The idea
A plan can fit historical data well and still disappoint on new observations. Mohajerin Esfahani and Kuhn consider decisions against a family of distributions near the empirical data distribution, rather than treating one fitted distribution as certain.
What the authors established
Using Wasserstein distance to define that family, the paper gives finite-sample guarantees and finite convex reformulations under stated assumptions. Some important cases become linear programs. These are conditional mathematical results, not protection against every possible future.
Applications
Planning under uncertainty involves a price for greater protection. Comparing typical and adverse outcomes makes that trade-off visible as the uncertainty set changes.
Where care is needed
The ambiguity-set radius, data assumptions and cost model matter. A poorly chosen set can produce overconfidence or excessive conservatism.
Sources and credits
- Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations
Peyman Mohajerin Esfahani, Daniel Kuhn, published
Mathematical Programming 171, 115–166 (2018); online 2017.
The reformulations and guarantees belong to the authors. The accompanying Pareto graphic illustrates trade-offs generally; it is not their figure or a robust-optimisation result.