Concentration of first hitting times under additive drift

作者: Timo Kötzing

DOI: 10.1145/2576768.2598364

关键词:

摘要: Recent advances in drift analysis have given us better and tools for understanding random processes, including the run time of randomized search heuristics. In setting multiplicative we do not only excellent bounds on expected time, but also more general results showing concentration}of time. this paper investigate additive under assumption strong concentration "step size" process. Under sufficiently towards goal show a hitting contrast to this, that presence small Gambler's-Ruin-like behavior process overrides influence drift. Finally, negative is superpolynomial with high probability; corresponds so-called theorem, which give new variants.

参考文章(21)
Nicholas Charles Wormald, The differential equation method for random graph processes and greedy algorithms Wydawnictwo Naukowe Pwn. pp. 73- 155 ,(1999)
Ottilia Chareka, Patrick Chareka, Sarah Kennendy, LOCALLY SUB-GAUSSIAN RANDOM VARIABLES AND THE STRONG LAW OF LARGE NUMBERS ,(2006)
Benjamin Doerr, Leslie Ann Goldberg, Adaptive Drift Analysis Algorithmica. ,vol. 65, pp. 224- 250 ,(2013) , 10.1007/S00453-011-9585-3
Daniel Johannsen, Random combinatorial structures and randomized search heuristics Universität des Saarlandes Saarbrücken. ,(2010) , 10.22028/D291-26016
Per Kristian Lehre, Carsten Witt, General Drift Analysis with Tail Bounds arXiv: Neural and Evolutionary Computing. ,(2013)
Bruce Hajek, Hitting-time and occupation-time bounds implied by drift analysis with applications Advances in Applied Probability. ,vol. 14, pp. 502- 525 ,(1982) , 10.2307/1426671
Xiequan Fan, Ion Grama, Quansheng Liu, Hoeffding's inequality for supermartingales Stochastic Processes and their Applications. ,vol. 122, pp. 3545- 3559 ,(2012) , 10.1016/J.SPA.2012.06.009
Devdatt P. Dubhashi, Alessandro Panconesi, Concentration of Measure for the Analysis of Randomized Algorithms ,(2012)
Kazuoki Azuma, Weighted sums of certain dependent random variables Tohoku Mathematical Journal. ,vol. 19, pp. 357- 367 ,(1967) , 10.2748/TMJ/1178243286
Pietro S. Oliveto, Carsten Witt, Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation Algorithmica. ,vol. 59, pp. 369- 386 ,(2011) , 10.1007/S00453-010-9387-Z