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arXiv · 1108.6160

Stochastic optimization by message passing

Fabrizio Altarelli·Alfredo Braunstein·Abolfazl Ramezanpour·Riccardo Zecchina
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Abstract

Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. In a recent work we introduced a message passing algorithm based on the cavity method of statistical physics to solve the two-stage matching problem with independently distributed stochastic parameters. In this paper we provide an in-depth explanation of the general method and caveats, show the details of the derivation and resulting algorithm for the matching problem and apply it to a stochastic version of the independent set problem, which is a computationally hard and relevant problem in communication networks. We compare the results with some greedy algorithms and briefly discuss the extension to more complicated stochastic multi-stage problems.

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Fabrizio Altarelli, Alfredo Braunstein, Abolfazl Ramezanpour, Riccardo Zecchina. 2011-08-31. Stochastic optimization by message passing. https://doi.org/10.1088/1742-5468%2F2011%2F11%2Fp11009

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