Convergent learning algorithms for potential games with unknown noisy rewards

In this paper, we address the problem of convergence to Nash equilibria in games with rewards that are initially unknown and which must be estimated over time from noisy observations. These games arise in many real-world applications, whenever rewards for actions cannot be prespecified and must be learned on-line. Standard results in game theory, however, do not consider such settings. Specifically, using results from stochastic approximation and differential inclusions, we prove the convergence of variants of fictitious play and adaptive play to Nash equilibria in potential games and weakly acyclic games, respectively. These variants all use a multi-agent version of Q-learning to estimate the reward functions and a novel form of the e-greedy decision rule to select an action. Furthermore, we derive e-greedy decision rules that exploit the sparse interaction structure encoded in two compact graphical representations of games, known as graphical and hypergraphical normal form, to improve the convergence rate of the learning algorithms. The structure captured in these representations naturally occurs in many distributed optimisation and control applications. Finally, we demonstrate the efficacy of the algorithms in a simulated ad hoc wireless sensor network management problem

Inbreeding in swine

The Oklahoma Cooperative Extension Service periodically issues revisions to its publications. The most current edition is made available. For access to an earlier edition, if available for this title, please contact the Oklahoma State University Library Archives by email at [email protected] or by phone at 405-744-6311

Evaluating breeds of swine for crossbreeding programs

The Oklahoma Cooperative Extension Service periodically issues revisions to its publications. The most current edition is made available. For access to an earlier edition, if available for this title, please contact the Oklahoma State University Library Archives by email at [email protected] or by phone at 405-744-6311

Inbreeding in cattle

The Oklahoma Cooperative Extension Service periodically issues revisions to its publications. The most current edition is made available. For access to an earlier edition, if available for this title, please contact the Oklahoma State University Library Archives by email at [email protected] or by phone at 405-744-6311

Swine crossbreeding systems

The Oklahoma Cooperative Extension Service periodically issues revisions to its publications. The most current edition is made available. For access to an earlier edition, if available for this title, please contact the Oklahoma State University Library Archives by email at [email protected] or by phone at 405-744-6311

Convergent learning algorithms for unknown reward games

In this paper, we address the problem of convergence to Nash equilibria in games with rewards that are initially unknown and must be estimated over time from noisy observations. These games arise in many real-world applications, whenever rewards for actions cannot be prespecified and must be learned online, but standard results in game theory do not consider such settings. For this problem, we derive a multiagent version of $\mathcal{Q}$-learning to estimate the reward functions using novel forms of the $\epsilon$-greedy learning policy. Using these $\mathcal{Q}$-learning schemes to estimate reward functions, we then provide conditions guaranteeing the convergence of adaptive play and the better-reply processes to Nash equilibria in potential games and games with more general forms of acyclicity, and of regret matching to the set of correlated equilibria in generic games. A secondary result is that we prove the strong ergoditicity of stochastic adaptive play and stochastic better-reply processes in the case of vanishing perturbations. Finally, we illustrate the efficacy of the algorithms in a set of randomly generated three-player coordination games and show the practical necessity of our results by demonstrating that violations to the derived learning parameter conditions can cause the algorithms to fail to converge

SNP and Haplotype Regional Heritability Mapping (SNHap-RHM):Joint Mapping of Common and Rare Variation Affecting Complex Traits

We describe a genome-wide analytical approach, SNP and Haplotype Regional Heritability Mapping (SNHap-RHM), that provides regional estimates of the heritability across locally defined regions in the genome. This approach utilises relationship matrices that are based on sharing of SNP and haplotype alleles at local haplotype blocks delimited by recombination boundaries in the genome. We implemented the approach on simulated data and show that the haplotype-based regional GRMs capture variation that is complementary to that captured by SNP-based regional GRMs, and thus justifying the fitting of the two GRMs jointly in a single analysis (SNHap-RHM). SNHap-RHM captures regions in the genome contributing to the phenotypic variation that existing genome-wide analysis methods may fail to capture. We further demonstrate that there are real benefits to be gained from this approach by applying it to real data from about 20,000 individuals from the Generation Scotland: Scottish Family Health Study. We analysed height and major depressive disorder (MDD). We identified seven genomic regions that are genome-wide significant for height, and three regions significant at a suggestive threshold (p-value < 1 × 10(−5)) for MDD. These significant regions have genes mapped to within 400 kb of them. The genes mapped for height have been reported to be associated with height in humans. Similarly, those mapped for MDD have been reported to be associated with major depressive disorder and other psychiatry phenotypes. The results show that SNHap-RHM presents an exciting new opportunity to analyse complex traits by allowing the joint mapping of novel genomic regions tagged by either SNPs or haplotypes, potentially leading to the recovery of some of the “missing” heritability

Generation Scotland: Donor DNA Databank; A control DNA resource

<p>Abstract</p> <p>Background</p> <p>Many medical disorders of public health importance are complex diseases caused by multiple genetic, environmental and lifestyle factors. Recent technological advances have made it possible to analyse the genetic variants that predispose to complex diseases. Reliable detection of these variants requires genome-wide association studies in sufficiently large numbers of cases and controls. This approach is often hampered by difficulties in collecting appropriate control samples. The Generation Scotland: Donor DNA Databank (GS:3D) aims to help solve this problem by providing a resource of control DNA and plasma samples accessible for research.</p> <p>Methods</p> <p>GS:3D participants were recruited from volunteer blood donors attending Scottish National Blood Transfusion Service (SNBTS) clinics across Scotland. All participants gave full written consent for GS:3D to take spare blood from their normal donation. Participants also supplied demographic data by completing a short questionnaire.</p> <p>Results</p> <p>Over five thousand complete sets of samples, data and consent forms were collected. DNA and plasma were extracted and stored. The data and samples were unlinked from their original SNBTS identifier number. The plasma, DNA and demographic data are available for research. New data obtained from analysis of the resource will be fed back to GS:3D and will be made available to other researchers as appropriate.</p> <p>Conclusions</p> <p>Recruitment of blood donors is an efficient and cost-effective way of collecting thousands of control samples. Because the collection is large, subsets of controls can be selected, based on age range, gender, and ethnic or geographic origin. The GS:3D resource should reduce time and expense for investigators who would otherwise have had to recruit their own controls.</p

Common Genetic Variants Explain the Majority of the Correlation Between Height and Intelligence : The Generation Scotland Study

Creative Commons Attribution LicensePeer reviewedPublisher PD