Robust Stochastic Approximation Approach to Stochastic Programming
- A. Nemirovski, A. Juditsky, Guanghui Lan, A. Shapiro
- Computer Science, MathematicsSIAM Journal on Optimization
- 1 December 2008
It is intended to demonstrate that a properly modified SA approach can be competitive and even significantly outperform the SAA method for a certain class of convex stochastic problems.
Acceleration of stochastic approximation by averaging
- Boris Polyak, A. Juditsky
- Computer Science
- 1 July 1992
Convergence with probability one is proved for a variety of classical optimization and identification problems and it is demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence.
Nonlinear black-box modeling in system identification: a unified overview
- J. Sjöberg, Qinghua Zhang, A. Juditsky
- Computer Scienceat - Automatisierungstechnik
- 1 December 1995
Solving variational inequalities with Stochastic Mirror-Prox algorithm
- A. Juditsky, A. Nemirovskii, Claire Tauvel
- Mathematics, Computer Science
- 4 September 2008
A novel Stochastic Mirror-Prox algorithm is developed for solving s.v.i. variational inequalities with monotone operators and it is shown that with the convenient stepsize strategy it attains the optimal rates of convergence with respect to the problem parameters.
Learning by mirror averaging
- A. Juditsky, P. Rigollet, A. Tsybakov
- Computer Science, Mathematics
- 18 November 2005
This work defines a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion and shows that the aggregate satisfies sharp oracle inequalities under some general assumptions.
On Minimax Wavelet Estimators
- B. Delyon, A. Juditsky
- Mathematics
- 1 July 1996
In the paper minimax rates of convergence for wavelet estimators are studied. The estimators are based on the shrinkage of empirical coefficients βjkof wavelet decomposition of unknown function with…
Direct estimation of the index coefficient in a single-index model
- M. Hristache, A. Juditsky, V. Spokoiny
- Mathematics
- 1 June 2001
Single-index modeling is widely applied in, for example, econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models.…
Accelerated Stochastic Approximation
- B. Delyon, A. Juditsky
- Computer Science, MathematicsSIAM Journal on Optimization
- 1 November 1993
Convergence with probability 1 is proved for the multidimensional analog of the Kesten accelerated stochastic approximation algorithm.
Functional aggregation for nonparametric regression
- A. Juditsky, A. Nemirovski
- Mathematics, Computer Science
- 1 May 2000
This paper addresses the following aggregation problem: given M functions f 1, ..., f M, and proposes algorithms which provide approximations of f * with expected L 2 accuracy O(N -1/4 In 1/4 M), and shows that this approximation rate cannot be significantly improved.
Deterministic and Stochastic Primal-Dual Subgradient Algorithms for Uniformly Convex Minimization
- A. Juditsky, Y. Nesterov
- Computer Science, Mathematics
- 25 February 2014
This work discusses non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives and provides accuracy bounds for these algorithms.
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