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### Constraint Optimization Approach to Context Based Word Selection

Consistent word selection in machine translation is currently realized by resolving word sense ambiguity through the context of a single sentence or neighboring sentences. However, consistent word selection over the whole article has yet to be achieved. Consistency over the whole article is extremely important when applying machine translation to collectively developed documents like Wikipedia. In this paper, we propose to consider constraints between words in the whole article based on their semantic relatedness and contextual distance. The proposed method is successfully implemented in both statistical and rule-based translators. We evaluate those systems by translating 100 articles in the English Wikipedia into Japanese. The results show that the ratio of appropriate word selection for common nouns increased to around 75% with our method, while it was around 55% without our method.

### DUCT: An Upper Confidence Bound Approach to Distributed Constraint Optimization Problems

The Upper Confidence Bounds (UCB) algorithm is a well-known near-optimal strategy for the stochastic multi-armed bandit problem. Its extensions to trees, such as the Upper Confidence Tree (UCT) algorithm, have resulted in good solutions to the problem of Go. This paper introduces DUCT, a distributed algorithm inspired by UCT, for solving Distributed Constraint Optimization Problems (DCOP). Bounds on the solution quality are provided, and experiments show that, compared to existing DCOP approaches, DUCT is able to solve very large problems much more efficiently, or to find significantly higher quality solutions.

### Online Convex Optimization with Stochastic Constraints

This paper considers online convex optimization (OCO) with stochastic constraints, which generalizes Zinkevich's OCO over a known simple fixed set by introducing multiple stochastic functional constraints that are i.i.d. This formulation arises naturally when decisions are restricted by stochastic environments or deterministic environments with noisy observations. It also includes many important problems as special case, such as OCO with long term constraints, stochastic constrained convex optimization, and deterministic constrained convex optimization. To solve this problem, this paper proposes a new algorithm that achieves $O(\sqrt{T})$ expected regret and constraint violations and $O(\sqrt{T}\log(T))$ high probability regret and constraint violations. Experiments on a real-world data center scheduling problem further verify the performance of the new algorithm.

### Berger

MINLP problems are hard constrained optimization problems, with nonlinear constraints and mixed discrete continuous variables. They can be solved using a Branch-and-Bound scheme combining several methods, such as linear programming, interval analysis, and cutting methods. Our goal is to integrate constraint programming techniques in this framework. Firstly, global constraints can be introduced to reformulate MINLP problems thus leading to clean models and more precise computations. Secondly, interval-based approximation techniques for nonlinear constraints can be improved by taking into account the integrality of variables early. These methods have been implemented in an interval solver and we present experimental results from a set of MINLP instances.

### Optimum Anytime Bounding for Constraint Optimization Problems Simon de Givry and G rard Verfaillie

Edouard Belin, BP 4025, 31055 Toulouse Cedex 4, France {degivry,verfaillie}@cert.fr Abstract In this paper, we consider Constraint Optimization Problems in a Resource-Bounded context. We observe that both exact and approximate methods produce only an anytime upper bound of the optimum (in case of minimization). No lower bound, and thus no quality is available at run time. For a meta-reasoning system, it is difficult to reason on the basis of a so poor piece of information. Therefore, we discuss some ways of producing an anytime lower bound.