We focus on the problem of minimizing a convex function f over a convex set S given T queries to a stochastic first order oracle. We argue that the complexity of convex minimization is only determined by the rate of growth of the function around its minimizer xf,S , as quantified by a Tsybakov-like noise condition. Specifically, we prove that if f grows at least as fast as ‖x − xf,S‖ around its...

A general framework for studying the transitivity of reciprocal relations is presented. The key feature is the cyclic evaluation of transitivity: triangles (i.e. any three points) are visited in a cyclic manner. An upper bound function acting upon the ordered weights encountered provides an upper bound for the ‘sum minus 1’ of these weights. Commutative quasi-copulas allow to translate a genera...

We study the task of learning from non-i.i.d. data. In particular, we aim at learning predictors that minimize the conditional risk for a stochastic process, i.e. the expected loss taking into account the set of training samples observed so far. For non-i.i.d. data, the training set contains information about the upcoming samples, so learning with respect to the conditional distribution can be ...

In this article, the sufficient Pontryagin’s maximum principle for infinite horizon discounted stochastic control problem is established. The sufficiency is ensured by an additional assumption of concavity of the Hamiltonian function. Throughout the paper, it is assumed that the control domain U is a convex set and the control may enter the diffusion term of the state equation. The general resu...

The performance of stochastic optimisers can be assessed experimentally on given problems by performing multiple optimisation runs, and analysing the results. Since an optimiser may be viewed as an estimator for the (Pareto) minimum of a (vector) function, stochastic optimiser performance is discussed in the light of the criteria applicable to more usual statistical estimators. Multiobjective o...

Aim of this paper is to set invariance in stochastic dynamical control systems. Given a set within which the state of the dynamical system should evolve, we study conditions for finding a control strategy that maximizes the probability for the state to be in the given set within a fixed a–priori finite time horizon. We formulate an optimal control problem and we solve the problem at hand by usi...

We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming [Saad and Pontelli, 2006; Saad, 2006; Saad, 2007a]. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the language of probability answer set programming to allow minimization or maximization of some desired crit...

We show that there exist bivariate proper quasi-copulas that do not induce a doubly stochastic signed measure on [0, 1]. We construct these quasi-copulas from the so-called proper quasitransformation square matrices.

A new kind of comparison theorem in which an SDE is compared with two deterministic ODEs is established by means of the generalized sample solutions of SDEs. Using this theorem, we can compare solutions of two SDEs with different diffusion coefficients and obtain some asymptotic estimations for the paths of diffusion processes. In the investigation of solutions of stochastic differential equati...

We present the Carnegie Mellon University Stat-XFER group submission to the WMT 2011 shared translation task. We built a hybrid syntactic MT system for French–English using the Joshua decoder and an automatically acquired SCFG. New work for this year includes training data selection and grammar filtering. Expanded training data selection significantly increased translation scores and lowered OO...