Frameworks and Results in Distributionally Robust Optimization

Rahimian, Hamed; Mehrotra, Sanjay

doi:10.5802/ojmo.15

Cited by 55 publications

(33 citation statements)

References 365 publications

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“…The (min-max) distributionally robust optimization (DRO) counterpart min x∈X max P∈C E P h(x, ξ) for the nominal model ( 2) is another potential approach to handle the distributional uncertainty in Pn [Rahimian and Mehrotra, 2022]. If the distributional family C contains the true distribution P 0 , then the true cost of the decision x evaluated at P 0 , i.e., E P0 h(x, ξ), would also be reduced through minimizing the worst-case cost max P∈C E P h(x, ξ) because the inequality E P0 h(x, ξ) ≤ max P∈C E P h(x, ξ) holds for all x; for more interpretations and justifications of the DRO method, see .…”

Section: A Appendices Of Section 1 A1 Extensive Literature Reviewmentioning

confidence: 99%

Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificity

Wang¹,

Wang²,

Honorio³

2023

Preprint

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Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust optimization (DRO), and regularization. However, two issues have to be raised: 1) All these methods are biased estimators of the true optimal cost; 2) the prior distribution in the Bayesian method, the radius of the distributional ball in the DRO method, and the regularizer in the regularization method are difficult to specify. This paper studies a new framework that unifies the three approaches and that addresses the two challenges mentioned above. The asymptotic properties (e.g., consistency and asymptotic normalities), non-asymptotic properties (e.g., unbiasedness and generalization error bound), and a Monte-Carlo-based solution method of the proposed model are studied. The new model reveals the trade-off between the robustness to the unseen data and the specificity to the training data.

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Section: A Appendices Of Section 1 A1 Extensive Literature Reviewmentioning

confidence: 99%

Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificity

Wang¹,

Wang²,

Honorio³

2023

Preprint

View full text Add to dashboard Cite

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“…Given a divergence 𝐷 𝜙 between two distributions 𝑃 and 𝑄, Distributionally Robust Optimization (DRO) aims to minimize the expected risk over the worst-case distribution 𝑄 [19,22,27], where 𝑄 is in a divergence ball around training distribution 𝑃. Formally, it can be defined as: min…”

Section: Distributionally Robust Optimizationmentioning

confidence: 99%

“…In contrast, AUC is a special case of OPAUC(𝛽) with 𝛽 = 1, which considers the whole ranking list. Our proof of the equivalence is based on the Distributionally Robust Optimization (DRO) framework [27] (cf. Section 3).…”

Section: Introductionmentioning

confidence: 99%

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On the Theories Behind Hard Negative Sampling for Recommendation

Shi,

Chen,

Feng

et al. 2023

Preprint

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Negative sampling has been heavily used to train recommender models on large-scale data, wherein sampling hard examples usually not only accelerates the convergence but also improves the model accuracy. Nevertheless, the reasons for the effectiveness of Hard Negative Sampling (HNS) have not been revealed yet. In this work, we fill the research gap by conducting thorough theoretical analyses on HNS. Firstly, we prove that employing HNS on the Bayesian Personalized Ranking (BPR) learner is equivalent to optimizing One-way Partial AUC (OPAUC). Concretely, the BPR equipped with Dynamic Negative Sampling (DNS) is an exact estimator, while with softmax-based sampling is a soft estimator. Secondly, we prove that OPAUC has a stronger connection with Top-𝐾 evaluation metrics than AUC and verify it with simulation experiments. These analyses establish the theoretical foundation of HNS in optimizing Top-𝐾 recommendation performance for the first time. On these bases, we offer two insightful guidelines for effective usage of HNS: 1) the sampling hardness should be controllable, e.g., via pre-defined hyper-parameters, to adapt to different Top-𝐾 metrics and datasets; 2) the smaller the 𝐾 we emphasize in Top-𝐾 evaluation metrics, the harder the negative samples we should draw. Extensive experiments on three real-world benchmarks verify the two guidelines. CCS CONCEPTS• Information systems → Recommender systems.

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“…In stochastic optimization, uncertainty is assumed to follow a specified probability distribution, usually through sampling (Powell, 2019; Rahimian & Mehrotra, 2019). Gautam et al.…”

Section: Introductionmentioning

confidence: 99%

Improving the resilience of power grids against typhoons with data‐driven spatial distributionally robust optimization

et al. 2022

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In recent years, the increased frequency of natural hazards has led to more disruptions in power grids, potentially causing severe infrastructural damages and cascading failures. Therefore, it is important that the power system resilience be improved by implementing new technology and utilizing optimization methods. This paper proposes a data‐driven spatial distributionally robust optimization (DS‐DRO) model to provide an optimal plan to install and dispatch distributed energy resources (DERs) against the uncertain impact of natural hazards such as typhoons. We adopt an accurate spatial model to evaluate the failure probability with regard to system components based on wind speed. We construct a moment‐based ambiguity set of the failure distribution based on historical typhoon data. A two‐stage DS‐DRO model is then formulated to obtain an optimal resilience enhancement strategy. We employ the combination of dual reformulation and a column‐and‐constraints generation algorithm, and showcase the effectiveness of the proposed approach with a modified IEEE 13‐node reliability test system projected in the Hong Kong region.

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Frameworks and Results in Distributionally Robust Optimization

Cited by 55 publications

References 365 publications

Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificity

Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificity

On the Theories Behind Hard Negative Sampling for Recommendation

Improving the resilience of power grids against typhoons with data‐driven spatial distributionally robust optimization

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