End-to-End Constrained Optimization Learning: A Survey

Kotary, James; Fioretto, Ferdinando; Hentenryck, Pascal Van; Wilder, Bryan

doi:10.48550/arxiv.2103.16378

Cited by 27 publications

(38 citation statements)

References 27 publications

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“…While these methods constitute a notable contribution to the state of the art, by being penalty-based, they inevitably present some of the limitations discussed in the previous section. In contrast, this paper introduces a novel LTR technique for learning fair rankings by the use of constrained optimization programs trained end-to-end with deep learning [12]. By integrating constrained optimization in the training cycle of a deep learning model, the proposed solution guarantees the satisfaction of fairness constraints, within a prescribed tolerance, in the resulting rankings.…”

Section: Related Workmentioning

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: Related Workmentioning

confidence: 99%

End-to-end Learning for Fair Ranking Systems

Kotary¹,

Fioretto²,

Hentenryck³

et al. 2021

Preprint

Self Cite

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show abstract

“…Ultimately, the goal is to produce a high quality prediction model that leads to a good decisions when implemented, such as a position that leads to a large return or a route that induces a small realized travel time. There has been a fair amount of recent work examining this paradigm and other closely related problems in data-driven decision making, such as the works of Bertsimas and Kallus [2020], Donti et al [2017], Elmachtoub and Grigas [2021], Kao et al [2009], Estes and Richard [2019], Ho and Hanasusanto [2019], Notz and Pibernik [2019], Kotary et al [2021], the references therein, and others.…”

Section: Introductionmentioning

confidence: 99%

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

Liu¹,

Grigas²

2021

Preprint

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The predict-then-optimize framework is fundamental in practical stochastic decision-making problems: first predict unknown parameters of an optimization model, then solve the problem using the predicted values. A natural loss function in this setting is defined by measuring the decision error induced by the predicted parameters, which was named the Smart Predict-then-Optimize (SPO) loss by Elmachtoub and Grigas [2021]. Since the SPO loss is typically nonconvex and possibly discontinuous, Elmachtoub and Grigas [2021] introduced a convex surrogate, called the SPO+ loss, that importantly accounts for the underlying structure of the optimization model. In this paper, we greatly expand upon the consistency results for the SPO+ loss provided by Elmachtoub and Grigas [2021]. We develop risk bounds and uniform calibration results for the SPO+ loss relative to the SPO loss, which provide a quantitative way to transfer the excess surrogate risk to excess true risk. By combining our risk bounds with generalization bounds, we show that the empirical minimizer of the SPO+ loss achieves low excess true risk with high probability. We first demonstrate these results in the case when the feasible region of the underlying optimization problem is a polyhedron, and then we show that the results can be strengthened substantially when the feasible region is a level set of a strongly convex function. We perform experiments to empirically demonstrate the strength of the SPO+ surrogate, as compared to standard 1 and squared 2 prediction error losses, on portfolio allocation and cost-sensitive multi-class classification problems.

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“…Fortunately, in many practical settings, one is interested in solving many instances sharing similar patterns. Therefore, the application of deep learning methods to aid the resolution of these optimization problems is gaining traction in the nascent area at the intersection between constrained optimization and machine learning [6,20,31]. In particular, supervised learning frameworks can train a model using pre-solved optimization instances and their solutions.…”

Section: Introductionmentioning

confidence: 99%

Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Method

Kotary¹,

Fioretto²,

Hentenryck³

2021

Preprint

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The Jobs shop Scheduling Problem (JSP) is a canonical combinatorial optimization problem that is routinely solved for a variety of industrial purposes. It models the optimal scheduling of multiple sequences of tasks, each under a fixed order of operations, in which individual tasks require exclusive access to a predetermined resource for a specified processing time. The problem is NP-hard and computationally challenging even for medium-sized instances. Motivated by the increased stochasticity in production chains, this paper explores a deep learning approach to deliver efficient and accurate approximations to the JSP. In particular, this paper proposes the design of a deep neural network architecture to exploit the problem structure, its integration with Lagrangian duality to capture the problem constraints, and a post-processing optimization to guarantee solution feasibility. The resulting method, called JSP-DNN, is evaluated on hard JSP instances from the JSPLIB benchmark library. Computational results show that JSP-DNN can produce JSP approximations of high quality at negligible computational costs.Preprint. Under review.

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End-to-End Constrained Optimization Learning: A Survey

Cited by 27 publications

References 27 publications

End-to-end Learning for Fair Ranking Systems

End-to-end Learning for Fair Ranking Systems

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

Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Method

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