  


Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization
Viet Anh Nguyen (vietanh.nguyenstanford.edu) Abstract: We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zerosum game between a statistician choosing an estimatorthat is, a measurable function of the observationand a fictitious adversary choosing a priorthat is, a pair of signal and noise distributions ranging over independent Wasserstein ballswith the goal to minimize and maximize the expected squared estimation error, respectively. We show that if the Wasserstein balls are centered at normal distributions, then the zerosum game admits a Nash equilibrium, where the players' optimal strategies are given by an affine estimator and a normal prior, respectively. We further prove that this Nash equilibrium can be computed by solving a tractable convex program. Finally, we develop a FrankWolfe algorithm that can solve this convex program orders of magnitude faster than stateoftheart general purpose solvers. We show that this algorithm enjoys a linear convergence rate and that its directionfinding subproblems can be solved in quasiclosed form. Keywords: Wasserstein distance, mean square error, affine estimator Category 1: Stochastic Programming Category 2: Infinite Dimensional Optimization Category 3: Applications  Science and Engineering (Statistics ) Citation: Download: [PDF] Entry Submitted: 11/08/2019 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  