5 research outputs found
Cross-Entropic Learning of a Machine for the Decision in a Partially Observable Universe
Revision of the paper previously entitled "Learning a Machine for the
Decision in a Partially Observable Markov Universe" In this paper, we are
interested in optimal decisions in a partially observable universe. Our
approach is to directly approximate an optimal strategic tree depending on the
observation. This approximation is made by means of a parameterized
probabilistic law. A particular family of hidden Markov models, with input
\emph{and} output, is considered as a model of policy. A method for optimizing
the parameters of these HMMs is proposed and applied. This optimization is
based on the cross-entropic principle for rare events simulation developed by
Rubinstein.Comment: Submitted to EJO
Deterministic Bayesian Logic
In this paper a conditional logic is defined and studied. This conditional
logic, Deterministic Bayesian Logic, is constructed as a deterministic
counterpart to the (probabilistic) Bayesian conditional. The logic is
unrestricted, so that any logical operations are allowed. This logic is shown
to be non-trivial and is not reduced to classical propositions. The Bayesian
conditional of DBL implies a definition of logical independence. Interesting
results are derived about the interactions between the logical independence and
the proofs. A model is constructed for the logic. Completeness results are
proved. It is shown that any unconditioned probability can be extended to the
whole logic DBL. The Bayesian conditional is then recovered from the
probabilistic DBL. At last, it is shown why DBL is compliant with Lewis
triviality.Comment: Fourth version. A sequent formalism is use
Deterministic modal Bayesian Logic: derive the Bayesian inference within the modal logic T
In this paper a conditional logic is defined and studied. This conditional
logic, DmBL, is constructed as a deterministic counterpart to the Bayesian
conditional. The logic is unrestricted, so that any logical operations are
allowed. A notion of logical independence is also defined within the logic
itself. This logic is shown to be non-trivial and is not reduced to classical
propositions. A model is constructed for the logic. Completeness results are
proved. It is shown that any unconditioned probability can be extended to the
whole logic DmBL. The Bayesian conditional is then recovered from the
probabilistic DmBL. At last, it is shown why DmBL is compliant with Lewis'
triviality.Comment: Second revision of: Definition of a Deterministic Bayesian Logi
Definition of a Deterministic Bayesian Logic, unpublished, http://hal.ccsd.cnrs.fr/ccsd-00003388 [13] Dambreville F., Cross-entropic learning of a machine for the decision in a partially observable universe
The Bayesian logic is generally associated to the definition of a prior probabilistic law. Conditional algebra have been investigated by some authors though, but somehow the background framework is still probabilistic and the entire logic is not specified. In this paper, the definition of a Deterministic Bayesian Logic is proposed. This logic is completely independent of any notion of probability. The coherence of this logic is proven and various logical theorems are derived. It is shown that this logic is probabilizable and avoids the negative result of Lewis. At last the probabilistic Bayesian rule is recovered by posteriorly probabilizing our logic
Deterministic modal Bayesian Logic: derive the Bayesian inference within the modal logic T, unpublished, http://hal.ccsd.cnrs.fr/ccsd-00127016 8. Dambreville F., Cross-entropic learning of a machine for the decision in a partially observable universe
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of logical independence is also defined within the logic itself. This logic is shown to be non trivial and is not reduced to classical propositions. A model is constructed for the logic. Completeness results are proved. It is shown that any unconditioned probability can be extended to the whole logic DmBL. The Bayesian is then recovered from the probabilistic DmBL. At last, it is shown why DmBL is compliant with Lewis triviality