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- Anatoli Juditsky, Alexander V. Nazin, Alexandre B. Tsybakov, Nicolas Vayatis
- Probl. Inf. Transm.
- 2005

We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is defined by a stochastic version of the mirror descent algorithm (i.e., of the method which performs gradient descent in… (More)

- Jacob Roll, Alexander V. Nazin, Lennart Ljung
- Automatica
- 2005

- Alexander V. Nazin
- CDC
- 2010

The problem of estimating the principal eigenvector related to the largest eigenvalue of a given (left) stochastic matrix A has many applications in ranking search results, multiagent consensus, networked control and data mining. The wellknown power method is a typical tool, but it modifies matrix and, therefore, the related solution. We propose and study… (More)

- A. Juditsky, A. V. Nazin
- 2007

We consider the stochastic multi-armed bandit problem with unknown horizon. We present a randomized decision strategy which is based on updating a probability distribution through a stochastic mirror descent type algorithm. We consider separately two assumptions: nonnegative losses or arbitrary losses with an exponential moment condition. We prove optimal… (More)

- Alexander V. Nazin, Boris T. Polyak
- 2009 IEEE Control Applications, (CCA…
- 2009

The problem of finding the eigenvector corresponding to the largest eigenvalue of a stochastic matrix has numerous applications in ranking search results, multi-agent consensus, networked control and data mining. The well known power method is a typical tool for its solution. However randomized methods could be competitors vs standard ones; they require… (More)

- Jacob Roll, Alexander Nazin, Lennart Ljung, MATIC NTROL
- 2003

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean… (More)

The direct weight optimization (DWO) approach is a method for finding optimal function estimates via convex optimization, applicable to nonlinear system identification. In this paper, an extended version of the DWO approach is introduced. A general function class description — which includes several important special cases — is presented, and different… (More)

- Alexander V. Nazin, Boris T. Polyak
- CDC
- 2009

The problem of finding the eigenvector corresponding to the largest eigenvalue of a stochastic matrix has numerous applications in ranking search results, multi-agent consensus, networked control and data mining. The well-known power method is a typical tool for its solution. However randomized methods could be competitors vs standard ones; they require… (More)

A general framework for estimating nonlinear functions and systems is described and analyzed in this paper. Identification of a system is seen as estimation of a predictor function. The considered predictor function estimate at a particular point is defined to be affine in the observed outputs, and the estimate is defined by the weights in this expression.… (More)

We consider the problem of constructing an aggregated estimator from a finite class of base functions which approximately minimizes a convex risk functional under the l1 constraint. For this purpose, we propose a stochastic procedure, the mirror descent, which performs gradient descent in the dual space. The generated estimates are additionally averaged in… (More)