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In recent years, Evolutionary Strategies were actively explored in robotic tasks for policy search as they provide a simpler alternative to reinforcement learning algorithms. However, this class of algorithms is often claimed to be…
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…
Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
Evolutionary optimization is a generic population-based metaheuristic that can be adapted to solve a wide variety of optimization problems and has proven very effective for combinatorial optimization problems. However, the potential of this…
We discuss a new optimization strategy, which considerably improves the effectivity of evolutionary algorithms applied to a certain class of optimization problems. The basic principle is to solve first a simpler related problem, which is…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
Differential Dynamic Programming is an optimal control technique often used for trajectory generation. Many variations of this algorithm have been developed in the literature, including algorithms for stochastic dynamics or state and input…
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a…
Recently, continuous-time dynamical systems, based on systems of ordinary differential equations, for mosquito populations are studied. In this paper we consider discrete-time dynamical system generated by an evolution quadratic operator of…
In this work, we systematically present a new dynamical systems approach to standard inflationary processes and their variants as constant-roll inflation. Using the techniques presented in our work one can in general investigate the…
The aim of global optimization is to find the global optimum of arbitrary classes of functions, possibly highly multimodal ones. In this paper we focus on the subproblem of global optimization for differentiable functions and we propose an…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…
Evolutionary algorithms have been widely applied for solving dynamic constrained optimization problems (DCOPs) as a common area of research in evolutionary optimization. Current benchmarks proposed for testing these problems in the…
Operational maturity of biological control systems have fuelled the inspiration for a large number of mathematical and logical models for control, automation and optimisation. The human brain represents the most sophisticated control…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
Population-based evolutionary algorithms are often considered when approaching computationally expensive black-box optimization problems. They employ a selection mechanism to choose the best solutions from a given population after comparing…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…