forecasts coming from on-line providers. To account for the energy needs of the tracking system, the technique employs a novel and generic consumption model. Our simulations show that the proposed methods can increase the power output of a PVS considerably, when compared to standard solar tracking techniques.

Model selection and hyperparameter optimization is crucial in applying machine learning to a novel dataset. Recently, a subcommunity of machine learning has focused on solving this problem with Sequential Model-based Bayesian Optimization (SMBO), demonstrating substantial successes in many applications. However, for computationally expensive algorithms the overhead of hyperparameter optimization can still be prohibitive. In this paper we mimic a strategy human domain experts use: speed up optimization by starting from promising configurations that performed well on similar datasets. The resulting initialization technique integrates naturally into the generic SMBO framework and can be trivially applied to any SMBO method. To validate our approach, we perform extensive experiments with two established SMBO frameworks (Spearmint and SMAC) with complementary strengths; optimizing two machine learning frameworks on 57 datasets. Our initialization procedure yields mild improvements for low-dimensional hyperparameter optimization and substantially improves the state of the art for the more complex combined algorithm selection and hyperparameter optimization problem.

Hyperparameter optimization is crucial for achieving peak performance with many machine learning algorithms; however, the evaluation of new optimization techniques on real-world hyperparameter optimization problems can be very expensive. Therefore, experiments are often performed using cheap synthetic test functions with characteristics rather different from those of real benchmarks of interest. In this work, we introduce another option: cheap-to-evaluate surrogates of real hyperparameter optimization benchmarks that share the same hyperparameter spaces and feature similar response surfaces. Specifically, we train regression models on data describing a machine learning algorithm’s performance depending on its hyperparameter setting, and then cheaply evaluate hyperparameter optimization methods using the model’s performance predictions in lieu of running the real algorithm. We evaluated a wide range of regression techniques, both in terms of how well they predict the performance of new hyperparameter settings and in terms of the quality of surrogate benchmarks obtained. We found that tree-based models capture the performance of several machine learning algorithms well and yield surrogate benchmarks that closely resemble real-world benchmarks, while being much easier to use and orders of magnitude cheaper to evaluate.

With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. In this paper, we focus on quasi-submodularity, a universal generalization, which satisfies weaker properties than submodularity but still enjoys favorable performance in optimization. Similar to the diminishing return property of submodularity, we first define a corresponding property called the single sub-crossing , then we propose two algorithms for unconstrained quasi-submodular function minimization and maximization, respectively. The proposed algorithms return the reduced lattices in O(n) iterations, and guarantee the objective function values are strictly monotonically increased or decreased after each iteration. Moreover, any local and global optima are definitely contained in the reduced lattices. Experimental results verify the effectiveness and efficiency of the proposed algorithms on lattice reduction.

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

Multi-document summarization is of great value to many real world applications since it can help people get the main ideas within a short time.In this paper, we tackle the problem of extracting summary sentences from multi-document sets by applying sparse coding techniques and present a novel framework to this challenging problem. Based on the data reconstruction and sentence denoising assumption, we present a two-level sparse representation model to depict the process of multi-document summarization. Three requisite properties is proposed to form an ideal reconstructable summary: Coverage, Sparsity and Diversity. We then formalize the task of multi-document summarization as an optimization problem according to the above properties, and use simulated annealing algorithm to solve it.Extensive experiments on summarization benchmark data sets DUC2006 and DUC2007 show that our proposed model is effective and outperforms the state-of-the-art algorithms.

Dynamic programming (DP) is a fundamental tool used to obtain exact, optimal solutions for many combinatorial optimization problems. Among these problems, important ones including the knapsack problems and the computation of edit distances between string pairs can be solved with a kind of DP that corresponds to solving the shortest path problem on a directed acyclic graph (DAG). These problems can be solved efficiently with DP, however, in practical situations, we want to solve the customized problems made by adding logical constraints to the original problems. Developing an algorithm specifically for each combination of a problem and a constraint set is unrealistic. The proposed method, BDD-Constrained Search (BCS), exploits a Binary Decision Diagram (BDD) that represents the logical constraints in combination with the DAG that represents the problem. The BCS runs DP on the DAG while using the BDD to check the equivalence and the validity of intermediate solutions to efficiently solve the problem. The important feature of BCS is that it can be applied to problems with various types of logical constraints in a unified way once we represent the constraints as a BDD. We give a theoretical analysis on the time complexity of BCS and also conduct experiments to compare its performance to that of a state-of-the-art integer linear programming solver.

Modern organizations (e.g., hospitals, social networks, government agencies) rely heavily on audit to detect and punish insiders who inappropriately access and disclose confidential information. Recent work on audit games models the strategic interaction between an auditor with a single audit resource and auditees as a Stackelberg game, augmenting associated well-studied security games with a configurable punishment parameter. We significantly generalize this audit game model to account for multiple audit resources where each resource is restricted to audit a subset of all potential violations, thus enabling application to practical auditing scenarios. We provide an FPTAS that computes an approximately optimal solution to the resulting non-convex optimization problem. The main technical novelty is in the design and correctness proof of an optimization transformation that enables the construction of this FPTAS. In addition, we experimentally demonstrate that this transformation significantly speeds up computation of solutions for a class of audit games and security games.