A Neural Network Model for Inter-problem Adaptive Online Time Allocation

Gagliolo, Matteo; Schmidhuber, Jürgen

doi:10.1007/11550907_2

Cited by 10 publications

(9 citation statements)

References 6 publications

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“…We considered a set of 4 parametric probability distributions (shown in Table 1 with exemplary instantiations shown in Figure 2), most of which have been widely studied to describe the RTDs of combinatorial problem solvers [Frost et al, 1997;Gagliolo and Schmidhuber, 2006a;Hutter et al, 2006]. First, we considered the Normal distribution (N) as a baseline, due to its widespread use throughout the sciences.…”

Section: Parametric Families Of Rtdsmentioning

confidence: 99%

“…Since the runtimes of hard combinatorial solvers often vary on an exponential scale (likely due to the N P-hardness of the problems studied), a much better fit of empirical RTDs is typically achieved by a lognormal distribution (LOG); this distribution is attained if the logarithm of the runtimes is normaldistributed and has been shown to fit empirical RTDs well in previous work [Frost et al, 1997].…”

Section: Parametric Families Of Rtdsmentioning

confidence: 99%

“…The work most closely related to ours is by Gagliolo and Schmidhuber (2005), who proposed to use NNs to learn a distribution of the time left until an algorithm solves a problem based on features describing the algorithm's current state and the problem to be solved; they used these predictions to dynamically assign time slots to algorithms. In contrast, we use NNs to predict RTDs for unseen problem instances.…”

Section: Introductionmentioning

confidence: 99%

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Neural Networks for Predicting Algorithm Runtime Distributions

Eggensperger

Lindauer

Hutter

2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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Many state-of-the-art algorithms for solving hard combinatorial problems in artificial intelligence (AI) include elements of stochasticity that lead to high variations in runtime, even for a fixed problem instance. Knowledge about the resulting runtime distributions (RTDs) of algorithms on given problem instances can be exploited in various meta-algorithmic procedures, such as algorithm selection, portfolios, and randomized restarts. Previous work has shown that machine learning can be used to individually predict mean, median and variance of RTDs. To establish a new state-of-the-art in predicting RTDs, we demonstrate that the parameters of an RTD should be learned jointly and that neural networks can do this well by directly optimizing the likelihood of an RTD given runtime observations. In an empirical study involving five algorithms for SAT solving and AI planning, we show that neural networks predict the true RTDs of unseen instances better than previous methods, and can even do so when only few runtime observations are available per training instance.2. We propose DistNet, a practical NN for predicting RTDs, and discuss the bells and whistles that make it work.3. We show that DistNet achieves substantially better performance than previous methods when trained only on a few observations per training instance.

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Section: Parametric Families Of Rtdsmentioning

confidence: 99%

Section: Parametric Families Of Rtdsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Neural Networks for Predicting Algorithm Runtime Distributions

Eggensperger

Lindauer

Hutter

2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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“…Other approaches include support vector machines (Hough & Williams, 2006;Arbelaez et al, 2009), reinforcement learning (Armstrong et al, 2006), neural networks (Gagliolo & Schmidhuber, 2005), decision tree ensembles (Hough & Williams, 2006), ensembles of general classification algorithms (Kotthoff, Miguel, & Nightingale, 2010), boosting (Bhowmick et al, 2006), hybrid approaches that combine regression and classification (Kotthoff, 2012a), multinomial logistic regression (Samulowitz & Memisevic, 2007), self-organising maps (Smith-Miles, 2008b) and clustering (Stamatatos & Stergiou, 2009;Stergiou, 2009;Kadioglu et al, 2010). Sayag et al (2006), Streeter et al (2007a compute schedules for running the algorithms in the portfolio based on a statistical model of the problem instance distribution and performance data for the algorithms.…”

Section: Per-portfolio Modelsmentioning

confidence: 99%

Algorithm Selection for Combinatorial Search Problems: A Survey

2014

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The Algorithm Selection Problem is concerned with selecting the best algorithm to solve a given problem on a case-by-case basis. It has become especially relevant in the last decade, as researchers are increasingly investigating how to identify the most suitable existing algorithm for solving a problem instead of developing new algorithms. This survey presents an overview of this work focusing on the contributions made in the area of combinatorial search problems, where Algorithm Selection techniques have achieved significant performance improvements. We unify and organise the vast literature according to criteria that determine Algorithm Selection systems in practice. The comprehensive classification of approaches identifies and analyses the different directions from which Algorithm Selection has been approached. This paper contrasts and compares different methods for solving the problem as well as ways of using these solutions. It closes by identifying directions of current and future research.

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“…This trade-off is typically ignored in offline algorithm selection, and the size of the training set is chosen heuristically. In our previous work [13,14,15], we have kept an online view of algorithm selection, in which the only input available to the meta-learner is a set of algorithms, of unknown performance, and a sequence of problem instances that have to be solved. Rather than artificially subdividing the problem set into a training and a test set, we iteratively update the model each time an instance is solved, and use it to guide algorithm selection on the next instance.…”

Section: Introductionmentioning

confidence: 99%

Algorithm Selection as a Bandit Problem with Unbounded Losses

Gagliolo

Schmidhuber

2010

Lecture Notes in Computer Science

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Algorithm selection is typically based on models of algorithm performance, learned during a separate offline training sequence, which can be prohibitively expensive. In recent work, we adopted an online approach, in which a performance model is iteratively updated and used to guide selection on a sequence of problem instances. The resulting exploration-exploitation trade-off was represented as a bandit problem with expert advice, using an existing solver for this game, but this required the setting of an arbitrary bound on algorithm runtimes, thus invalidating the optimal regret of the solver. In this paper, we propose a simpler framework for representing algorithm selection as a bandit problem, with partial information, and an unknown bound on losses. We adapt an existing solver to this game, proving a bound on its expected regret, which holds also for the resulting algorithm selection technique. We present preliminary experiments with a set of SAT solvers on a mixed SAT-UNSAT benchmark.Comment: 15 pages, 2 figure

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A Neural Network Model for Inter-problem Adaptive Online Time Allocation

Cited by 10 publications

References 6 publications

Neural Networks for Predicting Algorithm Runtime Distributions

Neural Networks for Predicting Algorithm Runtime Distributions

Algorithm Selection for Combinatorial Search Problems: A Survey

Algorithm Selection as a Bandit Problem with Unbounded Losses

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