Distributionally Robust Optimization: A Review

Rahimian, Hamed; Mehrotra, Sanjay

doi:10.48550/arxiv.1908.05659

Cited by 139 publications

(206 citation statements)

References 272 publications

(619 reference statements)

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“…Distributionally robust optimization (DRO) problems have long been studied in robust optimization community for ordinary optimization problems in which the objective function and the constraint functions are explicitly formulated (in contrast to expensive black-box functions as we consider in this study) [Scarf, 1958, Rahimian andMehrotra, 2019]. DRCC problem with explicitly formulated objective and constraint functions were also studied in [Xie, 2021, Ho-Nguyen et al, 2021, and they were applied to practical problems called power flow optimization [Xie andAhmed, 2017, Fang et al, 2019].…”

Section: Related Workmentioning

confidence: 99%

Bayesian Optimization for Distributionally Robust Chance-constrained Problem

Yu¹,

Takeno²,

Karasuyama³

et al. 2022

Preprint

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In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.

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Section: Related Workmentioning

confidence: 99%

Bayesian Optimization for Distributionally Robust Chance-constrained Problem

Yu¹,

Takeno²,

Karasuyama³

et al. 2022

Preprint

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“…Indeed, minimizing a Markov coherent risk measure in a risk-aware context is equivalent to minimizing a certain worst-case expectation where the uncertainty set is characterized by a concave function. Several researchers have developed algorithms to solve robust MDPs, for an overview see, e.g., Rahimian and Mehrotra (2019).…”

Section: Related Workmentioning

confidence: 99%

Reinforcement Learning with Dynamic Convex Risk Measures

Coache¹,

Jaimungal²

2021

Preprint

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We develop an approach for solving time-consistent risk-sensitive stochastic optimization problems using model-free reinforcement learning (RL). Specifically, we assume agents assess the risk of a sequence of random variables using dynamic convex risk measures. We employ a time-consistent dynamic programming principle to determine the value of a particular policy, and develop policy gradient update rules. We further develop an actor-critic style algorithm using neural networks to optimize over policies. Finally, we demonstrate the performance and flexibility of our approach by applying it to optimization problems in statistical arbitrage trading strategies and obstacle avoidance robot control.

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“…In distributionally robust optimization (DRO) (Ben-Tal et al, 2013;Rahimian and Mehrotra, 2019), one aims to minimize the worst-case expected loss over an 'uncertainty set' of distributions. In the group DRO setting (Hu et al, 2018;Oren et al, 2019;Sagawa et al, 2020), this minimisation is simply over the (instantaneous) worst-performing group of examples.…”

Section: Group Distributionally Robust Optimisationmentioning

confidence: 99%

Equitable modelling of brain imaging by counterfactual augmentation with morphologically constrained 3D deep generative models

Guilherme¹,

Gray²,

Cardoso³

et al. 2021

Preprint

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We describe Countersynth, a conditional generative model of diffeomorphic deformations that induce label-driven, biologically plausible changes in volumetric brain images. The model is intended to synthesise counterfactual training data augmentations for downstream discriminative modelling tasks where fidelity is limited by data imbalance, distributional instability, confounding, or underspecification, and exhibits inequitable performance across distinct subpopulations. Focusing on demographic attributes, we evaluate the quality of synthesized counterfactuals with voxel-based morphometry, classification and regression of the conditioning attributes, and the Fréchet inception distance. Examining downstream discriminative performance in the context of engineered demographic imbalance and confounding, we use UK Biobank magnetic resonance imaging data to benchmark CounterSynth augmentation against current solutions to these problems. We achieve state-of-the-art improvements, both in overall fidelity and equity. The source code for Coun-terSynth is available online.

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Distributionally Robust Optimization: A Review

Cited by 139 publications

References 272 publications

Bayesian Optimization for Distributionally Robust Chance-constrained Problem

Bayesian Optimization for Distributionally Robust Chance-constrained Problem

Reinforcement Learning with Dynamic Convex Risk Measures

Equitable modelling of brain imaging by counterfactual augmentation with morphologically constrained 3D deep generative models

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