- Series
- ACO Student Seminar
- Time
- Friday, March 11, 2016 - 1:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 256
- Speaker
- Rui Gao – Georgia Tech
- Organizer
- Yan Wang

Stochastic programming is a powerful
approach for decision-making under uncertainty. Unfortunately, the solution may
be misleading if the underlying distribution of the involved random parameters
is not known exactly. In this talk, we study distributionally robust stochastic
programming (DRSP), in which the decision hedges against the worst possible
distribution that belongs to an ambiguity set. More specifically, we consider
the DRSP with the ambiguity set comprising all distributions that are close to some
reference distribution in terms of Wasserstein distance. We derive a tractable
reformulation of the DRSP problem by constructing the worst-case distribution
explicitly via the first-order optimality condition of the dual problem. Our
approach has several theoretical and computational implications. First, using
the precise characterization of the worst-case distribution, we show that the
DRSP can be approximated by robust programs to arbitrary accuracy, and thus
many DRSP problems become tractable with tools from robust optimization.
Second, when the objective is concave in the uncertainty, the robust-program
approximation is exact and equivalent to a saddle-point problem, which can be
solved by a Mirror-Prox algorithm. Third, our framework can also be applied to
problems other than stochastic programming, such as a class of distributionally
robust transportation problems. Furthermore, we perform sensitivity analysis
with respect to the radius of the Wasserstein ball, and apply our results to
the newsvendor problem, two-stage linear program with uncertainty-affected
recourse, and worst-case Value-at-risk analysis.