Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems

Details Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems

2010-12-14

arxiv.org/abs/1012.3189v4

Computer Science

Data Structures and Algorithms

23 pages

Scientific paper

We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees, and minimum weight matchings over probabilistic graphs, and other combinatorial problems like knapsack. We observe that the expected value is inadequate in capturing different types of {\em risk-averse} or {\em risk-prone} behaviors, and instead we consider a more general objective which is to maximize the {\em expected utility} of the solution for some given utility function, rather than the expected weight (expected weight becomes a special case). We show that we can obtain a polynomial time approximation algorithm with {\em additive error} $\epsilon$ for any $\epsilon>0$, if there is a pseudopolynomial time algorithm for the {\em exact} version of the problem (This is true for the problems mentioned above) and the maximum value of the utility function is bounded by a constant. Our result generalizes several prior results on stochastic shortest path, stochastic spanning tree, and stochastic knapsack. Our algorithm for utility maximization makes use of the separability of exponential utility and a technique to decompose a general utility function into exponential utility functions, which may be useful in other stochastic optimization problems.

Affiliated with

Also associated with

No associations

Rating

Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-13032