Predict-Then-Optimize

Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds in simple settings. However, when predictions lack rigorous error bounds (as is typical of modern machine learning methods) classical robust models often yield vacuous guarantees, while regret formulations can paradoxically produce decisions that are more optimistic than even a nominal solution. We introduce Globalized Adversarial Regret Optimization (GARO), a decision framework that controls adversarial regret, defined as the gap between the worst-case cost and the oracle robust cost, uniformly across all possible uncertainty set sizes. By design, GARO delivers absolute or relative performance guarantees against an oracle with full knowledge of the prediction error, without requiring any probabilistic calibration of the uncertainty set. We show that GARO equipped with a relative rate function generalizes the classical adaptation method of Lepski to downstream decision problems. We derive exact tractable reformulations for problems with affine worst-case cost functions and polyhedral norm uncertainty sets, and provide a discretization and a constraint-generation algorithm with convergence guarantees for general settings. Finally, experiments demonstrate that GARO yields solutions with a more favorable trade-off between worst-case and mean out-of-sample performance, as well as stronger global performance guarantees.

Sleep quality is influenced by a complex interplay of behavioral, environmental, and psychosocial factors, yet most computational studies focus mainly on predictive risk identification rather than actionable intervention design. Although machine learning models can accurately predict subjective sleep outcomes, they rarely translate predictive insights into practical intervention strategies. To address this gap, we propose a personalized predictive-prescriptive framework that integrates interpretable machine learning with mixed-integer optimization. A supervised classifier trained on survey data predicts sleep quality, while SHAP-based feature attribution quantifies the influence of modifiable factors. These importance measures are incorporated into a mixed-integer optimization model that identifies minimal and feasible behavioral adjustments, while modelling resistance to change through a penalty mechanism. The framework achieves strong predictive performance, with a test F1-score of 0.9544 and an accuracy of 0.9366. Sensitivity and Pareto analyses reveal a clear trade-off between expected improvement and intervention intensity, with diminishing returns as additional changes are introduced. At the individual level, the model generates concise recommendations, often suggesting one or two high-impact behavioral adjustments and sometimes recommending no change when expected gains are minimal. By integrating prediction, explanation, and constrained optimization, this framework demonstrates how data-driven insights can be translated into structured and personalized decision support for sleep improvement.

Databricks job orchestration systems (e.g., LeJOT) reduce cloud costs by selecting low-priced compute configurations while meeting latency and dependency constraints. Accurate execution-time prediction under heterogeneous instance types and non-stationary runtime conditions is therefore critical. Existing pipelines rely on static, manually engineered features that under-capture runtime effects (e.g., partition pruning, data skew, and shuffle amplification), and predictive signals are scattered across logs, metadata, and job scripts-lengthening update cycles and increasing engineering overhead. We present LeJOT-AutoML, an agent-driven AutoML framework that embeds large language model agents throughout the ML lifecycle. LeJOT-AutoML combines retrieval-augmented generation over a domain knowledge base with a Model Context Protocol toolchain (log parsers, metadata queries, and a read-only SQL sandbox) to analyze job artifacts, synthesize and validate feature-extraction code via safety gates, and train/select predictors. This design materializes runtime-derived features that are difficult to obtain through static analysis alone. On enterprise Databricks workloads, LeJOT-AutoML generates over 200 features and reduces the feature-engineering and evaluation loop from weeks to 20-30 minutes, while maintaining competitive prediction accuracy. Integrated into the LeJOT pipeline, it enables automated continuous model updates and achieves 19.01% cost savings in our deployment setting through improved orchestration.

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.

Estimation error in machine learning prognostic models can propagate into poor maintenance decisions. We study a data-driven predictive maintenance problem coupling health-condition estimation with a joint ordering-replacement model. We show that the conventional Estimate-Then-Optimize (ETO) approach yields inconsistent, suboptimal decisions for a broad class of such problems. To bridge the gap, we propose an Integrated Estimate-Optimize (IEO) framework that directly targets maintenance cost as the prognostic learning objective, bypassing surrogate statistical accuracy metrics such as Kullback--Leibler divergence or mean squared error. Theoretically, we prove out-of-sample performance guarantees of the IEO framework under certain conditions, including i.i.d. and sliding-window data-generating processes. Computationally, we develop a training procedure combining Monte Carlo dropout, central-difference gradient approximation, and an ETO warm-start to handle discrete maintenance decisions and nonlinear costs. Experiments on the four CMAPSS subsets demonstrate that, under the nominal setting, IEO reduces mean maintenance cost by 14.8--22.7% relative to ETO and by 7.2--11.8% relative to a decision-oriented baseline, while also reducing failure rates and cost variation. These improvements are obtained despite higher prediction errors. Increasing the ratio of unplanned-downtime costs to planned-downtime costs makes this tradeoff more pronounced: IEO shifts predictions further toward RUL underestimation, accompanied by greater cost savings and fewer failures. These findings support aligning prognostic learning with maintenance objectives when imperfect predictions must guide decisions under costly unplanned downtime.

Machine learning can help sellers predict buyers' willingness to pay, but its predictions may be plausible and yet entirely unrelated to a buyer's value. We introduce a Bayesian auction model that distinguishes such hallucinations from ordinary measurement noise. We characterize revenue-maximizing auctions with publicly disclosed predictions in the benchmark where informative predictions are exact. For a single buyer, this characterization explains when the seller should follow a prediction and when to hedge against its failure by ignoring it or capping the price. These insights guide the design of simple auctions that account for both hallucinations and measurement noise. Numerical experiments show that the resulting auctions achieve near-optimal revenue.