1,066 research outputs found
A Unified Theory of Robust and Distributionally Robust Optimization via the Primal-Worst-Equals-Dual-Best Principle
Robust and distributionally robust optimization are modeling paradigms for
decision-making under uncertainty where the uncertain parameters are only known
to reside in an uncertainty set or are governed by any probability distribution
from within an ambiguity set, respectively, and a decision is sought that
minimizes a cost function under the most adverse outcome of the uncertainty. In
this paper, we develop a rigorous and general theory of robust and
distributionally robust nonlinear optimization using the language of convex
analysis. Our framework is based on a generalized
`primal-worst-equals-dual-best' principle that establishes strong duality
between a semi-infinite primal worst and a non-convex dual best formulation,
both of which admit finite convex reformulations. This principle offers an
alternative formulation for robust optimization problems that obviates the need
to mobilize the machinery of abstract semi-infinite duality theory to prove
strong duality in distributionally robust optimization. We illustrate the
modeling power of our approach through convex reformulations for
distributionally robust optimization problems whose ambiguity sets are defined
through general optimal transport distances, which generalize earlier results
for Wasserstein ambiguity sets.Comment: Previous title: Mathematical Foundations of Robust and
Distributionally Robust Optimizatio
Distributionally Robust Games with Risk-averse Players
We present a new model of incomplete information games without private
information in which the players use a distributionally robust optimization
approach to cope with the payoff uncertainty. With some specific restrictions,
we show that our "Distributionally Robust Game" constitutes a true
generalization of three popular finite games. These are the Complete
Information Games, Bayesian Games and Robust Games. Subsequently, we prove that
the set of equilibria of an arbitrary distributionally robust game with
specified ambiguity set can be computed as the component-wise projection of the
solution set of a multi-linear system of equations and inequalities. For
special cases of such games we show equivalence to complete information finite
games (Nash Games) with the same number of players and same action spaces.
Thus, when our game falls within these special cases one can simply solve the
corresponding Nash Game. Finally, we demonstrate the applicability of our new
model of games and highlight its importance.Comment: 11 pages, 3 figures, Proceedings of 5th the International Conference
on Operations Research and Enterprise Systems ({ICORES} 2016), Rome, Italy,
February 23-25, 201
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