joint work with Cagil Kocyigit, Daniel Kuhn
We study a robust monopoly pricing problem with a minimax regret objective, where a seller endeavors to sell multiple goods to a single buyer, only knowing that the buyer’s values for the goods range over a rectangular uncertainty set. We interpret this problem as a zero-sum game between the seller, who chooses a selling mechanism, and a fictitious adversary, who chooses the buyer’s values. We prove that this game admits a Nash equilibrium that can be computed in closed form. We further show that the deterministic restriction of the problem is solved by a deterministic posted price mechanism.
joint work with Zhi Chen, Daniel Kuhn
We provide an exact deterministic reformulation for data-driven chance constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the $1$-norm or the $\infty$-norm, the cone is the nonnegative orthant, and the chance constrained program can be reformulated as a mixed-integer linear program.
joint work with Renbo Zhao, Hien Le Thi Khanh
We propose an inexact primal-dual smoothing framework to solve a strongly-convex- generally-concave saddle point problem with non-bilinear structure, with potentially a large number of component functions. We develop a probabilistic version of our smoothing framework, which allows each sub-problem to be solved by randomized algorithms inexactly in expectation. In addition, we extend both our deterministic and probabilistic frameworks to solve generally convex-concave saddle point problems. We comment on the application of this method to robust data-driven optimization.