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Decision-Making Under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets.

Charita Dellaporta1, Patrick O'Hara2, Theodoros Damoulas2,3

  • 1Department of Statistical Science, University College London, London WC1E 6BT, UK.

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Summary
This summary is machine-generated.

Distributionally Robust Optimization (DRO) with Robust Bayesian Ambiguity Sets (DRO-RoBAS) addresses model misspecification in decision-making. This method improves robustness against noisy data and model errors for better risk management.

Keywords:
Bayesian inferencedivergence-based inferencemisspecificationrobustnessstochastic optimisation

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Area of Science:

  • Decision Sciences
  • Optimization Theory
  • Statistical Inference

Background:

  • Distributionally Robust Optimization (DRO) safeguards risk-averse decision-makers by evaluating worst-case risks within ambiguity sets.
  • Bayesian formulations enhance DRO by propagating uncertainty from posterior distributions, but struggle with model misspecification.
  • Model misspecification forces overly conservative decisions by requiring ambiguity sets to encompass the true data-generating process (DGP).

Purpose of the Study:

  • To introduce a novel approach, DRO with Robust Bayesian Ambiguity Sets (DRO-RoBAS), designed to effectively model and mitigate the impact of misspecification in DRO.
  • To develop a method that incorporates beliefs about the DGP into ambiguity sets, thereby avoiding overly conservative decision-making.

Main Methods:

  • DRO-RoBAS utilizes Maximum Mean Discrepancy (MMD) ambiguity sets.
  • These MMD sets are centered around a robust posterior predictive distribution that integrates prior beliefs about the data-generating process (DGP).
  • The optimization problem is reformulated with a dual representation in Reproducing Kernel Hilbert Space (RKHS), providing probabilistic guarantees on ambiguity set tolerance.

Main Results:

  • The proposed DRO-RoBAS method demonstrates superior out-of-sample performance compared to existing Bayesian and empirical DRO approaches.
  • Performance improvements were observed across various model misspecification scenarios.
  • The method was validated on standard decision-making problems, including the Newsvendor and Portfolio problems.

Conclusions:

  • DRO-RoBAS offers a robust framework for decision-making under uncertainty, particularly when models are misspecified.
  • The approach effectively balances risk aversion with the need for accurate decision-making in the presence of data and model imperfections.
  • This work provides a significant advancement in robust optimization techniques for practical applications facing real-world data complexities.