Decision-Focused Learning

Learning to Defer (L2D) enables a model to predict autonomously or defer to an expert, but prior work largely assumes flat label spaces. We study the first L2D setting with hierarchical multi-label decisions, motivated by medical-imaging workflows in which findings are organised by clinical taxonomies. In this setting, deferral is a delegation action rather than a label assignment, so treating it as an independent per-label decision can produce deferral incoherence, including taxonomic contradictions, delegation violations, and deferrals of labels already implied by the model's own assertions. We formalise coherent hierarchical deferral under a Selective-Exclusion handoff contract, characterise the Bayes-optimal coherent deferral rule, and show that even nodewise Bayes L2D can be action-incoherent. We then propose two remedies: exact coherent projection, a dynamic-programming decoder over the coherent action set, and Taxonomic Belief Propagation (TBP) with Recursive Policy Optimisation (RPO), a contract-aware joint action model trained through the same recursion used at inference. Across real-reader and controlled-expert medical-imaging benchmarks, naive binary-relevance L2D exhibits non-trivial incoherence. Projection removes it exactly, and fast TBP+RPO drives incoherence near zero while retaining strong utility.

Decision-Focused Learning (DFL) trains predictors to improve downstream decision quality, but computing regret gradients typically requires differentiating through solvers or relying on surrogate losses, which can be computationally expensive or deviate from the true objective. We show that, under standard regularity with locally stable active constraints, the regret gradient admits a closed-form geometric characterization, equivalent to the prediction error projected onto the tangent space of active constraints, scaled by local curvature. This reveals that regret gradients can be obtained by filtering decision-irrelevant components from the MSE gradient, providing a simpler and more direct alternative to existing approaches. Based on this, we propose PEAR (Projected Error As Regret-gradient), which computes regret gradients via a reduced linear system over active constraints, avoiding differentiation through solver iterations or additional optimization solves. Experiments on LP benchmarks and a real-world QP task show that PEAR achieves the best decision quality among all baselines while being the most computationally efficient, with gains that persist under constraint shifts.

Machine learning models for medical image analysis often exhibit subgroup-dependent performance, which impacts how decisions should be allocated between automated systems and human experts under limited resources. Prior work on AI fairness and human-AI cooperation, including learning to defer (L2D) and learning to complement (L2C), typically addresses these problems in isolation. We propose People-Centred Medical Image Analysis (PecMan), a framework for fairness-aware human-AI co-operative classification that jointly models subgroup-dependent reliability, decision allocation, and collaborative prediction. PecMan combines subgroup-specialised predictors with a gating and consolidation mechanism that dynamically assigns cases to automated models, human experts, or their combination, without requiring sensitive attributes at test time. We also introduce the FairHAI benchmark for evaluating trade-offs between predictive accuracy, subgroup equity, and human involvement. In addition, we provide a theoretical analysis of multi-agent gating via selection regret and characterise fairness-coverage trade-offs under input-dependent allocation. Experiments across multiple medical imaging datasets demonstrate that PecMan achieves consistently improved trade-offs compared to methods that address fairness or human-AI cooperation separately.

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.

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.

Learning-to-defer (L2D) lets a predictor decide, at each round, whether to issue its own forecast or pay for an expert's. In non-stationary time series this decision must keep adapting, although deployment reveals only the consulted expert's forecast while a historical archive records every expert with the target. L2D-SLDS learns from this archive a switching state-space model of the target and all expert forecasts, whose shared and expert-specific states describe how experts move together and apart. Its predictive law supplies the internal forecast and the expected cost of every consultation, which a greedy router minimizes, and one consultation also updates the beliefs about unconsulted and unavailable experts. We prove sublinear regret against a changing conditional-risk oracle without exploration, when the candidate models are accurate and either the archive separates them or live feedback reveals cost differences. On three real datasets, L2D-SLDS has the lowest cost among eight bandit routers and adapts its consultation rate to the fee.

Multi-period portfolio optimization is important for real portfolio management, as it accounts for transaction costs, path-dependent risks, and the intertemporal structure of trading decisions that single-period models cannot capture. Classical methods usually follow a two-stage framework: machine learning algorithms are employed to produce forecasts that closely fit the realized returns, and the predicted values are then used in a downstream portfolio optimization problem to determine the asset weights. This separation leads to a fundamental misalignment between predictions and decision outcomes, while also ignoring the impact of transaction costs. To bridge this gap, recent studies have proposed the idea of end-to-end learning, integrating the two stages into a single pipeline. This paper introduces IPMO (Integrated Prediction and Multi-period Portfolio Optimization), a model for multi-period mean-variance portfolio optimization with turnover penalties. The predictor generates multi-period return forecasts that parameterize a differentiable convex optimization layer, which in turn drives learning via portfolio performance. For scalability, we introduce a mirror-descent fixed-point (MDFP) differentiation scheme that avoids factorizing the Karush-Kuhn-Tucker (KKT) systems, which thus yields stable implicit gradients and nearly scale-insensitive runtime as the decision horizon grows. In experiments with real market data and two representative time-series prediction models, the IPMO method consistently outperforms the two-stage benchmarks in risk-adjusted performance net of transaction costs and achieves more coherent allocation paths. Our results show that integrating machine learning prediction with optimization in the multi-period setting improves financial outcomes and remains computationally tractable.

When solving optimization problems under uncertainty with contextual data, utilizing machine learning to predict the uncertain parameters' values is a popular and effective approach. Decision-focused learning (DFL) aims at learning a predictive model such that decision quality, instead of prediction accuracy, is maximized. Common practice is to predict a single scenario representing the uncertain parameters, implicitly assuming that there exists a deterministic problem approximation (proxy) that allows for optimal decision-making. The opposite has also been considered, where the underlying distribution is estimated with a parameterized distribution. However, little is known about when either choice is valid. This paper investigates for the first time problem properties that justify using a certain decision proxy. Using this, we present alternative decision proxies for DFL, with little or no compromise on the complexity of the learning task. We show the effectiveness of presented approaches in experiments on continuous and discrete problems, as well as problems with uncertainty in the objective function and in the constraints.