Computation in Valuation Algebras

Many different formalisms for treating uncertainty or, more generally, information and knowledge, have a common underlying algebraic structure. The essential algebraic operations are combination, which corresponds to aggregation of knowledge, and marginalization, which corresponds to focusing of knowledge. This structure is called a valuation algebra. Besides managing uncertainty in expert systems, valuation algebras can also be used to to represent constraint satisfaction problems, propositional logic, and discrete optimization problems. This chapter presents an axiomatic approach to valuation algebras. Based on this algebraic structure, different inference mechanisms that use local computations are described. These include the fusion algorithm and, derived from it, the Shenoy-Shafer architecture. As a particular case, computation in idempotent valuation algebras, also called information algebras, is discussed. The additional notion of continuers is introduced and, based on it, two more computational architectures, the Lauritzen-Spiegelhalter and the HUGIN architecture, are presented. Finally, different models of valuation algebras are considered. These include probability functions, Dempster-Shafer belief functions, Spohnian disbelief functions, and possibility functions. As further examples, linear manifolds and systems of linear equations, convex polyhedra and linear inequalities, propositional logic and information systems, and discrete optimization are mentioned

A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning

We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences

Application of the American Real Flexible Switch Options Methodology A Generalized Approach

The paper deals with the inclusion of flexibility in financial decision-making under risk. It describes the application of the real options methodology with the possibility of sequential multinomial decision-making. The basic intention is to describe and apply a generalized approach and methodology of the flexibility modeling and valuation based on multiple choices and non-symmetrical switching costs under risk. The stochastic dynamic Bellman optimization principle is explained and applied. The optimization criterion of the present expected value is derived and used. Likewise, an option valuation approach based on replication strategy and risk-neutral probability is applied. An illustrative example of the application of the real multinomial flexible non-symmetrical switch options methodology is presented for three chosen modes. The option flexible values are computed. The usefulness, effectiveness, and suitability of applying the generalized flexibility model in company valuation and project evaluation is verified and confirmed. The significance of applying the generalized methodology in transition market economies is discussed and verified.financial options; real options; Discrete Binomial Model; pricing; stochastic dynamic Bellman Optimization Principle; switch options