Risk Bounds and Calibration for a Smart Predict-then-Optimize Method

Liu, Heyuan; Grigas, Paul

doi:10.48550/arxiv.2108.08887

Cited by 2 publications

(2 citation statements)

References 15 publications

(26 reference statements)

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“…Remarkably, risk bounds about the SPO+ loss relative to the SPO loss can be derived [13], and the empirical minimizer of the SPO+ loss is shown to achieve low excess true risk with high probability. Note that, by definition, 𝒚 ⊤ Π * (𝒚) ≥ 𝒚 ⊤ Π * ( ŷ) and therefore L (𝒚, ŷ) ≥ 0.…”

Section: Regret Loss and Spo Trainingmentioning

confidence: 99%

End-to-end Learning for Fair Ranking Systems

Kotary¹,

Fioretto²,

Hentenryck³

et al. 2021

Preprint

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The learning-to-rank problem aims at ranking items to maximize exposure of those most relevant to a user query. A desirable property of such ranking systems is to guarantee some notion of fairness among specified item groups. While fairness has recently been considered in the context of learning-to-rank systems, current methods cannot provide guarantees on the fairness of the proposed ranking policies. This paper addresses this gap and introduces Smart Predict and Optimize for Fair Ranking (SPOFR), an integrated optimization and learning framework for fairness-constrained learning to rank. The end-to-end SPOFR framework includes a constrained optimization sub-model and produces ranking policies that are guaranteed to satisfy fairness constraints, while allowing for fine control of the fairness-utility tradeoff. SPOFR is shown to significantly improve current state-of-the-art fair learning-to-rank systems with respect to established performance metrics.

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Section: Regret Loss and Spo Trainingmentioning

confidence: 99%

End-to-end Learning for Fair Ranking Systems

Kotary¹,

Fioretto²,

Hentenryck³

et al. 2021

Preprint

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show abstract

“…Balghiti et al (2019) later provide finite-sample performance guarantee of the SPO loss in the form of generalization bounds. Recently, Liu and Grigas (2021) have strengthened the consistency of SPO+ by providing risk guarantees and a calibration analysis in the polyhedral and strongly convex cases. Elmachtoub et al (2020) propose a method to train decision trees using the SPO loss and demonstrate its excellent numerical performance and lower model complexity.…”

Section: Relevant Literaturementioning

confidence: 99%

Integrated Conditional Estimation-Optimization

Grigas¹,

Meng²,

Zuo-Jun³

et al. 2021

Preprint

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Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of uncertain parameters and then optimizing the objective based on the estimation, we propose an integrated conditional estimation-optimization (ICEO) framework that estimates the underlying conditional distribution of the random parameter while considering the structure of the optimization problem. We directly model the relationship between the conditional distribution of the random parameter and the contextual features, and then estimate the probabilistic model with an objective that aligns with the downstream optimization problem. We show that our ICEO approach is asymptotically consistent under moderate regularity conditions and further provide finite performance guarantees in the form of generalization bounds. Computationally, performing estimation with the ICEO approach is a non-convex and often non-differentiable optimization problem. We propose a general methodology for approximating the potentially non-differentiable mapping from estimated conditional distribution to optimal decision by a differentiable function, which greatly improves the performance of gradient-based algorithms applied to the non-convex problem. We also provide a polynomial optimization solution approach in the semi-algebraic case. Numerical experiments are also conducted to show the empirical success of our approach in different situations including with limited data samples and model mismatches.

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Risk Bounds and Calibration for a Smart Predict-then-Optimize Method

Cited by 2 publications

References 15 publications

End-to-end Learning for Fair Ranking Systems

End-to-end Learning for Fair Ranking Systems

Integrated Conditional Estimation-Optimization

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