Related papers: An Analytic Expression of Relative Approximation E…
Quality gain is the expected relative improvement of the function value in a single step of a search algorithm. Quality gain analysis reveals the dependencies of the quality gain on the parameters of a search algorithm, based on which one…
Evolutionary algorithms (EA), a class of stochastic search methods based on the principles of natural evolution, have received widespread acclaim for their exceptional performance in various real-world optimization problems. While…
In this paper we show how to find the exact error (not just an estimate of the error) of a conforming mixed approximation by using the functional type a posteriori error estimates in the spirit of Repin. The error is measured in a mixed…
When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning…
Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
Choosing the right selection rate is a long standing issue in evolutionary computation. In the continuous unconstrained case, we prove mathematically that a single parent $\mu=1$ leads to a sub-optimal simple regret in the case of the…
Genetic programming (GP) is an evolutionary computation technique to solve problems in an automated, domain-independent way. Rather than identifying the optimum of a function as in more traditional evolutionary optimization, the aim of GP…
The (1+1)-evolution strategy (ES) with success-based step-size adaptation is analyzed on a general convex quadratic function and its monotone transformation, that is, $f(x) = g((x - x^*)^\mathrm{T} H (x - x^*))$, where…
We study the computational limits of Low-Rank Adaptation (LoRA) for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient…
Evolutionary algorithms have been used in the digital art scene since the 1970s. A popular application of genetic algorithms is to optimize the procedural placement of vector graphic primitives to resemble a given painting. In recent years,…
This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…
The paper presents a solution for the problem of choosing a method for analytical determining of weight factors for a genetic algorithm additive fitness function. This algorithm is the basis for an evolutionary process, which forms a stable…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
Time-series prediction involves forecasting future values using machine learning models. Feature engineering, whereby existing features are transformed to make new ones, is critical for enhancing model performance, but is often manual and…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
Motivated by learning of correlated equilibria in non-cooperative games, we perform a large deviations analysis of a regret minimizing stochastic approximation algorithm. The regret minimization algorithm we consider comprises multiple…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
In the evolutionary computation community, it is widely believed that stagnation impedes convergence in evolutionary algorithms, and that convergence inherently indicates optimality. However, this perspective is misleading. In this study,…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…