Related papers: Global Convergence of the (1+1) Evolution Strategy
A (3+1)-evolutionary method in the framework of Regge Calculus, essentially a method of approximating manifolds with rigid simplices, makes an excellent tool to probe the evolution of manifolds with non-trivial topology or devoid of…
We derived a new speed limit in population dynamics, which is a fundamental limit on the evolutionary rate. By splitting the contributions of selection and mutation to the evolutionary rate, we obtained the new bound on the speed of…
The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a…
We propose a study of the Adaptive Biasing Force method's robustness under generic (possibly non-conservative) forces. We first ensure the flat histogram property is satisfied in all cases. We then introduce a fixed point problem yielding…
Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…
This work establishes new convergence guarantees for gradient descent in smooth convex optimization via a computer-assisted analysis technique. Our theory allows nonconstant stepsize policies with frequent long steps potentially violating…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage…
Global optimization of a non-convex objective function often appears in large-scale machine-learning and artificial intelligence applications. Recently, consensus-based optimization (in short CBO) methods have been introduced as one of the…
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…
In this paper, two-to-one mappings and involutions without any fixed point on finite fields of even characteristic are investigated. First, we characterize a closed relationship between them by implicit functions and develop an AGW-like…
A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. However, such an assumption is often violated in the real world due to non-stationarity of the…
Punctuated equilibrium is a mode of evolution in which phenetic change occurs in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but no major phenotypic change occurs. Punctuated…
A key property underlying the success of evolutionary algorithms (EAs) is their global search behavior, which allows the algorithms to `jump' from a current state to other parts of the search space, thereby avoiding to get stuck in local…
The dynamic problem of enclosing an expanding fire can be modelled by a discrete variant in a grid graph. While the fire expands to all neighbouring cells in any time step, the fire fighter is allowed to block $c$ cells in the average…
In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion…
In this two-part study we develop a unified approach to the analysis of the global exactness of various penalty and augmented Lagrangian functions for finite-dimensional constrained optimization problems. This approach allows one to verify…
A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…