Some upper bounds for relative entropy and applications

Dragomir, Sever S; Scholz, Michael; Sunde, Jadranka

doi:10.1016/s0898-1221(00)00089-4

Cited by 22 publications

(10 citation statements)

References 6 publications

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“…Our main contribution in Proposition 4 is the upper bound (the first term of the upper bound) for the KL-divergence of two bernoulli random variables. The last term of the upper bound is a direct derivation from the upper bounds in [6]. Our result in Proposition 4 shows a factor of 2 improvement in the leading term of the upper bound.…”

Section: Algorithms Description and Analysismentioning

confidence: 67%

Near-optimal Bayesian Solution For Unknown Discrete Markov Decision Process

Tossou,

Dimitrakakis,

Basu

2019

Preprint

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We tackle the problem of acting in an unknown finite and discrete Markov Decision Process (MDP) for which the expected shortest path from any state to any other state is bounded by a finite number D. An MDP consists of S states and A possible actions per state. Upon choosing an action a t at state s t , one receives a real value reward r t , then one transits to a next state s t+1 . The reward r t is generated from a fixed reward distribution depending only on (s t , a t ) and similarly, the next state s t+1 is generated from a fixed transition distribution depending only on (s t , a t ). The objective is to maximize the accumulated rewards after T interactions. In this paper, we consider the case where the reward distributions, the transitions, T and D are all unknown. We derive the first polynomial time Bayesian algorithm, BUCRL that achieves up to logarithm factors, a regret (i.e the difference between the accumulated rewards of the optimal policy and our algorithm) of the optimal order Õ( √ DSAT ). Importantly, our result holds with high probability for the worst-case (frequentist) regret and not the weaker notion of Bayesian regret. We perform experiments in a variety of environments that demonstrate the superiority of our algorithm over previous techniques. Our work also illustrates several results that will be of independent interest. In particular, we derive a sharper upper bound for the KL-divergence of Bernoulli random variables. We also derive sharper upper and lower bounds for Beta and Binomial quantiles. All the bound are very simple and only use elementary functions.Preprint. Under review.

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Section: Algorithms Description and Analysismentioning

confidence: 67%

Near-optimal Bayesian Solution For Unknown Discrete Markov Decision Process

Tossou,

Dimitrakakis,

Basu

2019

Preprint

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“…A contribuição da variabilidade da entropia é uma teoria moderna do conhecimento que vem sendo aplicada em diversas áreas da ciência, tais como em hidrologia, de acordo com , para a matemática, segundo Dragomir et al (2000), na economia, conforme Kaberger et al (2001), na ecologia, de acordo com Ricotta (2001), na climatologia, por Kawachi et al (2001), e na medicina, de acordo com Montaño et al (2001).…”

Section: Introductionunclassified

Entropia pluviométrica na grande metrópolis Recife-PE, Brasil

Medeiros¹

2019

J. Env. Anal. Progr.

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Objetiva-se analisar as oscilações dos padrões diários, mensais e anuais de ocorrência pluviais e debater acerca da sua disponibilidade hídrica, ressaltando o procedimento da entropia, da precipitação no período seco e chuvoso e dos seus respectivos desvios padrão da entropia e da precipitação no período 1962-2015 possibilitando compreender as características das chuvas na área estudada. Efetuaram-se preenchimentos de falhas, homogeneização e consistência com base no critério de analisar para aquelas séries contínuas após seus preenchimentos. Os dados diários de precipitação utilizados foram fornecidos pelo Instituto Nacional de Meteorologia. Na Grande Metrópole de Recife nos períodos de La Niña(o) não causa influencia nos seus índices precipitados. O desvio-padrão da entropia anual varia uniformemente aos valores de entropia, mostrando com isso pequena oscilação de seus dados em torno dos valores médios. A técnica da entropia se constitui em ferramenta apropriada para expressar as flutuações de dados em torno da média do que a técnica convencional do desvio.

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“…The Shannon entropy has since been employed in numerous areas (Singh and Rajagopal, 1987), such as mathematics (Dragomir et al, 2000), economics (Kaberger and Mansson, 2001), ecology (Ricotta, 2002), climatology (Kawachi et al, 2001), medicine (Montaño et al, 2001) and hydrology (Singh, 1997). One measure of uncertainty or disorder of a variable is entropy.…”

Section: Introductionmentioning

confidence: 99%