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Optimal Transport-Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes

Author

Listed:
  • Jose Blanchet

    (Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Karthyek Murthy

    (Engineering Systems and Design, Singapore University of Technology & Design, Singapore 487372, Singapore)

  • Fan Zhang

    (Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

We consider optimal transport-based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss function, we obtain structural results about the value function, the optimal policy, and the worst-case optimal transport adversarial model. These results expose a rich structure embedded in the DRO problem (e.g., strong convexity even if the non-DRO problem is not strongly convex, a suitable scaling of the Lagrangian for the DRO constraint, etc., which are crucial for the design of efficient algorithms). As a consequence of these results, one can develop efficient optimization procedures that have the same sample and iteration complexity as a natural non-DRO benchmark algorithm, such as stochastic gradient descent.

Suggested Citation

  • Jose Blanchet & Karthyek Murthy & Fan Zhang, 2022. "Optimal Transport-Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes," Mathematics of Operations Research, INFORMS, vol. 47(2), pages 1500-1529, May.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:2:p:1500-1529
    DOI: 10.1287/moor.2021.1178
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