arXiv subjects

Ali İrfan Mahmutoğulları

Publications and source records attributed to Ali İrfan Mahmutoğulları.

5 recordsLinked to original sources

arXiv2026

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

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is to estimate said parameters via machine learning (ML) models trained to minimize the prediction error, which however is not necessarily aligned with the downstream task-level error. The decision-focused learning (DFL) paradigm overcomes this limitation by training to directly minimize a task loss, e.g. regret. Since the latter has non-informative gradients for combinatorial problems, state-of-the-art DFL methods introduce surrogates and approximations that enable training. But these methods exploit specific assumptions about the problem structures (e.g., convex or linear problems, unknown parameters only in the objective function). We propose an alternative method that makes no such assumptions, it combines stochastic smoothing with score function gradient estimation which works on any task loss. This opens up the use of DFL methods to nonlinear objectives, uncertain parameters in the problem constraints, and even two-stage stochastic optimization. Experiments show that it typically requires more epochs, but that it is on par with specialized methods and performs especially well for the difficult case of problems with uncertainty in the constraints, in terms of solution quality, scalability, or both.

cs.LG↗

arXiv2025

Solver-Free Decision-Focused Learning for Linear Optimization Problems

Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from contextual features. This gives rise to predict-then-optimize problems, where a machine learning model predicts problem parameters that are then used to make decisions via optimization. A growing body of work on decision-focused learning (DFL) addresses this setting by training models specifically to produce predictions that maximize downstream decision quality, rather than accuracy. While effective, DFL is computationally expensive, because it requires solving the optimization problem with the predicted parameters at each loss evaluation. In this work, we address this computational bottleneck for linear optimization problems, a common class of problems in both DFL literature and real-world applications. We propose a solver-free training method that exploits the geometric structure of linear optimization to enable efficient training with minimal degradation in solution quality. Our method is based on the insight that a solution is optimal if and only if it achieves an objective value that is at least as good as that of its adjacent vertices on the feasible polytope. Building on this, our method compares the estimated quality of the ground-truth optimal solution with that of its precomputed adjacent vertices, and uses this as loss function. Experiments demonstrate that our method significantly reduces computational cost while maintaining high decision quality.

cs.LG↗

arXiv2025

Minimizing Surrogate Losses for Decision-Focused Learning using Differentiable Optimization

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.

cs.LG↗

arXiv2023

Leveraging Contextual Information for Robustness in Vehicle Routing Problems

We investigate the benefit of using contextual information in data-driven demand predictions to solve the robust capacitated vehicle routing problem with time windows. Instead of estimating the demand distribution or its mean, we introduce contextual machine learning models that predict demand quantiles even when the number of historical observations for some or all customers is limited. We investigate the use of such predicted quantiles to make routing decisions, comparing deterministic with robust optimization models. Furthermore, we evaluate the efficiency and robustness of the decisions obtained, both using exact or heuristic methods to solve the optimization models. Our extensive computational experiments show that using a robust optimization model and predicting multiple quantiles is promising when substantial historical data is available. In scenarios with a limited demand history, using a deterministic model with just a single quantile exhibits greater potential. Interestingly, our results also indicate that the use of appropriate quantile demand values within a deterministic model results in solutions with robustness levels comparable to those of robust models. This is important because, in most applications, practitioners use deterministic models as the industry standard, even in an uncertain environment. Furthermore, as they present fewer computational challenges and require only a single demand value prediction, deterministic models paired with an appropriate machine learning model hold the potential for robust decision-making.

math.OC↗

arXiv2017

Multi-objective risk-averse two-stage stochastic programming problems

We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of Benson's algorithm to solve this problem. Using Lagrangian duality, we develop scenario-wise decomposition methods to solve the two scalarization problems appearing in Benson's algorithm. Then, we propose a procedure to recover the primal solutions of these scalarization problems from the solutions of their Lagrangian dual problems. Finally, we test our algorithms on a multi-asset portfolio optimization problem under transaction costs.

math.OC↗