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Anastasia Lagunovskaya

Publications and source records attributed to Anastasia Lagunovskaya.

8 recordsLinked to original sources
arXiv2018

Algorithmic models of human behavior and stochastic optimization

In this article we describe the solutions of three problems posed at different time by Yurii Nesterov. First problem is 'Mage vs Experts': Assume that we live in some enviroment that characterized by unobservable convex function $f(x)$. Each day we can observe only the stochastic gradient of $f(x)$ (with heavy tails). We want to know where is a minimum of $f(x)$. What is better to live one long live or to live in parallel many short lives? The second problem is a variant of the previous one (we'd like to find the minimum of convex function $f(x)$) but we can observe only the (noise) value of the function at each day. The additional difficulties here is $f(x)$ isn't necessarily smooth and $x$ belongs to unit simplex. The third problem is to interprete equillibrium in Stable dynamic traffic assignment model (Nesterov-dePalma, 2000) as atractor of the best response dynamic. All these problems required proper generalizations of mirror descent (MD) algorithm. In this paper we collect different special versions of MD to solve the described problems.

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arXiv2017

Universal similar triangulars method for searching equilibriums in traffic flow distribution models

We describe how primal-dual version of Nesterov's Universal Method (with one projection) can be applied to solve the dual problem for the problem of searching equilibrium traffic flow distribution in transport networks (BMW-model, Stable Dynamic model). We observe that although the dual problem isn't smooth Universal Methods works as it is Mirror Prox method and we consider saddle-point type problem.

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arXiv2017

Gradient-free two-points optimal method for non smooth stochastic convex optimization problem with additional small noise

Using double-smoothing technique and stochastic mirror descent with inexact oracle we built an optimal algorithm (up to a multiplicative factor) for two-points gradient-free non-smooth stochastic convex programming. We investigate how much can be the level of noise (the nature of this noise isn't necessary stochastic) for the rate of convergence to be maintained (up to a multiplicative factor).

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arXiv2017

Nonlinear stochastic multiarmed bandit problems with inexact oracle

In the paper we consider one point and two point multiarmed bamdit problems. In other words we consider the online stochastic convex optimization problems with oracle that return the value (realization) of the function at one point or at two points. We allow these values to be inexact, but the level of noise should be small enough. We generalize well known results for inexact oracle case. And we also generalize classical results to prox-structures differ from euclidian.

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arXiv2017

Parallel algorithms and probability of large deviation for stochastic optimization problems

We consider convex stochastic optimization problems under different assumptions on the properties of available stochastic subgradient. It is known that, if the value of the objective function is available, one can obtain, in parallel, several independent approximate solutions in terms of the objective residual expectation. Then, choosing the solution with the minimum function value, one can control the probability of large deviation of the objective residual. On the contrary, in this short paper, we address the situation, when the value of the objective function is unavailable or is too expensive to calculate. Under "`light-tail"' assumption for stochastic subgradient and in general case with moderate large deviation probability, we show that parallelization combined with averaging gives bounds for probability of large deviation similar to a serial method. Thus, in these cases, one can benefit from parallel computations and reduce the computational time without loss in the solution quality.

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arXiv2016

Efficient calculation of stochastic equilibriums in the Beckmann's and stable dynamic models

We propose composite approache to the special sum-type convex optimization problem with affine restriction and special entropy type regularization. Since the fuctional has a penalty type form, we reformulate initial conditional optimization problem in a special unconstrained form that allows us to put the penalty type functional into the composite term. We also describe the characteristic functions on graphs technique (Yu. Nesterov, 2007) in application to the dual problem.

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arXiv2016

Gradient-free prox-methods with inexact oracle for stochastic convex optimization problems on a simplex

In the paper we show that euclidian randomization in some situations (i.e. for gradient-free method on a simplex) can be as good as the randomization on the unit sphere in 1-norm. That is on the simplex example we show that for gradient-free methods the choise of the prox-structure and the choise of a way of randomization have to be connected to each other. We demonstrate how it can be done in an optimal way. It is important that we consider inexact oracle.

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