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We consider a recursive algorithm to construct an aggregated esti-mator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the ℓ 1-constraint. It is defined by a stochastic version of the mirror descent algorithm (i.e., of the method which performs gradient descent… (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)

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)

— 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)

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)

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)

The concept of Just-in-Time models has been introduced for models that are not estimated until they are really needed. The prediction is taken as a weighted average of neighboring points in the regressor space, such that an optimal bias/variance trade-off is achieved. The asymptotic properties of the method are investigated, and are compared to the… (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 ℓ 1 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)