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The problem considered in this paper is the minimization of expected cumulative losses in a stochastic system. The losses over time horizon are formed by the values of an unknown loss function at the consecutive jump times of a renewal process. The loss is assumed to be a convex function of a vector parameter, and the only available information is represented by an oracle which provides stochastic...
In local modelling, function estimates are computed from observations in a local neighborhood of the point of interest. A central question is how to choose the size of the neighborhood. Often this question has been tackled using asymptotic (in the number of observations) arguments. The recently introduced direct weight optimization approach is a non-asymptotic approach, minimizing an upper bound on...
We treat a convex problem to minimize average loss function for a stochastic system operating in continuous time. The losses on time horizon T arise at the jump times of a Poisson process with intensity being an unknown random process. The oracle gives randomly noised gradients of the loss function; the noises are additive, unbiased, with the bounded dual norm in average square sense. The goal consists...
The paper is devoted to designing an efficient recursive algorithm for solving the robust PageRank problem recently proposed by Juditsky and Polyak (2012) [4]. To this end, we reformulate the problem to a specific convex-concave saddle point problem minx∈X maxy∈Y q(x, y) with simple convex sets X ∈ ℝN and Y ∈ ℝN, i.e., standard simplex and Euclidean unit ball, respectively. Aiming this goal we develop...
In this article, we study the effectiveness of the Mirror Descent Randomized Control Algorithm recently developed to a class of homogeneous finite Markov chains governed by the stochastic multi-armed bandit with unknown mean losses. We prove the explicit, non-asymptotic both upper and lower bounds for the mean losses at a given (finite) time horizon. These bounds are very similar as functions of problem...
This article further develops an adaptive approach to the control of observable Markov chains with a finite number of states. We apply the Mirror Descent Randomized Control Algorithm (MDRCA) to a class of homogeneous finite Markov chains governed by the multi-armed bandit with unknown mean losses. The article develops the approach represented in [18]. As opposed to the partially observable Markov...
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