# Mean Robust Optimization

@inproceedings{Wang2022MeanRO, title={Mean Robust Optimization}, author={Irina Wang and Cole Becker and Bart P. G. Van Parys and Bartolomeo Stellato}, year={2022} }

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions because of pessimistic assumptions on the uncertain parameters. Wasserstein distributionally robust optimization can reduce conservatism by being closely data-driven, but it often leads to very large problems with prohibitive solution times. We introduce mean robust optimization, a general framework that combines the best of both worlds by providing…

## References

SHOWING 1-10 OF 40 REFERENCES

### The Price of Robustness

- Computer Science, MathematicsOper. Res.
- 2004

An approach is proposed that flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, and an attractive aspect of this method is that the new robust formulation is also a linear optimization problem, so it naturally extend to discrete optimization problems in a tractable way.

### Distributionally Robust Convex Optimization

- Computer ScienceOper. Res.
- 2014

A unifying framework for modeling and solving distributionally robust optimization problems and introduces standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold.

### Distributionally Robust Optimization and Its Tractable Approximations

- MathematicsOper. Res.
- 2010

A modular framework is presented to obtain an approximate solution to the problem that is distributionally robust and more flexible than the standard technique of using linear rules.

### Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

- Computer ScienceMath. Program.
- 2018

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.

### Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

- Computer ScienceOper. Res.
- 2010

This paper proposes a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix) and demonstrates that for a wide range of cost functions the associated distributionally robust stochastic program can be solved efficiently.

### Likelihood robust optimization for data-driven problems

- Mathematics, Computer ScienceComput. Manag. Sci.
- 2016

The asymptotic behavior of the distribution set is proved and the relationship between the model and other distributionally robust models is established and to test the performance of the model, it is applied to the newsvendor problem and the portfolio selection problem.

### Probabilistic Guarantees in Robust Optimization

- Computer ScienceSIAM Journal on Optimization
- 2021

The notion of robust complexity of an uncertainty set is introduced, which is a robust analog of the Rademacher or Gaussian complexity encountered in high-dimensional statistics, and which connects geometry of the uncertainty set and a priori probabilistic guarantee.

### On distributionally robust chance constrained programs with Wasserstein distance

- Computer ScienceMath. 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.

### Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality

- Computer ScienceOperations Research
- 2022

This paper develops the first finite-sample guarantee without suffering from the curse of dimensionality, which describes how the out-of-sample performance of a robust solution depends on the sample size, dimension of the uncertainty, and the complexity of the loss function class in a nearly optimal way.

### Distributionally Robust Stochastic Optimization with Wasserstein Distance

- Mathematics, Computer ScienceMathematics of Operations Research
- 2022

This paper derives a strong duality reformulation of the corresponding DRSO problem and construct approximate worst-case distributions explicitly via the first-order optimality conditions of the dual problem, and shows that data-driven DRSo problems can be approximated to any accuracy by robust optimization problems, and thereby many D RSO problems become tractable by using tools from robust optimization.