Random Search Problem Research Articles

EVAE: Evolutionary Variational Autoencoder.

Variational autoencoders (VAEs) are challenged by the imbalance between representation inference and task fitting caused by surrogate loss. To address this issue, existing methods adjust their balance by directly tuning their coefficients. However, these methods suffer from a tradeoff uncertainty, i.e., nondynamic regulation over iterations and inflexible hyperparameters for learning tasks. Accordingly, we make the first attempt to introduce an evolutionary VAE (eVAE), building on the variational information bottleneck (VIB) theory and integrative evolutionary neural learning. eVAE integrates a variational genetic algorithm (VGA) into VAE with variational evolutionary operators, including variational mutation (V-mutation), crossover, and evolution. Its training mechanism synergistically and dynamically addresses and updates the learning tradeoff uncertainty in the evidence lower bound (ELBO) without additional constraints and hyperparameter tuning. Furthermore, eVAE presents an evolutionary paradigm to tune critical factors of VAEs and addresses the premature convergence and random search problem in integrating evolutionary optimization into deep learning. Experiments show that eVAE addresses the KL-vanishing problem for text generation with low reconstruction loss, generates all the disentangled factors with sharp images, and improves image generation quality. eVAE achieves better disentanglement, generation performance, and generation-inference balance than its competitors. Code available at: https://github.com/amasawa/eVAE.

On the random search for a randomly moving particle

ABSTRACT This paper discusses some methods based on the random search problem over the bound domain. The particle moves randomly with a bounded two-dimensional stochastic process in a bounded area. The physical phenomenon determines the boundaries of this area. We have a smart nanosensor tracks randomly for this particle. The necessary condition that maximizes the probability of the first meeting time between the nanosensor and the particle is derived.

On minimum expected search time for a multiplicative random search problem

In this paper, we obtain the minimum expected search time for a multiplicative random search problem from a viewpoint of computational optimisation. The target is drifting in one of m-disjoint bounded regions. Each region has a one searcher. We get a probabilistic multi-objective nonlinear fractional programming problem and we focus on a new method for solving it to obtain the minimum expected search time for detecting the target. An illustrative example has been given to demonstrate the applicability of this method.

Random search in a bounded area

This paper investigates a random search problem for a randomly moving target in a bounded area in which any time information of the target position is not available to the searcher. Let (X, Y) be two independent truncated random variables represent the position of the target at any time. We have one searcher starts searching for this target from a random point in the plane. In this paper, we found the distribution of the first meeting time between the searcher and the target and found the expected value of it.

On minimum expected search time for a multiplicative random search problem

In this paper, we obtain the minimum expected search time for a multiplicative random search problem from a viewpoint of computational optimisation. The target is drifting in one of m-disjoint bounded regions. Each region has a one searcher. We get a probabilistic multi-objective nonlinear fractional programming problem and we focus on a new method for solving it to obtain the minimum expected search time for detecting the target. An illustrative example has been given to demonstrate the applicability of this method.

Robustness of optimal random searches in fragmented environments.

The random search problem is a challenging and interdisciplinary topic of research in statistical physics. Realistic searches usually take place in nonuniform heterogeneous distributions of targets, e.g., patchy environments and fragmented habitats in ecological systems. Here we present a comprehensive numerical study of search efficiency in arbitrarily fragmented landscapes with unlimited visits to targets that can only be found within patches. We assume a random walker selecting uniformly distributed turning angles and step lengths from an inverse power-law tailed distribution with exponent μ. Our main finding is that for a large class of fragmented environments the optimal strategy corresponds approximately to the same value μ(opt)≈2. Moreover, this exponent is indistinguishable from the well-known exact optimal value μ(opt)=2 for the low-density limit of homogeneously distributed revisitable targets. Surprisingly, the best search strategies do not depend (or depend only weakly) on the specific details of the fragmentation. Finally, we discuss the mechanisms behind this observed robustness and comment on the relevance of our results to both the random search theory in general, as well as specifically to the foraging problem in the biological context.

The Proof of Quantum Search Algorithm Optimization and the Simulation of the Algorithm Implementation

This paper illustrated the optimality of Grover quantum search algorithm, and simulated the number of iterations and the specific implementation steps of quantum search algorithm with QCL in Linux operating systems, then validated the time complexity of Grover's quantum searching algorithm is O(√(N)) while the algorithm's time complexity on classical computers is O(N). The Grover quantum search algorithm were shown to improve the performance significantly in the random database search problem. This conclusion was drawn from the simulation in the Linux operating systems adopted to quantum computation language. The present study highlighted the importance of high efficiency of the Grover quantum search algorithm to achieve the best possible performance in such cases. The existence of such efficiency is an outstanding advantage of quantum search algorithm over the conventional approach.

Optimizing Persistent Random Searches

We consider a minimal model of persistent random searcher with a short range memory. We calculate exactly for such a searcher the mean first-passage time to a target in a bounded domain and find that it admits a nontrivial minimum as function of the persistence length. This reveals an optimal search strategy which differs markedly from the simple ballistic motion obtained in the case of Poisson distributed targets. Our results show that the distribution of targets plays a crucial role in the random search problem. In particular, in the biologically relevant cases of either a single target or regular patterns of targets, we find that, in strong contrast to repeated statements in the literature, persistent random walks with exponential distribution of excursion lengths can minimize the search time, and in that sense perform better than any Levy walk.

Multi-scale properties of random walk models of animal movement: lessons from statistical inference

The random search problem has long attracted continuous interest owing to its broad interdisciplinary range of applications, including animal foraging, facilitated target location in biological systems and human motion. In this paper, we address the issue of statistical inference for ordinary Gaussian, Pareto, tempered Pareto and fractional Gaussian random walk models, which are among the most studied random walk models proposed as the best strategy in the random search problem. Based on rigorous analysis of the local asymptotic normality property and the Fisher information, we discuss some issues in unbiased joint estimation of the model parameters, in particular, the maximum-likelihood estimation. We present that there exist both theoretical and practical difficulties in more realistic tempered Pareto and fractional Gaussian random walk models from a statistical standpoint. We discuss our findings in the context of individual animal movement and show how our results may be used to facilitate the analysis of movement data and to improve the understanding of the underlying stochastic process.

Lévy flights and random searches

In this work we discuss some recent contributions to the random search problem. Our analysis includes superdiffusive Lévy processes and correlated random walks in several regimes of target site density, mobility and revisitability. We present results in the context of mean-field-like and closed-form average calculations, as well as numerical simulations. We then consider random searches performed in regular lattices and lattices with defects, and we discuss a necessary criterion for distinguishing true superdiffusion from correlated random walk processes. We invoke energy considerations in relation to critical survival states on the edge of extinction, and we analyze the emergence of Lévy behavior in deterministic search walks. Finally, we comment on the random search problem in the context of biological foraging.

Socially Rational Models for Autonomous Agents

Autonomous multi-agent systems that are to coordinate must be designed according to models that accom- modate such complex social behavior as compromise, negotiation, and altruism. In contrast to individually rational models, where each agent seeks to maximize its own welfare without regard for others, socially rational agents have interests beyond themselves. Such models require a new type of utility function—a social utility—to ensure three de- sirable properties: (a) conditional preferences—agents may adjust their preferences to account for the preferences of others; (b) endogeny—group preferences are determined internally by interactions between individual agents; (c) fram- ing invariance—reformulations of the social model using exactly the same information should not alter the conclusions; and (d) social coherence—no individual's welfare is categorically subjugated to th e welfare of the group. Social utilities in turn require a compatible solution concept—optimal failure-avoidance. Satisficing game theory embodies both social rationality and optimal failure-avoidance and provides a formal mathematical framework in which to balance group and individual interests in mixed-motive societies. The satis ficing approach is applied to two scenarios: the Ultimatum ga me and a random graph search problem. The Ultimatum game is one for which game-theoretic analysis does not correspond well to empirical data regarding human behavior; it is thus an important test case for a new theory. The graph search scenario is an idealization of an important resource alloca tion problem in which the ability to compromise and negotiate can greatly facilitate the search for a solution.

A statistical foundation for machine learning, with application to Go-Moku

In the context of the research study reported here, “learning” refers to identification of optimal parameters in value and graph traversing procedures. Of course, graph traversing lies at the heart of artificial intelligence (AI) schemes. We abstract the learning problem to the problem of choosing value functions and traversing rules on the basis of performance during repetitive AI solutions, to achieve improvement as time goes on. Viewed in this fashion, for many AI problems and games, the learning problem is equivalent to the problem of trying to find the minimum of a function f( x) on the basis of noisy measurements Y( i) = f[ x( i)] + W[ x( i)] at domain points x( i) which are to be chosen by the decision maker (e.g. a computer) on the basis of past sample values. This particular random search problem does not seem to have been addressed in the statistical or optimization literature. This study reports some theoretical properties of a minimization method and results of computational experiments on Go-Moku, a tic-tac-toe style game.