Thompson Sampling: An Asymptotically Optimal Finite Time Analysis

The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case.Comment: 15 pages, 2 figures, submitted to ALT (Algorithmic Learning Theory

A Stochastic Search on the Line-Based Solution to Discretized Estimation

Recently, Oommen and Rueda [11] presented a strategy by which the parameters of a binomial/multinomial distribution can be estimated when the underlying distribution is nonstationary. The method has been referred to as the Stochastic Learning Weak Estimator (SLWE), and is based on the principles of continuous stochastic Learning Automata (LA). In this paper, we consider a new family of stochastic discretized weak estimators pertinent to tracking time-varying binomial distributions. As opposed to the SLWE, our proposed estimator is discretized , i.e., the estimate can assume only a finite number of values. It is well known in the field of LA that discretized schemes achieve faster convergence speed than their corresponding continuous counterparts. By virtue of discretization, our estimator realizes extremely fast adjustments of the running estimates by jumps, and it is thus able to robustly, and very quickly, track changes in the parameters of the distribution after a switch has occurred in the environment. The design principle of our strategy is based on a solution, pioneered by Oommen [7], for the Stochastic Search on the Line (SSL) problem. The SSL solution proposed in [7], assumes the existence of an Oracle which informs the LA whether to go “right” or “left”. In our application domain, in order to achieve efficient estimation, we have to first infer (or rather simulate ) such an Oracle. In order to overcome this difficulty, we rather intelligently construct an “Artificial Oracle” that suggests whether we are to increase the current estimate or to decrease it. The paper briefly reports conclusive experimental results that demonstrate the ability of the proposed estimator to cope with non-stationary environments with a high adaptation rate, and with an accuracy that depends on its resolution. The results which we present are, to the best of our knowledge, the first reported results that resolve the problem of discretized weak estimation using a SSL-based solution

Solution of Dual Fuzzy Equations Using a New Iterative Method

In this paper, a new hybrid scheme based on learning algorithm of fuzzy neural network (FNN) is offered in order to extract the approximate solution of fully fuzzy dual polynomials (FFDPs). Our FNN in this paper is a five-layer feed-back FNN with the identity activation function. The input-output relation of each unit is defined by the extension principle of Zadeh. The output from this neural network, which is also a fuzzy number, is numerically compared with the target output. The comparison of the feed-back FNN method with the feed-forward FNN method shows that the less error is observed in the feed-back FNN method. An example based on applications are given to illustrate the concepts, which are discussed in this paper

Exploring Effects of Hyperdimensional Vectors for Tsetlin Machines

Tsetlin machines (TMs) have been successful in several application domains, operating with high efficiency on Boolean representations of the input data. However, Booleanizing complex data structures such as sequences, graphs, images, signal spectra, chemical compounds, and natural language is not trivial. In this paper, we propose a hypervector (HV) based method for expressing arbitrarily large sets of concepts associated with any input data. Using a hyperdimensional space to build vectors drastically expands the capacity and flexibility of the TM. We demonstrate how images, chemical compounds, and natural language text are encoded according to the proposed method, and how the resulting HV-powered TM can achieve significantly higher accuracy and faster learning on well-known benchmarks. Our results open up a new research direction for TMs, namely how to expand and exploit the benefits of operating in hyperspace, including new booleanization strategies, optimization of TM inference and learning, as well as new TM applications.Comment: 9 pages, 17 figure

Morphotaxonomy and chorology of the genus <i>Hypoxylon</i> (Xylariaceae) in Norway

Abstract The Norwegian species of Hypoxylon have been treated with respect to their ecology, morphology and taxonomy. Their host trees have been identified and percentage frequency of each host and substrate type (bark/wood) calculated. Ecologically the species are grouped according to their saprobic ability, and to their preferred hosts and substrates (bark or wood). From a chorological point of view the species are grouped into three different geoelements according to the distributional centre for each species in Norway, thereby also taking into consideration the total Nordic distribution. Complete locality lists for each species are given and a key to all Nordic species is presented. Twelve species of Hypoxylon have so far been recognized in Norway: Hypoxylon cercidicola, H. cohaerens, H.fragiforme, H.fuscum, H. howeianum, H. laschii, H. macrosporum, H. multiforme, H. porphyreum, H. rubiginosum, H. salicicola and H. vogesiacum. Two species belong to Hypoxylon sect. Annulata: Hypoxylon cohaerens and Hypoxylon multiforme, the remainder belong to Hypoxylon sect. Hypoxylon. Two new species are described: H. porphyreum and H. sa/icicola. In a previous treatment of Nordic species of Biscogniauxia and Hypoxylon, Hypoxylon cercidicola and H. salicico/a were included in and reported as H. rubiginosum and H. rutilum, respectively, while H. porphyreum was included in H. juscum. Hypoxylon macrosporum and H. laschii, by several authors considered as varieties of H. vogesiacum and H. rubiginosum, respectively, are treated as species.</jats:p

The genus <i>Nemania</i> s.l. (Xylariaceae) in Norden

Abstract A taxonomic study of Nemania Gray, Entoleuca Syd. and Euepixylon Füisting (= Nemania s.l.; Xylariaceae) was carried out for the Nordic countries: Norway, Sweden, Finland and Denmark. No species of Nemania have been found in the remaining Norden: Iceland and the Faeroes. Fourteen species of Nemania s. str. were found in the area: Nemania aenea, N. aureolutea comb. n., N. atropurpurea, N. carbonacea, N. chestersii, N. colliculosa comb. n., N. con.fluens, N. diffusa, N. effusa, N. prava n. sp., N. reticulata comb. n., N. serpens, and two unknown species (Nemania spp. A and B) not formally described because of scanty material. In addition the two split-outs fromNemania, Entoleuca mammata andEuepixylon udum, are treated. A dichotomous key has been prepared and the species are reviewed alphabetically with comments on taxonomy, ecology and chorology. All species have been drawn, photographed and mapped. In addition to conventional taxonomic procedures, a selection of species from Nemania s.l., Biscogniauxia and Hypoxylon were subjected to an ITS nrDNA sequencing study. This study supported the delimitation of taxa as defined in this work, and confirms Nemani a as different from Hypoxylon and Biscogniauxia. Four EuropeanNemania taxa are still unknown in Norden: Nemania gwyneddii (Whalley, R.L. Edwards &amp; S.M. Francis) Pouzar, N. illita (Schwein.) Pouzar, Nemania serpens (Pers.: Fr.) Gray var. macrospora (J.H. Mill.) Pouzar. The fourth taxon, Hypoxylon terricola J.H. Mill. certainly also belongs to Nemania. </jats:p