Dynamic Programming

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Overview

Dynamic programming uses Bellman recurrences to break a large sequential decision or optimization problem into smaller subproblems whose solutions can be reused. Exact methods—including memoization, state-space pruning, constraint propagation, and memory-saving algorithms such as Hirschberg’s—are used in scheduling, clustering, speech alignment, and control; approximate methods use neural value functions, sampling, or Monte Carlo tree search for larger problems. Researchers evaluate these approaches on settings such as stochastic control, dynamic pricing, combinatorial benchmarks, and long speech sequences. A central tension is preserving solution quality and guarantees while controlling the time, memory, and state-space costs that can make exact methods impractical.

Latest papers

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31 papers1 paper in the last four weeks, down 67% on the four weeks before. 0.0% of all new papers.

  1. Bellman Error Minimization Via Linear Programming Normalization

    Oct 2, 2026Haining YuFunction Approximation in RLDynamic Programming

    Independent Consultant

  2. Scaffold-Constrained Subset Dynamic Programming for Exact SSE Clustering

    Sep 24, 2026Yordan P. Raykov, Max A. LittleClusteringDynamic Programming

    School of Mathematical Sciences, University of Nottingham · School of Computer Science, University of Birmingham

  3. Scaling Forced Alignment to End-User Devices

    Sep 17, 2026Lawry Sorenson, Michael Crandall, Eric K. Ringger +1Forced AlignmentAudio-Text Alignment

    Brigham Young University Computer Science Department Provo, UT, United States

  4. Scaling Optimal Classification Trees via Adaptive Feature and Sample Reduction

    Sep 5, 2026Jiancheng Tu, Wenqi FanDecision Tree LearningDynamic Programming

    Department of Computing, The Hong Kong Polytechnic University · Department of Management and Marketing, The Hong Kong Polytechnic University

  5. On the Representational Geometry of Dynamic Programs

    Aug 25, 2026Richard F. M. Lim, Ruriko YoshidaDynamic ProgrammingRepresentation Geometry

    Departments of Mathematics and Computer Science, Bowdoin College, Brunswick, Maine · Department of Operations Research, Naval Postgraduate School, Monterey, California · Department of Mathematical Sciences, Aalborg University, Denmark

  6. Memory-Efficient Activation Checkpointing with Sliding Window and Hirschberg's Algorithm for 0/1 Knapsack Solving in PyTorch

    Aug 9, 2026Jędrzej MaczanDynamic ProgrammingMemory-Efficient Optimization

    Cohere Labs Community Poland

  7. Recycling computational processes of dynamic programming for combinatorial optimization problems: a reservoir computing approach

    Jul 25, 2026Sora Todaka, Akihiro Yamamoto, Nozomi AkashiAutomated Algorithm DiscoveryDynamic Programming

    Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto, Japan. · Institute for Liberal Arts and Sciences, Kyoto University, Sakyo-ku, Kyoto, Japan.

  8. Long-Term Sequential Decision Making under Risk

    Jul 22, 2026Irmaan, Mirzanejad, Nadjet Bourdache +1Markov Decision ProcessesDynamic Programming

    Mohammad · Université de Caen Normandie, ENSICAEN, CNRS, Normandie Univ, GREYC UMR 6072, France

  9. Generalised Bellman recurrence and three dualities in sequential decision-making

    Jul 20, 2026Fernando E. Rosas, David Hyland, Daniel PolaniMarkov Decision ProcessesSequential Decision Making

    Department of Informatics, University of Sussex · Department of Computer Science, University of Oxford · Department of Computer Science, University of Hertfordshire

  10. Deep Learning for Dynamic Programming with Recursive Utility

    Jul 5, 2026Xianhua Peng, Wu GuoStochastic Optimal ControlDynamic Programming

    HSBC Business School, Peking University, University Town, Nanshan District, Shenzhen, 518055, China.

  11. Parallel Dynamic Programming for Conic Linear Quadratic Control

    Jun 23, 2026Luyao Zhang, Gabriel Bravo-Palacios, Brian Plancher +1Dynamic ProgrammingFeedback Control

    Delft Center for Systems and Control, TU Delft, The Netherlands · Barnard College, Columbia University, New York, NY 10027 USA · & Dartmouth College, Hanover, NH 03755, USA

  12. FOSC-X: An Extended Framework for Optimal Local Cuts and Non-Horizontal Cluster Selection from Clustering Hierarchies

    Jun 17, 2026Connor Simpson, Ricardo J. G. B. CampelloDynamic ProgrammingClustering

    Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark.

  13. Multilingual Word-Level Forced Alignment with Self-Supervised Representations and Learned Dynamic Programming

    Jun 9, 2026Roy Weber, Meidan Zehavi, Rotem Rousso +1Dynamic Programming

    Faculty of Electrical and Computer Engineering, Technion – Israel Institute of Technology, Haifa, 3200003, Israel

  14. A Dynamic Programming Framework for Discovering Count and Values of Multilevel Image Thresholding

    May 26, 2026Eslam Hegazy, Mohamed GabrDynamic Programming

    Computer Science and Engineering Department German University in Cairo, New Cairo, 11865, Cairo, Egypt

  15. Time Segmented Beamforming via Dynamic Programming: Theory and Implementation

    May 24, 2026Manan Mittal, Ryan M. Corey, Diego Cuji +2Dynamic ProgrammingNon-Stationary Time Series

    Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY 11794 USA · Department of Electrical and Computer Engineering, University of Illinois, Chicago, IL 60607 USA · Department of Electrical and Computer Engineering, University of Massachusetts Dartmouth, Dartmouth, MA 02747 USA +1

  16. CP or DP? Why Not Both: A Case Study in the Partial Shop Scheduling Problem

    May 22, 2026Emma Legrand, Roger Kameugne, Pierre SchausDynamic ProgrammingCombinatorial Optimization

    ICTEAM, UCLouvain, Belgium

  17. Efficient Banzhaf-Based Data Valuation for kk-Nearest Neighbors Classification

    May 20, 2026Guangyi Zhang, Lutz Oettershagen, Lixu Wang +1Dynamic ProgrammingData Valuation

    Shenzhen Technology University Shenzhen, China · University of Liverpool Liverpool, United Kingdom · Nanyang Technological University Singapore +1

  18. Towards Distillation Guarantees under Algorithmic Alignment for Combinatorial Optimization

    May 19, 2026Thien Le, Melanie WeberDynamic ProgrammingCombinatorial Optimization

    SEAS, Harvard University · Cambridge, MA

  19. Adaptive Multi-Round Allocation with Stochastic Arrivals

    May 12, 2026Yuqi Pan, Davin Choo, Haichuan Wang +3Stochastic OptimizationSequential Decision Making

    Harvard University · University of Witwatersrand · Wits Health Consortium +1

  20. Online Segmented Beamforming via Dynamic Programming

    May 8, 2026Manan Mittal, Ryan M. Corey, Diego Cuji +2Dynamic ProgrammingCovariance Estimation

    Stony Brook University1 · University of Illinois Chicago2 · University of Massachusetts Darthmouth3

  21. A Comparative Study of Dynamic Programming and Reinforcement Learning in Finite Horizon Dynamic Pricing

    Apr 15, 2026Lev Razumovskiy, Nikolay KareninDynamic PricingReinforcement Learning

  22. Leveraging the Value of Information in POMDP Planning

    Apr 1, 2026Zakariya Laouar, Qi Heng Ho, Zachary SunbergPartially Observable Markov Decision ProcessesBelief-Space Planning

    Department of Aerospace Engineering Sciences, University of Colorado Boulder · Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Tech

  23. Domain-Independent Dynamic Programming with Constraint Propagation

    Mar 17, 2026Imko Marijnissen, J. Christopher Beck, Emir Demirović +1Resource-Constrained Project SchedulingConstraint Propagation

    Delft University of Technology, The Netherlands · University of Toronto, Canada · National Institute of Informatics, Japan +1

  24. Weakly Time-Coupled Approximation of Markov Decision Processes

    Mar 13, 2026Negar Soheili, Selvaprabu Nadarajah, Bo YangMarkov Decision ProcessesSequential Decision Making

    Information and Decision Sciences Department, University of Illinois at Chicago, Chicago, IL, 60607 · Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR

  25. Relating Reinforcement Learning to Dynamic Programming-Based Planning

    Mar 8, 2026Filip V. Georgiev, Kalle G. Timperi, Başak Sakçak +1Markov Decision ProcessesDynamic Programming

    Center for Applied Computing, Faculty of Information Technology and Electrical Engineering, University of Oulu, Finland · Dept. of Advanced Computing Sciences, Maastricht University, the Netherlands

  26. Automating the Analysis and Improvement of Dynamic Programming Algorithms with Applications to Natural Language Processing

    Feb 20, 2026Tim VieiraDynamic ProgrammingAutomated Algorithm Discovery

    The Johns Hopkins University

  27. Poincaré Meets Bellman: Revisable Memory, Operational Quotients, and Evidence-Supported Learning in Changing Environments

    Nov 28, 2025Xin LiMarkov Decision ProcessesDynamic Programming

    Department of Computer Science University at Albany

  28. Column Generation with Domain-Independent Dynamic Programming

    Oct 16, 2025Ryo Kuroiwa, Edward LamDynamic ProgrammingCombinatorial Optimization

    Department of Data Science and Artificial Intelligence, Monash University, Melbourne, Australia · The Graduate University for Advanced Studies, SOKENDAI, Kanagawa, Japan

  29. Unbiased Binning for Fairness-aware Attribute Representation

    Sep 26, 2025Abolfazl Asudeh, Zeinab Asoodeh, Bita Asoodeh +1Dynamic ProgrammingAlgorithmic Fairness

    University of Illinois Chicago · Independent Researcher · University of Edinburgh +1

  30. Instance Generation for Patient-to-room Assignment and Admission Scheduling Based on Real Hospital Data

    Jul 4, 2025Tabea Brandt, Christina Büsing, Johanna Leweke +2HealthcareDynamic Programming

    Chair of Combinatorial Optimization, RWTH Aachen University, Im Süsterfeld 9, 52072 Aachen, Germany · Chair of Algorithms and Complexity, RWTH Aachen University, Ahornstraße 55, 52074 Aachen, Germany