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Aur

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IJCAI Conference 2015 Conference Paper

Optimization of Probabilistic Argumentation with Markov Decision Models

Emmanuel Hadoux
Aur
eacute; lie Beynier
Nicolas Maudet
Paul Weng
Anthony Hunter

One prominent way to deal with conflicting viewpoints among agents is to conduct an argumentative debate: by exchanging arguments, agents can seek to persuade each other. In this paper we investigate the problem, for an agent, of optimizing a sequence of moves to be put forward in a debate, against an opponent assumed to behave stochastically, and equipped with an unknown initial belief state. Despite the prohibitive number of states induced by a naive mapping to Markov models, we show that exploiting several features of such interaction settings allows for optimal resolution in practice, in particular: (1) as debates take place in a public space (or common ground), they can readily be modelled as Mixed Observability Markov Decision Processes, (2) as argumentation problems are highly structured, one can design optimization techniques to prune the initial instance. We report on the experimental evaluation of these techniques.

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IJCAI Conference 2011 Conference Paper

Pairwise Decomposition for Combinatorial Optimization in Graphical Models

Aur
eacute; lie Favier
Simon de Givry
Andr
eacute; s Legarra
Thomas Schiex

We propose a new additive decomposition of probability tables that preserves equivalence of the joint distribution while reducing the size of potentials, without extra variables. We formulate the Most Probable Explanation (MPE) problem in belief networks as a Weighted Constraint Satisfaction Problem (WCSP). Our pairwise decomposition allows to replace a cost function with smaller-arity functions. The resulting pairwise decomposed WCSP is then easier to solve using state-of-the-art WCSP techniques. Although testing pairwise decomposition is equivalent to testing pairwise independence in the original belief network, we show how to efficiently test and enforce it, even in the presence of hard constraints. Furthermore, we infer additional information from the resulting nonbinary cost functions by projecting and subtracting them on binary functions. We observed huge improvements by preprocessing with pairwise decomposition and project&subtract compared to the current state-of-the-art solvers on two difficult sets of benchmark.

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