Related papers: Momentum Accelerates Evolutionary Dynamics
Previous evolutionary studies demonstrated how evaluating evolving agents in variable environmental conditions enable them to develop solutions that are robust to environmental variation. We demonstrate how the robustness of the agents can…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
LLM-driven evolutionary systems have shown promise for automated science discovery, yet existing approaches such as AlphaEvolve rely on full-code histories that are context-inefficient and potentially provide weak evolutionary guidance. In…
Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time…
Recent studies revealed complex convergence dynamics in gradient-based methods, which has been little understood so far. Changing the step size to balance between high convergence rate and small generalization error may not be sufficient:…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
The vertebrate motor system employs dimensionality-reducing strategies to limit the complexity of movement coordination, for efficient motor control. But when environments are dense with hidden action-outcome contingencies, movement…
It is well-known that population structure is a catalyst for the evolution of cooperation since individuals can reciprocate with their neighbors through local interactions defined by network structures. Previous research typically relies on…
We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of…
Distributed stochastic gradient methods are widely used to preserve data privacy and ensure scalability in large-scale learning tasks. While existing theory on distributed momentum Stochastic Gradient Descent (mSGD) mainly focuses on…
Evolutionary algorithms are popular heuristics for solving various combinatorial problems as they are easy to apply and often produce good results. Island models parallelize evolution by using different populations, called islands, which…
Stochastic difference-of-convex (DC) optimization is prevalent in numerous machine learning applications, yet its convergence properties under small batch sizes remain poorly understood. Existing methods typically require large batches or…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
In evolutionary optimization, it is important to understand how fast evolutionary algorithms converge to the optimum per generation, or their convergence rate. This paper proposes a new measure of the convergence rate, called average…
In addition to their undisputed success in solving classical optimization problems, neuroevolutionary and population-based algorithms have become an alternative to standard reinforcement learning methods. However, evolutionary methods often…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current…
Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid…