A Rigorous Runtime Analysis for Quasi-Random Restarts and Decreasing Stepsize

Schoenauer, Marc; Teytaud, Fabien; Teytaud, Olivier

doi:10.1007/978-3-642-35533-2_4

Cited by 11 publications

(21 citation statements)

References 21 publications

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“…Introductions to practical approaches for such restart strategies are given by Martí [2003] and Lourenço et al [2010]. A relatively recent theoretical result is presented by Schoenauer et al (2012). Several studies show the substantial impact of the restart policy on the efficiency of solvers for satisfiability problems (Biere andFröhlich 2015, Huang 2007).…”

Section: Related Workmentioning

confidence: 99%

An Improved Generic Bet-and-Run Strategy with Performance Prediction for Stochastic Local Search

Weise

Wagner

2019

AAAI

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A commonly used strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. Building on the recent success of BET-AND-RUN approaches for restarted local search solvers, we introduce an improved generic BET-AND-RUN strategy. The goal is to obtain the best possible results within a given time budget t using a given black-box optimization algorithm. If no prior knowledge about problem features and algorithm behavior is available, the question about how to use the time budget most efficiently arises. We propose to first start k ≥ 1 independent runs of the algorithm during an initialization budget t1 < t, pausing these runs, then apply a decision maker D to choose 1 ≤ m < k runs from them (consuming t2 ≥ 0 time units in doing so), and then continuing these runs for the remaining t3 = t − t1 − t2 time units. In previous BET-AND-RUN strategies, the decision maker D = currentBest would simply select the run with the best-so-far results at negligible time. We propose using more advanced methods to discriminate between "good" and "bad" sample runs, with the goal of increasing the correlation of the chosen run with the a-posteriori best one. We test several different approaches, including neural networks trained or polynomials fitted on the current trace of the algorithm to predict which run may yield the best results if granted the remaining budget. We show with extensive experiments that this approach can yield better results than the previous methods, but also find that the currentBest method is a very reliable and robust baseline approach.

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Section: Related Workmentioning

confidence: 99%

An Improved Generic Bet-and-Run Strategy with Performance Prediction for Stochastic Local Search

Weise

Wagner

2019

AAAI

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“…Step-size (QRDS) [14] is an Evolution-Strategy-based Multi-Modal Optimization algorithm which uses the restarting technique. It consists in a single-optimum local search (see Algorithm 1), controlled by a restart strategy (see Algorithm 2).…”

Section: Quasi-random Restart With Decreasingmentioning

confidence: 99%

“…Another classic MMO technique is the restarting technique [10]- [13]. The algorithm proposed in [14] uses a quasirandom restart strategy with a decreasing step-size search. This algorithm has good performances when the optima are quite equally distributed over the search space or when the function is locally simple.…”

Section: Introductionmentioning

confidence: 99%

Improving Multi-modal Optimization Restart Strategy Through Multi-armed Bandit

Dubois

Dehos

Teytaud

2018

2018 17th IEEE International Conference on Machine Learning and Applications (ICMLA)

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Multi-Modal Optimization problems are widespread and can be solved using numerous methods, such as niching, sharing or clearing. In this paper, we are interested in algorithms based on restart strategies, where the searching point is restarted at another initial position when an optimum is found. Previous works show that the choice of these initial positions greatly impacts the performance of the algorithm but is not easy to make. In this paper, we propose a new restart strategy, based on reinforcement learning. Our algorithm subdivides the search space and uses a Multi-Armed Bandit technique to choose the successive restart positions. We experiment this algorithm on various functions and on a modified Hump function with more complex local areas. Our results show significant improvements over previous algorithms, such as the Quasi-Random restart with Decreasing Step-size algorithm.

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“…Fewer results are known for the optimisation case. Marti [13] and Lourenço et al [11] present practical approaches, and a recent theoretical result is presented by Schoenauer et al [14]. Particularly for the satis ability problem, several studies make an empirical comparison of a number of restart policies [1,7].…”

Section: Gecco '17 Berlin Germanymentioning

confidence: 99%

Theoretical results on bet-and-run as an initialisation strategy

Lissovoi

Sudholt

Wagner

et al. 2017

Proceedings of the Genetic and Evolutionary Computation Conference

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Sponsor: Australian Research Council (Early Career Researcher Award DE160100850); Engineering and Physical Sciences Research Council (EP/M004252/1); Seventh Framework Programme (FP7/2007-2013)Bet-and-run initialisation strategies have been experimentally shown to be beneficial on classical NP-complete problems such as the travelling salesperson problem and minimum vertex cover. We analyse the performance of a bet-and-run restart strategy, where k independent islands run in parallel for t1 iterations, after which the optimisation process continues on only the best-performing island. We define a family of pseudo-Boolean functions, consisting of a plateau and a slope, as an abstraction of real fitness landscapes with promising and deceptive regions. The plateau shows a high fitness, but does not allow for further progression, whereas the slope has a low fitness initially, but does lead to the global optimum. We show that bet-and-run strategies with non-trivial k and t1 are necessary to find the global optimum efficiently. We show that the choice of t1 is linked to properties of the function. Finally, we provide a fixed budget analysis to guide selection of the bet-and-run parameters to maximise expected fitness after t = k * t1 + t2 fitness evaluations

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A Rigorous Runtime Analysis for Quasi-Random Restarts and Decreasing Stepsize

Cited by 11 publications

References 21 publications

An Improved Generic Bet-and-Run Strategy with Performance Prediction for Stochastic Local Search

An Improved Generic Bet-and-Run Strategy with Performance Prediction for Stochastic Local Search

Improving Multi-modal Optimization Restart Strategy Through Multi-armed Bandit

Theoretical results on bet-and-run as an initialisation strategy

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