Related papers: Upper Bounds on the Runtime of the Univariate Marg…
Unlike traditional evolutionary algorithms which produce offspring via genetic operators, Estimation of Distribution Algorithms (EDAs) sample solutions from probabilistic models which are learned from selected individuals. It is hoped that…
We perform a rigorous runtime analysis for the Univariate Marginal Distribution Algorithm on the LeadingOnes function, a well-known benchmark function in the theory community of evolutionary computation with a high correlation between…
With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LeadingOnes benchmark function in the desirable regime with low genetic drift. If the population size is…
Estimation of Distribution Algorithms (EDAs) are stochastic heuristics that search for optimal solutions by learning and sampling from probabilistic models. Despite their popularity in real-world applications, there is little rigorous…
Understanding how crossover works is still one of the big challenges in evolutionary computation research, and making our understanding precise and proven by mathematical means might be an even bigger one. As one of few examples where…
Recent research in the runtime analysis of estimation of distribution algorithms (EDAs) has focused on univariate EDAs for multi-valued decision variables. In particular, the runtime of the multi-valued cGA (r-cGA) and UMDA on multi-valued…
A class of metaheuristic techniques called estimation-of-distribution algorithms (EDAs) are employed in optimization as more sophisticated substitutes for traditional strategies like evolutionary algorithms. EDAs generally drive the search…
Despite significant progress in the theory of evolutionary algorithms, the theoretical understanding of evolutionary algorithms which use non-trivial populations remains challenging and only few rigorous results exist. Already for the most…
We introduce a new benchmark problem called Deceptive Leading Blocks (DLB) to rigorously study the runtime of the Univariate Marginal Distribution Algorithm (UMDA) in the presence of epistasis and deception. We show that simple Evolutionary…
In the first and so far only mathematical runtime analysis of an estimation-of-distribution algorithm (EDA) on a multimodal problem, Hasen\"ohrl and Sutton (GECCO 2018) showed for any $k = o(n)$ that the compact genetic algorithm (cGA) with…
Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…
The compact genetic algorithm (cGA) is one of the simplest estimation-of-distribution algorithms (EDAs). Next to the univariate marginal distribution algorithm (UMDA) -- another simple EDA -- , the cGA has been subject to extensive…
We argue that proven exponential upper bounds on runtimes, an established area in classic algorithms, are interesting also in heuristic search and we prove several such results. We show that any of the algorithms randomized local search,…
Recently, the runtime analysis of multi-valued estimation-of-distribution algorithms in the framework of Ben Jedidia et al. (TCS 2024) has made significant advancements. However, almost all existing analyses are limited to multi-valued…
We show that any randomised Monte Carlo distributed algorithm for the Lov\'asz local lemma requires $\Omega(\log \log n)$ communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the…
The sharpest known high probability generalization bounds for uniformly stable algorithms (Feldman, Vondr\'{a}k, 2018, 2019), (Bousquet, Klochkov, Zhivotovskiy, 2020) contain a generally inevitable sampling error term of order…
Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation.…
The expected running time of the classical (1+1) EA on the OneMax benchmark function has recently been determined by Hwang et al. (2018) up to additive errors of $O((\log n)/n)$. The same approach proposed there also leads to a full…
Neural networks are gaining popularity in the reinforcement learning field due to the vast number of successfully solved complex benchmark problems. In fact, artificial intelligence algorithms are, in some cases, able to overcome human…
Evolutionary algorithms (EAs) are population-based general-purpose optimization algorithms, and have been successfully applied in various real-world optimization tasks. However, previous theoretical studies often employ EAs with only a…