Correlation Robust Stochastic Optimization

We consider a robust model proposed by Scarf, 1958, for stochastic optimization when only the marginal probabilities of (binary) random variables are given, and the correlation between the random variables is unknown. In the robust model, the objective is to minimize expected cost against worst possible joint distribution with those marginals. We introduce the concept of correlation gap to compare this model to the stochastic optimization model that ignores correlations and minimizes expected cost under independent Bernoulli distribution. We identify a class of functions, using concepts of summable cost sharing schemes from game theory, for which the correlation gap is well-bounded and the robust model can be approximated closely by the independent distribution model. As a result, we derive efficient approximation factors for many popular cost functions, like submodular functions, facility location, and Steiner tree. As a byproduct of our analysis, we also improve some existing result...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Shipra Agrawal, Yichuan Ding, Amin Saberi, Yinyu Ye
• Keywords: Discrete Algorithms, Independent Distribution Model, Robust Model, SODA 2010, Stochastic Optimization Model