Related papers: The Fitness Level Method with Tail Bounds

The fitness level method is a popular tool for analyzing the hitting time of elitist evolutionary algorithms. Its idea is to divide the search space into multiple fitness levels and estimate lower and upper bounds on the hitting time using…

The fitness level method is a widely used technique for estimating the mean hitting time of elitist evolutionary algorithms on level-based fitness functions. However, this paper identifies its main limitation: the linear lower bound derived…

One of the first and easy to use techniques for proving run time bounds for evolutionary algorithms is the so-called method of fitness levels by Wegener. It uses a partition of the search space into a sequence of levels which are traversed…

We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…

While most theoretical run time analyses of discrete randomized search heuristics focused on finite search spaces, we consider the search space $\mathbb{Z}^n$. This is a further generalization of the search space of multi-valued decision…

We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. Drawing from Steinke & Zakynthinou (2020), this framework leads to bounds that depend on the conditional…

The fine-tuning paradigm has emerged as a prominent approach for addressing long-tail learning tasks in the era of foundation models. However, the impact of fine-tuning strategies on long-tail learning performance remains unexplored. In…

In this paper, we consider a fitness-level model of a non-elitist mutation-only evolutionary algorithm (EA) with tournament selection. The model provides upper and lower bounds for the expected proportion of the individuals with fitness…

Performance analysis of all kinds of randomised search heuristics is a rapidly growing and developing field. Run time and solution quality are two popular measures of the performance of these algorithms. The focus of this paper is on the…

The $(1+(\lambda,\lambda))$ genetic algorithm, first proposed at GECCO 2013, showed a surprisingly good performance on so me optimization problems. The theoretical analysis so far was restricted to the OneMax test function, where this GA…

Test-time scaling has emerged as a critical avenue for enhancing the reasoning capabilities of Large Language Models (LLMs). Though the straight-forward ''best-of-$N$'' (BoN) strategy has already demonstrated significant improvements in…

The best arm identification problem requires identifying the best alternative (i.e., arm) in active experimentation using the smallest number of experiments (i.e., arm pulls), which is crucial for cost-efficient and timely decision-making…

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,…

In the last decade remarkable progress has been made in development of suitable proof techniques for analysing randomised search heuristics. The theoretical investigation of these algorithms on classes of functions is essential to the…

The search for binary sequences with low peak sidelobe level value represents a formidable computational problem. To locate better sequences for this problem, we designed a stochastic algorithm that uses two fitness functions. In these…

We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying…

We present a new method for analyzing the running time of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel running time. This allows…

The fine-tuning paradigm in addressing long-tail learning tasks has sparked significant interest since the emergence of foundation models. Nonetheless, how fine-tuning impacts performance in long-tail learning was not explicitly quantified.…

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…

The conventional detectors tend to make imbalanced classification and suffer performance drop, when the distribution of the training data is severely skewed. In this paper, we propose to use the mean classification score to indicate the…