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Tag: math.OC

  • Infinitesimal Operator World Models: Finite-Sample Guarantees for Offline Reinforcement Learning

    Infinitesimal Operator World Models: Finite-Sample Guarantees for Offline Reinforcement Learning

    [Submitted on 13 Nov 2025 (v1), last revised 9 Oct 2026 (this version, v2)]

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    Abstract:Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline reinforcement learning from historical data. However, there is limited statistical understanding of the approximation errors inherent in learning policies from offline datasets. We address this by linking reinforcement learning to the Hamilton-Jacobi-Bellman equation and proposing an operator-theoretic algorithm based on a simple dynamic programming recursion. Specifically, we represent our world model in terms of the infinitesimal generator of controlled diffusion processes learned in a reproducing kernel Hilbert space. By integrating statistical learning methods and operator theory, we establish global convergence of the value function under sufficiently small generator-approximation error and derive explicit finite-sample guarantees with bounds tied directly to system properties such as smoothness and stability. Our theoretical and proof-of-concept results indicate that operator-based approaches may hold promise for solving offline reinforcement learning using continuous-time optimal control.

    Submission history

    From: Nicolas Hoischen [view email]
    [v1] Thu, 13 Nov 2025 14:58:30 UTC (1,427 KB)
    [v2] Fri, 9 Oct 2026 13:08:08 UTC (2,717 KB)

  • Bayesian dynamic scheduling of multipurpose batch processes under incomplete look-ahead information

    Bayesian dynamic scheduling of multipurpose batch processes under incomplete look-ahead information

    [Submitted on 30 Nov 2025 (v1), last revised 9 Oct 2026 (this version, v2)]

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    Abstract:Multipurpose batch processes become increasingly popular in manufacturing industries since they adapt to low-volume, high-value products and shifting demands. These processes often operate in a dynamic environment, which faces disturbances such as processing delays and demand changes. To minimise long-term cost and system nervousness (i.e., disruptive changes to schedules), schedulers must design rescheduling strategies to address such disturbances effectively. Existing methods often assume complete look-ahead information over the scheduling horizon. This assumption contrasts with realistic situations where schedulers can only access incomplete look-ahead information. Sticking with existing methods may lead to suboptimal long-term costs and high-level system nervousness. In this work we propose a Bayesian dynamic scheduling method. Our method relies on learning a Bayesian Network from the probability distribution of disturbances. Specifically, the Bayesian Network represents how likely each operation will be impacted by disturbances. During the online execution, when new disturbances become observed, this method updates the posterior distribution and therefore guides the rescheduling strategy. We compare our method with the existing periodic rescheduling strategy (which generates new schedules from scratch at fixed intervals) on four benchmark problems. Computational results show that our method achieves statistically better long-term costs and system nervousness. In the theoretical aspect, we prove that if disturbances are mutually independent, the impact-quantifying variables inherently satisfy the independence assumptions required by Bayesian Networks. As an implication, practitioners can extend the method to other scheduling problems (such as job shop scheduling and continuous processes), given that they define the problem-specific dependencies between operations.

    Submission history

    From: Taicheng Zheng [view email]
    [v1] Sun, 30 Nov 2025 21:27:52 UTC (1,350 KB)
    [v2] Fri, 9 Oct 2026 09:42:06 UTC (2,695 KB)

  • Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models

    Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models

    [Submitted on 7 May 2026 (v1), last revised 8 Oct 2026 (this version, v2)]

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    Abstract:We propose a Constrained Triple-Head Price Optimization (C3PO) network for real-time bi-level decision making in discrete-choice environments. In these settings, a seller selects product or service offerings to achieve business objectives, while heterogeneous users make personalized acceptance or rejection decisions based on their preferences, ultimately determining seller outcomes. Existing approaches that fine-tune pre-trained tabular foundation models on synthetic data are limited by their imitation-learning paradigm and inability to enforce common pricing rules, including cross-product and global constraints. C3PO addresses these limitations through a novel transformer-based architecture that jointly integrates price imitation learning, multi-task revenue prediction, and in-context elasticity learning to generate robust pricing recommendations across domains without retraining. A lightweight differentiable constraint layer enables generated prices to satisfy business constraints while optimizing the revenue objective. We demonstrate strong out-of-distribution performance on simulated, synthetic, and real-world datasets. Across simulated benchmarks where the calibrated MNL model is misspecified relative to the ground-truth choice model, C3PO improves expected revenue by 1.4 to 7.9 percentage points over a calibrated MNL baseline. The constraint layer reduces average absolute constraint violations by more than 50%. We further deploy the model in real-world applications, including healthcare tender pricing and airline ancillary pricing, where C3PO improves directional pricing effectiveness, measured by price-increase and price-decrease recall, by 18–34 percentage points depending on the baselines considered, including calibrated MNL, classical optimization, and off-the-shelf tabular foundation-models.

    Submission history

    From: Yingdong Lu [view email]
    [v1] Thu, 7 May 2026 20:55:47 UTC (1,034 KB)
    [v2] Thu, 8 Oct 2026 18:22:06 UTC (1,047 KB)