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Jayanta Mandi

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10 papers

2 author rows

JAIR Journal 2026 Journal Article

Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning

Mattia Silvestri
Senne Berden
Gaetano Signorelli
Ali İrfan Mahmutoğulları
Jayanta Mandi
Brandon Amos
Tias Guns
Michele Lombardi

Background: Real-world optimization problems often contain parameters that are unknown at solving time. For example, in delivery problems, these parameters may be travel times or customer demands. A common strategy in such scenarios is to first predict the parameter values from contextual features using a machine learning model, and then solve the resulting optimization problem. To train the machine learning model, two paradigms can be distinguished. In prediction-focused learning, the model is trained to maximize predictive accuracy. However, this can lead to suboptimal decision-making, because it does not account for how prediction errors affect the quality of the downstream decisions. To address this, decision-focused learning (DFL) minimizes a task loss that captures how the predictions affect decision quality. Objectives: One challenge in DFL is that the task loss has zero-valued gradients when the optimization problem is combinatorial, which hinders gradient-based training. For this reason, state-of-the-art DFL methods use surrogate losses and problem smoothing. However, these methods make specific assumptions about the problem structure (e.g., linear or convex problems with unknown parameters occurring only in the objective function). The goal of our work is to overcome these limitations and extend the applicability of DFL. Method: We propose an alternative DFL approach that makes only minimal assumptions by combining stochastic smoothing with score function gradient estimation. This makes the approach broadly applicable, including to problems with nonlinear objectives, uncertainty in the constraints, and two-stage stochastic optimization problems. Results: Our experiments show that our method matches or outperforms specialized methods for the problems they are designed for, while also extending to settings where no existing method is applicable. In addition, our method always outperforms models trained with prediction-focused learning. Conclusions: In this work we demonstrate that by combining stochastic smoothing and score function gradient estimation to estimate the gradients of a smoothed loss, we can train a machine learning model in a DFL fashion without assuming any structural property of the optimization problem. This approach extends the applicability of DFL to a wider range of optimization problems, including those with uncertainty in the constraints. At the same time, it achieves performance that is competitive with or superior to existing DFL methods when they are applicable.

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NeurIPS Conference 2025 Conference Paper

Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints

Jayanta Mandi
Marianne Defresne
Senne Berden
Tias Guns

When some parameters of a constrained optimization problem (COP) are uncertain, this gives rise to a predict-then-optimize (PtO) problem, comprising two stages: the \textit{prediction} of the unknown parameters from contextual information and the subsequent \textit{optimization} using those predicted parameters. Decision-focused learning (DFL) implements the first stage by training a machine learning (ML) model to optimize the quality of the decisions made using the predicted parameters. When the predicted parameters occur in the constraints, they can lead to infeasible solutions. Therefore, it is important to simultaneously manage both feasibility and decision quality. We develop a DFL framework for predicting constraint parameters in a generic COP. While prior works typically assume that the underlying optimization problem is a linear program (LP) or integer LP (ILP), our approach makes no such assumption. We derive two novel loss functions based on maximum likelihood estimation (MLE): the first one penalizes infeasibility (by penalizing predicted parameters that lead to infeasible solutions), while the second one penalizes suboptimal decisions (by penalizing predicted parameters that make the true optimal solution infeasible). We introduce a single tunable parameter to form a weighted average of the two losses, allowing decision-makers to balance suboptimality and feasibility. We experimentally demonstrate that adjusting this parameter provides decision-makers control over this trade-off. Moreover, across several COP instances, we show that adjusting the tunable parameter allows a decision-maker to prioritize either suboptimality or feasibility, outperforming the performance of existing baselines in either objective.

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ECAI Conference 2025 Conference Paper

Minimizing Surrogate Losses for Decision-Focused Learning Using Differentiable Optimization

Jayanta Mandi
Ali Irfan Mahmutogullari
Senne Berden
Tias Guns

Decision-focused learning (DFL) trains a machine learning (ML) model to predict parameters of an optimization problem, to directly minimize decision regret, i. e. , maximize decision quality. Gradient-based DFL requires computing the derivative of the solution to the optimization problem with respect to the predicted parameters. However, for many optimization problems, such as linear programs (LPs), the gradient of the regret with respect to the predicted parameters is zero almost everywhere. Existing gradient-based DFL approaches for LPs try to circumvent this issue in one of two ways: (a) smoothing the LP into a differentiable optimization problem by adding a quadratic regularizer and then minimizing the regret directly or (b) minimizing surrogate losses that have informative (sub)gradients. In this paper, we show that the former approach still results in zero gradients, because even after smoothing the regret remains constant across large regions of the parameter space. To address this, we propose minimizing surrogate losses, even when a differentiable optimization layer is used and regret can be minimized directly. Our experiments demonstrate that minimizing surrogate losses allows differentiable optimization layers to achieve regret comparable to or better than surrogate-loss based DFL methods. Further, we demonstrate that this also holds for DYS-Net, a recently proposed differentiable optimization technique for LPs, that computes approximate solutions and gradients through operations that can be performed using feedforward neural network layers. Because DYS-Net executes the forward and the backward pass very efficiently, by minimizing surrogate losses using DYS-Net, we are able to attain regret on par with the state-of-the-art while reducing training time by a significant margin.

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IJCAI Conference 2025 Conference Paper

Preference Elicitation for Multi-objective Combinatorial Optimization with Active Learning and Maximum Likelihood Estimation

Marianne Defresne
Jayanta Mandi
Tias Guns

Real-life combinatorial optimization problems often involve several conflicting objectives, such as price, product quality and sustainability. A computationally-efficient way to tackle multiple objectives is to aggregate them into a single-objective function, such as a linear combination. However, defining the weights of the linear combination upfront is hard; alternatively, the use of interactive learning methods that ask users to compare candidate solutions is highly promising. The key challenges are to generate candidates quickly, to learn an objective function that leads to high-quality solutions and to do so with few user interactions. We build upon the Constructive Preference Elicitation framework and show how each of the three properties can be improved: to increase the interaction speed we investigate using pools of (relaxed) solutions, to improve the learning we adopt Maximum Likelihood Estimation of a Bradley-Terry preference model; and to reduce the number of user interactions, we select the pair of candidates to compare with an ensemble-based acquisition function inspired from Active Learning. Our careful experimentation demonstrates each of these improvements: on a PC configuration task and a realistic multi-instance routing problem, our method selects queries faster, needs fewer queries and synthesizes higher-quality combinatorial solutions than previous CPE methods.

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ECAI Conference 2024 Conference Paper

Decision-Focused Learning to Predict Action Costs for Planning

Jayanta Mandi
Marco Foschini
Daniel Höller
Sylvie Thiébaux
Jörg Hoffmann 0001
Tias Guns

In many automated planning applications, action costs can be hard to specify. An example is the time needed to travel through a certain road segment, which depends on many factors, such as the current weather conditions. A natural way to address this issue is to learn to predict these parameters based on input features (e. g. , weather forecasts) and use the predicted action costs in automated planning afterward. Decision-Focused Learning (DFL) has been successful in learning to predict the parameters of combinatorial optimization problems in a way that optimizes solution quality rather than prediction quality. This approach yields better results than treating prediction and optimization as separate tasks. In this paper, we investigate for the first time the challenges of implementing DFL for automated planning in order to learn to predict the action costs. There are two main challenges to overcome: (1) planning systems are called during gradient descent learning, to solve planning problems with negative action costs, which are not supported in planning. We propose novel methods for gradient computation to avoid this issue. (2) DFL requires repeated planner calls during training, which can limit the scalability of the method. We experiment with different methods approximating the optimal plan as well as an easy-to-implement caching mechanism to speed up the learning process. As the first work that addresses DFL for automated planning, we demonstrate that the proposed gradient computation consistently yields significantly better plans than predictions aimed at minimizing prediction error; and that caching can temper the computation requirements.

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JAIR Journal 2024 Journal Article

Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities

Jayanta Mandi
James Kotary
Senne Berden
Maxime Mulamba
Victor Bucarey
Tias Guns
Ferdinando Fioretto

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL.

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ICML Conference 2022 Conference Paper

Decision-Focused Learning: Through the Lens of Learning to Rank

Jayanta Mandi
Víctor Bucarey
Maxime Mulamba Ke Tchomba
Tias Guns

In the last years decision-focused learning framework, also known as predict-and-optimize, have received increasing attention. In this setting, the predictions of a machine learning model are used as estimated cost coefficients in the objective function of a discrete combinatorial optimization problem for decision making. Decision-focused learning proposes to train the ML models, often neural network models, by directly optimizing the quality of decisions made by the optimization solvers. Based on a recent work that proposed a noise contrastive estimation loss over a subset of the solution space, we observe that decision-focused learning can more generally be seen as a learning-to-rank problem, where the goal is to learn an objective function that ranks the feasible points correctly. This observation is independent of the optimization method used and of the form of the objective function. We develop pointwise, pairwise and listwise ranking loss functions, which can be differentiated in closed form given a subset of solutions. We empirically investigate the quality of our generic methods compared to existing decision-focused learning approaches with competitive results. Furthermore, controlling the subset of solutions allows controlling the runtime considerably, with limited effect on regret.

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IJCAI Conference 2021 Conference Paper

Contrastive Losses and Solution Caching for Predict-and-Optimize

Maxime Mulamba
Jayanta Mandi
Michelangelo Diligenti
Michele Lombardi
Victor Bucarey
Tias Guns

Many decision-making processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. Recently, problems in this class have been successfully addressed via end-to-end learning approaches, which rely on solving one optimization problem for each training instance at every epoch. In this context, we provide two distinct contributions. First, we use a Noise Contrastive approach to motivate a family of surrogate loss functions, based on viewing non-optimal solutions as negative examples. Second, we address a major bottleneck of all predict-and-optimize approaches, i. e. the need to frequently recompute optimal solutions at training time. This is done via a solver-agnostic solution caching scheme, and by replacing optimization calls with a lookup in the solution cache. The method is formally based on an inner approximation of the feasible space and, combined with a cache lookup strategy, provides a controllable trade-off between training time and accuracy of the loss approximation. We empirically show that even a very slow growth rate is enough to match the quality of state-of-the-art methods, at a fraction of the computational cost.

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NeurIPS Conference 2020 Conference Paper

Interior Point Solving for LP-based prediction+optimisation

Jayanta Mandi
Tias Guns

Solving optimization problem is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or energy- or stock prices. Machine learning (ML) models, especially neural networks, are increasingly being used to estimate these coefficients in a data-driven way. Hence, end-to-end predict-and-optimize approaches, which consider how effective the predicted values are to solve the optimization problem, have received increasing attention. In case of integer linear programming problems, a popular approach to overcome their non-differentiabilty is to add a quadratic penalty term to the continuous relaxation, such that results from differentiating over quadratic programs can be used. Instead we investigate the use of the more principled logarithmic barrier term, as widely used in interior point solvers for linear programming. Instead of differentiating the KKT conditions, we consider the homogeneous self-dual formulation of the LP and we show the relation between the interior point step direction and corresponding gradients needed for learning. Finally, our empirical experiments demonstrate our approach performs as good as if not better than the state-of-the-art QPTL (Quadratic Programming task loss) formulation of Wilder et al. and SPO approach of Elmachtoub and Grigas.

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AAAI Conference 2020 Conference Paper

Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems

Jayanta Mandi
Emir Demirovi?
Peter J. Stuckey
Tias Guns

Combinatorial optimization assumes that all parameters of the optimization problem, e. g. the weights in the objective function, are ﬁxed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for their estimation. Recently, Smart Predict and Optimize (SPO) has been proposed for problems with a linear objective function over the predictions, more speciﬁcally linear programming problems. It takes the regret of the predictions on the linear problem into account, by repeatedly solving it during learning. We investigate the use of SPO to solve more realistic discrete optimization problems. The main challenge is the repeated solving of the optimization problem. To this end, we investigate ways to relax the problem as well as warm-starting the learning and the solving. Our results show that even for discrete problems it often sufﬁces to train by solving the relaxation in the SPO loss. Furthermore, this approach outperforms the state-of-the-art approach of Wilder, Dilkina, and Tambe. We experiment with weighted knapsack problems as well as complex scheduling problems, and show for the ﬁrst time that a predict-and-optimize approach can successfully be used on large-scale combinatorial optimization problems.

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