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1. Is Algorithm Selection Worth It? Comparing Selecting Single Algorithms and Parallel Execution

   Kashgarani, Haniye; Kotthoff, Lars (January 2021, Proceedings of Machine Learning Research)

   null (Ed.)

   For many practical problems, there is more than one algorithm or approach to solve them. Such algorithms often have complementary performance – where one fails, another performs well, and vice versa. Per-instance algorithm selection leverages this by employing portfolios of complementary algorithms to solve sets of difficult problems, choosing the most appropriate algorithm for each problem instance. However, this requires complex models to effect this selection and introduces overhead to compute the data needed for those models. On the other hand, even basic hardware is more than capable of running several algorithms in parallel. We investigate the tradeoff between selecting a single algorithm and running multiple in parallel and incurring a slowdown because of contention for shared resources. Our results indicate that algorithm selection is worth it, especially for large portfolios. 

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2. MAPFAST: A Deep Algorithm Selector for Multi Agent Path Finding using Shortest Path Embeddings

   Ren, Jingyao; Sathiyanarayanan, Vikraman; Ewing, Eric; Senbaslar, Baskin; Ayanian, Nora (May 2021, Autonomous agents and multiagent systems)

   null (Ed.)

   Solving the Multi-Agent Path Finding (MAPF) problem optimally is known to be NP-Hard for both make-span and total arrival time minimization. While many algorithms have been developed to solve MAPF problems, there is no dominating optimal MAPF algorithm that works well in all types of problems and no standard guidelines for when to use which algorithm. In this work, we develop the deep convolutional network MAPFAST (Multi-Agent Path Finding Algorithm SelecTor), which takes a MAPF problem instance and attempts to select the fastest algorithm to use from a portfolio of algorithms. We improve the performance of our model by including single-agent shortest paths in the instance embedding given to our model and by utilizing supplemental loss functions in addition to a classification loss. We evaluate our model on a large and di- verse dataset of MAPF instances, showing that it outperforms all individual algorithms in its portfolio as well as the state-of-the-art optimal MAPF algorithm selector. We also provide an analysis of algorithm behavior in our dataset to gain a deeper understanding of optimal MAPF algorithms’ strengths and weaknesses to help other researchers leverage different heuristics in algorithm designs. 

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3. Online Summarization via Submodular and Convex Optimization

   Elhamifar, E.; De Paolis Kaluza, M. C. (January 2017, IEEE Conference on Computer Vision and Pattern Recognition)

   We consider the problem of subset selection in the online setting, where data arrive incrementally. Instead of storing and running subset selection on the entire dataset, we propose an incremental subset selection framework that, at each time instant, uses the previously selected set of representatives and the new batch of data in order to update the set of representatives. We cast the problem as an integer bi- nary optimization minimizing the encoding cost of the data via representatives regularized by the number of selected items. As the proposed optimization is, in general, NP-hard and non-convex, we study a greedy approach based on un- constrained submodular optimization and also propose an efficient convex relaxation. We show that, under appropriate conditions, the solution of our proposed convex algorithm achieves the global optimal solution of the non-convex problem. Our results also address the conventional problem of subset selection in the offline setting, as a special case. By extensive experiments on the problem of video summarization, we demonstrate that our proposed online subset selection algorithms perform well on real data, capturing diverse representative events in videos, while they obtain objective function values close to the offline setting. 

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4. Online Summarization via Submodular and Convex Optimization

   Elhamifar, E.; De Paolis Kaluza, M. C. (January 2017, IEEE Conference on Computer Vision and Pattern Recognition)

   We consider the problem of subset selection in the online setting, where data arrive incrementally. Instead of storing and running subset selection on the entire dataset, we propose an incremental subset selection framework that, at each time instant, uses the previously selected set of representatives and the new batch of data in order to update the set of representatives. We cast the problem as an integer binary optimization minimizing the encoding cost of the data via representatives regularized by the number of selected items. As the proposed optimization is, in general, NP-hard and non-convex, we study a greedy approach based on unconstrained submodular optimization and also propose an efficient convex relaxation. We show that, under appropriate conditions, the solution of our proposed convex algorithm achieves the global optimal solution of the non-convex problem. Our results also address the conventional problem of subset selection in the offline setting, as a special case. By extensive experiments on the problem of video summarization, we demonstrate that our proposed online subset selection algorithms perform well on real data, capturing diverse representative events in videos, while they obtain objective function values close to the offline setting. 

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5. Machine Learning and Data Mining with Combinatorial Optimization Algorithms

   https://doi.org/10.1287/educ.2018.0179  

   Dorit S. Hochbaum (October 2018, INFORMS TutORials in Operations Research)

   Binary classification is a fundamental machine learning task defined as correctly assigning new objects to one of two groups based on a set of training objects. Driven by the practical importance of binary classification, numerous machine learning techniques have been developed and refined over the last three decades. Among the most popular techniques are artificial neural networks, decision trees, ensemble methods, logistic regression, and support vector machines. We present here machine learning and pattern recognition algorithms that, unlike the commonly used techniques, are based on combinatorial optimization and make use of information on pairwise relations between the objects of the data set, whether training objects or not. These algorithms solve the respective problems optimally and efficiently, in contrast to the primarily heuristic approaches currently used for intractable problem models in pattern recognition and machine learning. The algorithms described solve efficiently the classification problem as a network flow problem on a graph. The technical tools used in the algorithm are the parametric cut procedure and a process called sparse computation that computes only the pairwise similarities that are “relevant.” Sparse computation enables the scalability of any algorithm that uses pairwise similarities. We present evidence on the effectiveness of the approaches, measured in terms of accuracy and running time, in pattern recognition, image segmentation, and general data mining. 

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