Predict-Then-Optimize

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4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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Latest papers 20

Oct 6, 2026cs.LG

FedRSPO+: A Heterogeneity-aware Algorithm for Decision-focused Federated Learning

Decision-focused learning (DFL) trains predictive models for downstream optimization, but existing methods largely assume centralized data. In cross-silo settings, federated learning offers a natural alternative, yet standard federated methods optimize prediction over decision quality and do not address heterogeneity in downstream objectives or feasible sets. This heterogeneity is especially challenging for DFL because small perturbations in polyhedral problems can cause discontinuous changes in optimal decisions, destabilizing client updates and aggregation. We propose FedRSPO+, a heterogeneity-aware framework for decision-focused federated learning, built on RSPO+, a regularized predict-then-optimize surrogate that smooths the decision map through projection. We show that RSPO+ upper bounds decision error and regret for the regularized decision and, under exact regularization and consistent LP solution selection, for the original LP decision. We further derive cross-client heterogeneity bounds that depend on both objective and feasible-set heterogeneity, vanish at homogeneity, and require no strong convexity. FedRSPO+ uses an annealed, modular training procedure compatible with standard federated personalization and aggregation methods. Experiments on synthetic knapsack, shortest-path, and real-world energy pricing tasks compare against prediction-only federated learning and DFL baselines under varying heterogeneity and communication budgets. Results suggest that smoothing is a useful ingredient for stable collaborative decision learning and provide a heterogeneity-aware foundation for federated DFL.

Konstantinos Ziliaskopoulos, Alexander Vinel, Jiaqi Wang

Auburn University

Decision-Focused Learning Federated Learning Predict-Then-Optimize Heterogeneous Federated Learning

Oct 2, 2026cs.LG

DePICT: Decision-Preserving Interface for Constrained Downstream Tasks

A constrained optimization problem may involve a parameter in its objective and active constraints, yet the final decision may remain insensitive to small changes in that parameter. This raises a fundamental question: which inputs does a decision making system truly depend on? Building on this question, we introduce DePICT, a procedure for constructing decision preserving interfaces by ranking context directions according to the optimizer's solution sensitivity and aggregating them across an operating regime. We study this problem in a high dimensional setting where primitive context parameterizes a constrained task and the downstream agent observes only a selected subset of context directions. For locally regular constrained programs, we derive a Karush Kuhn Tucker (KKT) based characterization of when a context direction is optimizer relevant. Our analysis shows that appearing in the active optimization problem does not necessarily imply that a variable affects the final decision. Some context directions can alter the KKT conditions while leaving the optimal solution unchanged because their effect is absorbed by the dual variables. DePICT is designed to remove exactly these directions. In a controlled diagnosis, it recovers the decision relevant interface exactly and reduces linear predictor regret to 0.009, compared with 0.475 for the strongest competing baseline.

Utkarsh Grover, Ravi Ranjan, Agoritsa Polyzou +4

University of South Florida · Florida International University · DEVCOM Army Research Lab

Predict-Then-Optimize Constrained Optimization Feature Selection Sensitivity Analysis

Sep 27, 2026cs.LG

Geometric Identification in Predict-Then-Optimize Learning

Decision-focused surrogates can recover downstream decisions without identifying the quotient report. We characterize the equality set of the convex Smart Predict-then-Optimize surrogate (SPO+) population risk. Under central symmetry, the centered mean class is the unique Bayes minimizer exactly when every nonzero effective displacement makes the old optimizer leave the shifted optimal face with positive probability. This condition separates face crossing from selected-oracle disagreement and gives quantitative local coercivity. Without symmetry, strict crossing alone need not identify the mean; selection balance with reflected crossing restores quotient-report identification, and conditional versions extend the result to measurable predictors. These are population statements, without finite-sample report-recovery or generic transfer-regret guarantees. Closed-form mechanisms reproduce the analytic identities and rates. Portfolio, complete-matrix KuaiRec, and Energy/Storage studies measure predictive fidelity, shifted regret, and fitted-report geometry. A known data-generating process (DGP) companion retains their application geometries while isolating conditional-mean recovery and crossing, without testing the original observational assumptions.

Jiaxiao Xu, Changhong Mou, Keji Liu +2

Shanghai University of Finance and Economics · Utah State University

Predict-Then-Optimize Decision-Focused Learning Statistical Learning Theory

Sep 14, 2026econ.EM

Eigenvalue-Decomposition Cost Denoising as an Alternative to Predict-then-Optimize for Shortest-Path Problems

Predict-then-optimize methods such as Smart "Predict, then Optimize" (SPO+) of Elmachtoub and Grigas (2022) learn a mapping from contextual features to unknown edge costs and then solve the induced combinatorial problem on the predicted costs. This approach is powerful but relies on the predictive model being well specified: when the true cost-generating process is nonlinear in the features and the predictor is linear, SPO+'s performance degrades as the misspecification grows. We propose and evaluate a structurally different remedy for a specific but common setting: when the decision-maker observes many noisy realizations of the same underlying cost process, the realized cost vectors themselves can be treated as a noisy signal and denoised directly, via eigenvalue decomposition (equivalently, Principal Component Analysis) of their covariance matrix, before ever invoking a predictive model. We instantiate this idea on the

5\times5

grid shortest-path benchmark introduced by Elmachtoub and Grigas (2022), retaining only the top-

k

eigenvectors of the training cost covariance matrix and projecting new noisy cost observations onto that subspace prior to solving with Dijkstra's (1959) algorithm. We find that the choice of

k

is decisive: keeping only

k{=}2

eigenvectors discards real signal and underperforms even the naive noisy-cost baseline, while setting

k{=}5

to match the true latent feature dimension makes eigenvalue-denoised Dijkstra the best-performing method at every misspecification level tested, outperforming SPO+ by a wide margin under high misspecification.

Henry Aldridge-Krawciw, Irene Aldridge

Predict-Then-Optimize Combinatorial Optimization

Sep 14, 2026cs.LG

Optimizing for the decision not the prediction: an exploration of Smooth Net Benefit as a training objective

Objective Prediction models are commonly trained using objectives such as Bernoulli negative log-likelihood (NLL), although downstream clinical decisions may depend on specific risk thresholds. We introduce Smooth Net Benefit (

\sigma

NB), a differentiable approximation of Net Benefit designed to align model training with threshold-specific clinical utility. Materials and Methods We evaluated

\sigma

NB as a training objective for logistic regression, generalized additive models (GAMs), and XGBoost with three Hessian implementations. Experiments used the Framingham cardiovascular risk dataset and 44 TabZilla datasets comprising 72 dataset-threshold combinations. Results

\sigma

NB training did not consistently improve Net Benefit in Framingham. Across the TabZilla benchmark, mean standardized Net Benefit for logistic regression increased from 0.5669 with NLL to 0.5765 with

\sigma

NB (mean difference 0.0096, 95% CI -0.0001 to 0.0193). For GAMs, mean standardized Net Benefit decreased from 0.5921 to 0.5625 (mean difference -0.0296, 95% CI -0.0721 to 0.0129). For XGBoost, NLL achieved 0.6745 compared with 0.6723--0.6735 across

\sigma

NB implementations. In logistic regression,

\sigma

NB gains were positively associated with the performance advantage of XGBoost over NLL-trained logistic regression. Discussion The effect of

\sigma

NB was context dependent, with modest gains concentrated in logistic regression and little benefit for more flexible model classes. This suggests that decision-focused optimization may be most useful when limited model flexibility leaves greater scope for improvement. Conclusion Our results do not support

\sigma

NB as a general replacement for NLL training, but support further investigation of decision-focused objectives in settings where conventional likelihood-based training may not adequately capture decision-relevant structure.

Koen M. F. Gorgels, Lasai Barreñada, Maarten van Smeden +3

Department of Data Science and Biostatistics, Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, the Netherlands · Coo peratie VGZ, Arnhem, the Netherlands · Department of Development and Regeneration, KU Leuven, Leuven, Belgium

Predict-Then-Optimize Decision-Focused Learning Clinical Decision-Making Clinical Risk Prediction

Aug 13, 2026stat.ME

Chance-constrained selection of sequential intervention strategies from counterfactual estimates

Many operational decisions are sequences of interventions under a cumulative resource limit, such as a maintenance schedule within a crew-hour budget. Choosing among them calls for the outcome and the cumulative cost each would produce, counterfactual quantities identified from observational data. Two strategies with the same expected cost can exceed the budget at very different rates, so constraining the mean does not bound how often an overrun occurs. Prior two-step architectures, recently extended to continuous doses, constrain the mean cost rather than its tail and allocate at a single decision point. Methods that do bound a cost tail take its distribution from a specified model rather than identifying it from data. We present a predict-then-optimize framework. In the prediction step, any estimator returning an outcome value and a cost distribution supplies what the decision rule consumes, so the predictor is interchangeable. In the optimization step, a chance-constrained selection over a finite candidate set bounds the probability that the cumulative cost exceeds the budget. That tail does not decompose across stages, so each strategy is scored whole. Sweeping the tolerated violation probability traces a safety-utility frontier, and distribution-free finite-sample bounds cover violation and outcome shortfall. Four of five environments, spanning clinical treatment and equipment maintenance, supply exact counterfactual ground truth; the fifth carries real outcomes from a digital-health micro-randomized trial. Across them, the rule holds the budget where a point-estimate rule overruns it, at an outcome cost the frontier makes explicit. All code is available at https://github.com/mfriendly/counterfactual-chance-selection

Minkyoung Kim, Beakcheol Jang

Graduate School of Information, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 03722, Republic of Korea

Stochastic Optimization Chance-Constrained Optimization Predict-Then-Optimize Sequential Decision Making Counterfactual Learning

Aug 5, 2026cs.LG

Local Violation Certification for Linear Predict-Then-Optimize Pipelines

Data-driven decision pipelines combining predictive machine learning models with downstream optimization software are increasingly used to make high-stakes operational decisions. Certifying the safety, fairness, and reliability of these decisions is essential, yet traditional scenario generation methods rely on repeated random testing, which becomes computationally prohibitive when failure events are rare and offers little insight into why failures occur. We present a framework for local violation certification designed specifically for linear decision pipelines under input uncertainty. We mathematically demonstrate that standard sampling methods fail efficiently for rare violations, motivating a direct structural approach. By analyzing the fixed decision boundary of a deployed pipeline, we show that the local risk of failure can be calculated directly in closed form using a single optimization solve. Furthermore, we introduce an exact sampling procedure and closed-form risk statistics that provide feature-level attributions (identifying which input characteristics contribute most to potential non-compliance) without requiring repetitive random trials or complex sampling algorithms. We demonstrate our approach on an economic power dispatch system subject to emissions regulations, delivering precise, auditable risk assessments at a fraction of the traditional computational cost.

Ş. İlker Birbil, Wenhao Chi

Faculty of Economics and Business, University of Amsterdam, The Netherlands · Yau Mathematical Sciences Center, Tsinghua University

Algorithmic Auditing Predict-Then-Optimize Decision-Making under Uncertainty

Jul 23, 2026cs.LG

Smart predict-then-robustly-optimize

In this paper, we propose and study a robust variant of the smart predict-then-optimize approach that accounts for prediction shifts due to disturbance in the covariate feature space. While traditional integrated-learning-and-optimization models assume that side information is perfectly revealed, empirical data-driven features are frequently corrupted or noisy at the time of decision-making, leading to fragile operational policies. To bridge this gap, we integrate principles of robust optimization directly into the predictive-prescriptive pipeline via a smart predict-then-robustly optimize loss and establish a computationally tractable convex surrogate, designed to hedge against worst-case feature perturbations. On the theoretical front, we formalize the structural validity of this surrogate by proving its approximation error probability decays exponentially according to a sub-Gaussian concentration profile. Furthermore, we establish that under mild assumptions, the surrogate is Fisher consistent with high probability. We also prove necessary conditions under which our framework outperforms standard smart predict-then-optimize and maintain its superiority even when the standard method is equipped with regularized upstream predictions. Numerical experiments validate that our robust framework consistently yields significant performance improvements over standard methods, both in out-of-sample terms and in training stability.

Aakil Caunhye, Xuefei Lu, Belen Martin-Barragan

Distribution Shift Robustness Predict-Then-Optimize Decision-Focused Learning Robust Optimization Robust Loss Functions Statistical Learning Theory

Jun 29, 2026cs.LG

Decision-Value Attribution in Predict-then-Optimize Systems

Predictive models are increasingly embedded in operational decision-making, yet standard explanation methods typically explain forecasts rather than the decisions those forecasts induce. This distinction is important in predict-then-optimize systems: large forecast changes may leave the optimizer's action unchanged, while small changes can alter the selected decision and its realized value. We propose Decision Value Attribution (DVA), a Shapley-based framework for attributing the value of a fixed prediction--optimization pipeline. The framework defines cooperative games whose payoff is the downstream decision value, allowing the players to be information sources, optimization or design parameters, or both. We present three variants: InfoDVA attributes value to features, DesignDVA attributes value to operational configurations, and Decision-Value Interactions (DVI) quantifies how information and design jointly create value. We further distinguish post-DVA, which evaluates decisions using realized outcomes, from pre-DVA, which evaluates decisions under the model's full prediction. This separation turns attribution into a decision-level diagnostic of whether the model's operational beliefs align with realized performance. The resulting attributions are expressed in the units of the operational objective and decompose the gain or loss relative to a baseline. Case studies in electricity storage arbitrage and emergency medical service coverage show that predictive explanations can be poor proxies for operational value, that DVA can guide targeted information-control interventions, and that optimization configurations determine when predictive information is decision-relevant.

Konstantinos Ziliaskopoulos, Alexander Vinel, Alice E. Smith

Auburn University, Industrial & Systems Engineering, 36849, Auburn, AL, USA · University of Alabama, Mechanical Engineering & Computer Science, 35487, Tuscaloosa, AL, USA

Feature Attribution Predict-Then-Optimize Shapley Value Attribution

Jun 24, 2026math.OC

Generating Input Distributions for Explaining Portfolio Optimization Pipelines

We propose a predict-optimize-explain framework that uses gradient-based sample generation to interpret various portfolio models by identifying macroeconomic conditions that induce specified portfolio outcomes. Unlike traditional feature-importance methods, this approach directly probes decision pipelines (predictive models coupled with portfolio optimization) by constructing economically meaningful what-if questions. We focus on four such questions: under what macroeconomic conditions a predict-then-optimize pipeline closes or reverses its return gap with a predict-and-optimize pipeline; what conditions lead a pipeline to diversify rather than concentrate its allocation; when a pipeline trained on calm markets overtakes one trained through crises; and what conditions would let a pipeline match a benchmark return. These examples illustrate how our framework uncovers key behavioral differences between various decision pipelines. Beyond these cases, the proposed framework is flexible and can support a wide range of probing questions tailored to specific portfolio objectives. Our findings highlight the value of integrating prediction, optimization, and explanation to produce more robust and transparent portfolio strategies.

Batuhan Ataş, Nurşen Aydın, E. Mehmet Kıral +1

Faculty of Economics and Business, University of Amsterdam, The Netherlands · Warwick Business School, University of Warwick, United Kingdom · RIKEN AIP, Japan

Counterfactual Explanations Predict-Then-Optimize Portfolio Optimization

Jun 19, 2026cs.LG

Decision-Focused Learning: When and Why Traditional Prediction Models Fail

Plugging predictions of unknown parameters into downstream optimization problems, often referred to as the ``predict-then-optimize'' paradigm, has long been a standard approach in decision-making under uncertainty. However, improved predictive accuracy does not, in general, translate into improved decision quality. This disconnect has motivated growing interest in decision-focused learning (DFL) within the operations research community. This tutorial reviews recent developments in DFL and highlights key methodological insights, with a particular focus on stochastic linear programming as the downstream decision-making problem. We discuss why several widely used tools in traditional statistical learning are not directly suited to decision-focused settings and must be rethought, including (i) data collection strategies driven purely by predictive uncertainty and (ii) distributional distance measures such as the Wasserstein distance. We summarize properties of DFL that distinguish it from conventional predictive modeling and provide insights into the development of new decision-focused tools.

Mo Liu

Department of Statistics and Operations Research, University of North Carolina at Chapel Hill

Predict-Then-Optimize Decision-Focused Learning Decision-Making under Uncertainty

Jun 17, 2026stat.ML

A Solver-Free Training Method for Predict-then-Optimize

We propose a scalable method for training prediction (machine learning) models in the predict-then-optimize paradigm, where model outputs serve as coefficients for a subsequent linear optimization task. Directly minimizing the empirical decision regret is intractable for linear programming and combinatorial optimization since the decision mapping is piecewise constant, and the gradients are zero almost everywhere. While existing methods address this by smoothing the differentiation process, they suffer from scalability issues, since a computationally expensive solver call is required for every gradient evaluation. To address this, we propose a decision-focused learning pipeline based on a measure transformation principle, which yields a new surrogate loss that is completely optimization-solver-free during training. We establish theoretical guarantees, including Fisher consistency and excess risk bounds. Empirically, our method achieves decision quality competitive with state-of-the-art methods while reducing training time by orders of magnitude.

Beichen Wan, Mo Liu

Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, NC, USA.

Predict-Then-Optimize Learning to Optimize Decision-Focused Learning

Jun 7, 2026cs.LG

Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition

Decision-focused learning has shown great promise for addressing predict-then-optimize problems, particularly in the presence of under-specified models. However, its practical deployment is often hindered by high computational costs and limited scalability, as it requires solving a constrained optimization problem for each training instance at every iteration. To address these challenges, we propose a novel framework that incorporates Lagrangian decomposition into the decision-focused learning paradigm. Specifically, we introduce a new surrogate objective along with two loss functions for evaluating and training the underlying prediction model. We further propose two variants of our approach, which offer different trade-offs between computational efficiency and solution quality. Our framework can be seamlessly integrated with standard decision-focused learning methods, including Smart Predict-then-Optimize (SPO+) and Implicit Maximum Likelihood Estimation (IMLE). Through experiments on two standard benchmarks, the multi-dimensional knapsack problem and quadratic portfolio optimization, we demonstrate that our approach achieves competitive performance while remaining amenable to parallelization. In particular, it consistently outperforms traditional decision-focused learning methods on large-scale instances, involving up to eight times more variables than those typically considered in related work. The implementation is available at https://github.com/corail-research/DFL-LD.

Stéphane Eilles-Chan Way, Hugo Percot, Quentin Cappart +2

Polytechnique Montréal, Montreal, Canada · Ecole Polytechnique, Palaiseau, France · UCLouvain, Louvain-la-Neuve, Belgium +2

Predict-Then-Optimize Learning to Optimize Combinatorial Optimization Decision-Focused Learning

May 31, 2026cs.LG

Decision-Focused On-Policy Learning for Contextual Linear Optimization with Partial Feedback

Decision-focused learning (DFL) trains predictive models by optimizing downstream decision quality rather than standalone prediction accuracy. For contextual linear optimization, most existing DFL methods assume offline data and full observations of the objective cost vector. We develop an on-policy learning method for sequential contextual linear optimization under partial feedback, generalizing the standard bandit feedback setting. Our method learns a stochastic predict-then-optimize policy that samples a cost-vector prediction from a conditional distribution and solves the resulting downstream linear optimization problem. To update this distributional model, we introduce a two-component hybrid gradient estimator. The first component is a score function estimator, which provides an unbiased but potentially high-variance policy gradient estimate. The second is a decision-focused plug-in component that uses an auxiliary nuisance estimate of the latent cost vector to exploit the downstream optimization structure, becoming more informative as the estimate improves. We prove an O(T^-1/2) bound on the average squared policy-gradient norm, matching the standard non-convex SGD rate. Experiments on top-k selection, shortest path, combinatorial pricing, and a real-data energy-scheduling benchmark show that, under bandit feedback, the hybrid gradient approach achieves lower mean cumulative regret than the contextual-bandit baselines on all four benchmarks and than linear Thompson sampling on three, and that it also works with richer conditional generative cost models. Code is available at https://github.com/Joeyetinghan/on-policy-bandit-dfl.

Wyame Benslimane, Tinghan Ye, Pascal Van Hentenryck +1

Department of Industrial Engineering and Operations Research University of California, Berkeley · H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology

Predict-Then-Optimize Decision-Focused Learning Policy Gradient Methods Contextual Bandits Policy Learning

May 15, 2026cs.GT

Misspecified Estimate-then-Optimize Leads to Supra-Competitive Prices

We study whether simple algorithmic pricing systems can systematically produce collusive-like prices in multi-firm markets. We consider firms that price using a myopic estimate-then-optimize rule: each repeatedly fits a demand model to its own price and sales history and sets the price that maximizes estimated profit. This demand model is misspecified, omitting competitors' prices. We analyze the dynamics of this rule when it is initialized by an exploration phase of independent random prices. We characterize when this pipeline converges to supra-competitive prices above the Nash equilibrium, via a fluid-limit ordinary differential equation analysis. We show that supra-competitive prices arise when firms initially explore within similar price ranges on the same side of the Nash price. Moreover, prices can be substantially above the Nash price; we show that prices can reach monopoly levels under symmetric exploration. Simulations calibrated to a real multifamily rental market confirm that supra-competitive outcomes arise robustly beyond our theoretical assumptions, including under finite horizons, heterogeneous products, and nonlinear logit demand.

Jackie Baek, Vivek F. Farias, Farrell Wu

Stern School of Business, New York University · Massachusetts Institute of Technology

Predict-Then-Optimize Learning to Optimize Algorithmic Collusion Dynamic Pricing

May 12, 2026cs.LG

IGT-OMD: Implicit Gradient Transport for Decision-Focused Learning under Delayed Feedback

Decision-focused learning trains predictive models end-to-end against downstream decision loss, but online settings suffer delayed feedback: outcomes may not arrive for many environment interactions. We identify \emph{staleness amplification}, a failure mode unique to bilevel optimization under delay, in which gradient staleness couples with inner-solver sensitivity to inflate regret beyond single-level delay theory. We prove that any black-box delayed optimizer incurs an irreducible regret cost from inner-solver approximation error, and that gradient staleness contributes a quadratically growing transport error without bilevel-aware correction. Our algorithm, \textbf{IGT-OMD}, applies Implicit Gradient Transport to hypergradients within Online Mirror Descent, re-evaluating stale gradients at the current parameters using stored inner solutions. This method reduces transport error from a quadratic to a linear dependence on delay and achieves the first sublinear regret bound for delayed bilevel optimization with queue-length-adaptive step sizes. Controlled experiments provide a \emph{mechanistic fingerprint}: transport benefit is exactly

0.0\%

(

p=1.00

) at unit delay and grows monotonically to

9.5\%

at fifty rounds (

p<0.001

), isolating the correction's effect. On Linear Quadratic Regulator, Warcraft shortest-path, and Sinkhorn optimal transport, IGT-OMD reduces decision loss by

17

--

55\%

relative to single-level baselines, with phase transitions matching the theory.

Benjamin Amoh, Geoffrey G. Parker, Wesley Marrero

Thayer School of Engineering, Dartmouth College

Predict-Then-Optimize Decision-Focused Learning Online Mirror Descent Bilevel Optimization

May 12, 2026cs.LG

Plan Before You Trade: Inference-Time Optimization for RL Trading Agents

Reinforcement learning agents for portfolio management are typically trained and deployed as static policies, with no mechanism for using price forecasts at inference time. We propose

\text{FPILOT}

(Financial Plugin Inference-time Learning for Optimal Trading), a plugin inference-time optimization framework inspired by Model Predictive Control (MPC). Our key structural insight is that future prices mostly do not depend on one agent's portfolio allocation, so a suitable predictive model can produce a multi-step price trajectory without iterative action-conditioned rollouts as in typical reinforcement learning. At each decision step, we use the forecaster's predicted price trajectory to construct an allocation-based imagined return objective, and optimize the policy at inference-time before executing one step of the trade. Our framework is compatible with any pre-trained agent and adapts the policy to the forecaster's predictions without any retraining. Evaluated across five policy learning algorithms on the TradeMaster DJ30 benchmark,

\text{FPILOT}

produces consistent improvements in total return and return-based risk-adjusted metrics (Sharpe, Sortino, Calmar), with stochastic policies benefiting more than deterministic ones. Further, using synthetic forecasts at calibrated quality levels, we show that gains consistently improve with forecaster quality, suggesting that our performance will improve based on advances in financial forecasting.

Eun Go, Rohan Deb, Arindam Banerjee

Siebel School of Computing and Data Science University of Illinois Urbana-Champaign

Reinforcement Learning Inference-Time Optimization Predict-Then-Optimize Portfolio Optimization Finance Algorithmic Trading

Apr 21, 2026math.OC

Decision-Focused Federated Learning Under Heterogeneous Objectives and Constraints

We consider Decision-Focused Federated Learning (DFFL), a predict-then-optimize setting in which multiple clients collaboratively train predictive models for downstream linear optimization problems without exchanging raw data. Besides the data heterogeneity typical of standard federated learning, clients may also have different objective functions and feasible regions. Building on the SPO+ surrogate loss, we derive heterogeneity bounds that separate objective shift, measured through cost-vector distances, from feasible-set shift, measured through support-function and shape-distance terms. We show that, for general compact feasible sets, small objective perturbations can still induce nonvanishing decision-focused loss discrepancies, while strongly convex feasible regions yield sharper stability-based bounds. We then lift these pointwise bounds to a local-versus-federated excess-risk comparison, showing that federation is beneficial when the statistical advantage of pooling exceeds a client-specific heterogeneity penalty. Computational experiments on polyhedral and strongly convex problems confirm that federation is substantially more robust under strongly convex feasible regions. Finally, we evaluate a simple validation-based interpolation between local and federated DFFL models. This interpolation mitigates the theoretical tradeoff and reduces aggregate regret and worst-client harm in both synthetic experiments and a PJM energy-pricing case study.

Konstantinos Ziliaskopoulos, Alexander Vinel

Auburn University

Predict-Then-Optimize Learning to Optimize Decision-Focused Learning Constrained Optimization Federated Learning Heterogeneous Federated Learning

Apr 13, 2026math.OC

Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management science (OR/MS), which has long provided methodological foundations for sequential decision making under uncertainty. At the same time, deep learning advances, including feedforward neural networks, recurrent architectures, transformers, large language models (LLMs), and deep reinforcement learning, have expanded data-driven modeling for large-scale decisions. This tutorial presents an OR/MS-centered perspective on deep learning for sequential decision making under uncertainty, bridging neural architectures and OR/MS approaches to decision making. Its premise: deep learning complements optimization rather than replacing it. Deep learning brings adaptability and scalable approximation, whereas OR/MS provides the mathematical rigor to represent constraints, recourse, uncertainty, and decision quality. The tutorial reviews key decision making foundations, connects them to the major neural architectures in modern AI, and organizes the field around three central themes: predict-then-optimize and decision-aware learning, learning-based decision generation under constraints for continuous and discrete problems with temporal coupling, and deep reinforcement learning for sequential and combinatorial decision making. Impact spans supply chains, service systems, healthcare and epidemic response, agriculture, energy, environmental sustainability, and autonomous operations. This tutorial frames these developments as part of a shift from predictive AI toward decision-capable AI, highlighting OR/MS's role in shaping the next generation of integrated learning--optimization systems.

I. Esra Buyuktahtakin

Grado Department of Industrial and Systems Engineering, Virginia Tech Blacksburg, VA 24061, USA

Reinforcement Learning Predict-Then-Optimize Sequential Decision Making Learning to Optimize Decision-Focused Learning Decision-Making under Uncertainty

Sep 2, 2025cs.LG

Simulating Classification Models for Ex-Ante Evaluation of Predict-Then-Optimize Methods

Predict-Then-Optimize combines machine learning predictions with downstream optimization to support decision-making when problem parameters are unknown at the time of solving. However, better predictive performance does not necessarily lead to better decisions, making it useful to assess this relationship before investing in the development of a prediction model. Existing simulation-based approaches enable such ex-ante evaluation, but are limited to binary classification and may require solving the downstream optimization problem many times. We generalize this methodology to optimization problems with categorical uncertain parameters by introducing a method for simulating multiclass predictions at prescribed performance levels and using it to construct a prediction-error-to-decision-regret mapping. To reduce the computational effort required to obtain this mapping, we also propose a first-order approximation based on the regret caused by individual misclassifications. Computational experiments confirm that the proposed prediction simulation algorithm reproduces the target classification performance and that the first-order approximation closely matches the simulation-based error-to-regret mapping for some problems. Its accuracy decreases when interactions between simultaneous misclassifications become more important. These results demonstrate the potential of the proposed approach and identify new questions about when simple approximations of the error-to-regret relationship are sufficiently accurate.

Pieter Smet

KU Leuven, Department of Computer Science, NUMA · Gebroeders De Smetstraat 1, 9000 Gent, Belgium

Predict-Then-Optimize