207 research outputs found
Evaluating Stationary Distribution of the Binary GA Markov Chain in Special Cases
The evolutionary algorithm stochastic process is well-known to be
Markovian. These have been under investigation in much of the
theoretical evolutionary computing research. When mutation rate is
positive, the Markov chain modeling an evolutionary algorithm is
irreducible and, therefore, has a unique stationary distribution,
yet, rather little is known about the stationary distribution. On the other
hand, knowing the stationary distribution may provide
some information about the expected times to hit optimum, assessment of the biases due to recombination and is of importance in population
genetics to assess what\u27s called a ``genetic load" (see the
introduction for more details). In this talk I will show how the quotient
construction method can be exploited to derive rather explicit bounds on the ratios of the stationary distribution values of various subsets of
the state space. In fact, some of the bounds obtained in the current
work are expressed in terms of the parameters involved in all the
three main stages of an evolutionary algorithm: namely selection,
recombination and mutation. I will also discuss the newest developments which may allow for further improvements of the bound
Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes
New algorithms for computing of asymptotic expansions for stationary
distributions of nonlinearly perturbed semi-Markov processes are presented. The
algorithms are based on special techniques of sequential phase space reduction,
which can be applied to processes with asymptotically coupled and uncoupled
finite phase spaces.Comment: 83 page
A Version of Geiringer-like Theorem for Decision Making in the Environments with Randomness and Incomplete Information
Purpose: In recent years Monte-Carlo sampling methods, such as Monte Carlo
tree search, have achieved tremendous success in model free reinforcement
learning. A combination of the so called upper confidence bounds policy to
preserve the "exploration vs. exploitation" balance to select actions for
sample evaluations together with massive computing power to store and to update
dynamically a rather large pre-evaluated game tree lead to the development of
software that has beaten the top human player in the game of Go on a 9 by 9
board. Much effort in the current research is devoted to widening the range of
applicability of the Monte-Carlo sampling methodology to partially observable
Markov decision processes with non-immediate payoffs. The main challenge
introduced by randomness and incomplete information is to deal with the action
evaluation at the chance nodes due to drastic differences in the possible
payoffs the same action could lead to. The aim of this article is to establish
a version of a theorem that originated from population genetics and has been
later adopted in evolutionary computation theory that will lead to novel
Monte-Carlo sampling algorithms that provably increase the AI potential. Due to
space limitations the actual algorithms themselves will be presented in the
sequel papers, however, the current paper provides a solid mathematical
foundation for the development of such algorithms and explains why they are so
promising.Comment: 53 pages in size. This work has been recently submitted to the IJICC
(International Journal on Intelligent Computing and Cybernetics
06061 Abstracts Collection -- Theory of Evolutionary Algorithms
From 05.02.06 to 10.02.06, the Dagstuhl Seminar 06061 ``Theory of Evolutionary Algorithms\u27\u27 was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
A combinatorial approach to biological structures and networks in predictive medicine
This work concerns the study of combinatorial models for biological structures and networks as motivated by questions in predictive medicine. Through multiple examples, the power of combinatorial models to simplify problems and facilitate computation is explored. First, continuous time Markov models are used as a model to study the progression of Alzheimer’s disease and identify which variables best predict progression at each stage. Next, RNA secondary structures are modeled by a thermodynamic Gibbs distribution on plane trees. The limiting distribution (as the number of edges in the tree goes to infinity) is studied to gain insight into the limits of the model. Additionally, a Markov chain is developed to sample from the distribution in the finite case, creating a tool for understanding what tree properties emerge from the thermodynamics. Finally, knowledge graphs are used to encode relationships extracted from the biomedical literature, and algorithms for efficient computation on these graphs are explored.Ph.D
Modeling of chemical reaction systems with detailed balance using gradient structures
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels
Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels
Modeling of chemical reaction systems with detailed balance using gradient structures
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels
- …