Consistency of Distributionally Robust Risk- and Chance-Constrained Optimization Under Wasserstein Ambiguity Sets

  title={Consistency of Distributionally Robust Risk- and Chance-Constrained Optimization Under Wasserstein Ambiguity Sets},
  author={A. Cherukuri and A. Hota},
  journal={IEEE Control Systems Letters},
  • A. Cherukuri, A. Hota
  • Published 2021
  • Computer Science, Mathematics, Engineering
  • IEEE Control Systems Letters
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where the constraints are required to hold for a family of distributions constructed from the observed realizations of the uncertainty via the Wasserstein distance. Our main results establish that if the samples are drawn independently from an underlying… Expand
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledgeExpand
Bayesian Joint Chance Constrained Optimization: Approximations and Statistical Consistency
This paper rigorously proves a frequentist consistency result demonstrating the convergence of the optimalvalue to the optimal value of a fixed, parameterized constrained optimization problem, and proves the convex feasibility of the approximate Bayesian stochastic optimization problem. Expand
A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems
It is shown that the data-driven value function converges to its nominal counterpart as the sample size grows to infinity, and the resulting MPC scheme renders the closed-loop system mean-square stable with respect to the truebut-unknown distributions, while remaining less conservative than a fully robust approach. Expand
Data-Driven Distributionally Robust Optimization for Real-Time Economic Dispatch Considering Secondary Frequency Regulation Cost
A data-driven distributionally robust optimization (DRO) method for RTED considering automatic generation control (AGC) is proposed and can reduce the total cost of power generation and frequency regulation. Expand


Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations
It is demonstrated that the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs—in many interesting cases even as tractable linear programs. Expand
Distributionally Robust Stochastic Optimization with Wasserstein Distance
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is an underlying probability distribution that isExpand
On distributionally robust chance constrained programs with Wasserstein distance
  • Weijun Xie
  • Computer Science, Mathematics
  • Math. Program.
  • 2021
It is shown that a DRCCP can be reformulated as a conditional value-at-risk constrained optimization problem, and thus admits tight inner and outer approximations and a big-M free formulation. Expand
Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets
This work reformulates DRCCPs under data-driven Wasserstein ambiguity sets and a general class of constraint functions and presents a convex reformulation of the program and shows its tractability when the constraint function is affine in both the decision variable and the uncertainty. Expand
Distributionally robust chance-constrained programs with right-hand side uncertainty under Wasserstein ambiguity
An improved formulation of exact deterministic mixed-integer programming (MIP) reformulations of distributionally robust chance-constrained programs (DR-CCP) with random right-hand sides over Wasserstein ambiguity sets is considered and several hidden connections are revealed. Expand
Quantitative stability analysis for minimax distributionally robust risk optimization
This paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the secondExpand
Convergence Analysis for Mathematical Programs with Distributionally Robust Chance Constraint
The convergence analysis focuses on impact of the variation of the ambiguity set on the optimal value and the optimal solutions of optimization problems with distributionally robust chance constraints where the true probability distribution is unknown. Expand
A Convex Optimization Approach to Distributionally Robust Markov Decision Processes With Wasserstein Distance
  • Insoon Yang
  • Mathematics, Computer Science
  • IEEE Control Systems Letters
  • 2017
The existence and optimality of Markov policies are proved and convex optimization-based tools to compute and analyze the policies are developed and a sensitivity analysis tool is developed to quantify the effect of ambiguity set parameters on the performance of distributionally robust policies. Expand
Regularization via Mass Transportation
This paper introduces new regularization techniques using ideas from distributionally robust optimization, and gives new probabilistic interpretations to existing techniques to minimize the worst-case expected loss, where the worst case is taken over the ball of all distributions that have a bounded transportation distance from the empirical distribution. Expand
Risk-averse risk-constrained optimal control
A decomposition method for such nested problems with nested conditional risk mappings is proposed that allows them to solve via efficient numerical optimization methods and a new form of risk constraints which accounts for the propagation of uncertainty in time is proposed. Expand