IDEAS home Printed from https://ideas.repec.org/p/iik/wpaper/556.html
   My bibliography  Save this paper

A Note on Generalized Second Order Value Iteration in Markov Decision Processes

Author

Listed:
  • V Anthony Vijesh

    (Indian Institute of Technology Indore)

  • Shreyas S R

    (Indian Institute of Management Kozhikode)

  • Mohammed Shahid Abdulla

    (Indian Institute of Management Kozhikode)

Abstract

Value iteration is one of the first-order algorithms to approximate the solution of the Bellman equation arising from the Markov Decision Process (MDP). In recent literature, by approximating the max operator in the Bellman equation by a smooth function, an interesting second-order iterative method was discussed to solve the new Bellman equation. During the numerical simulation, it was observed that this second-order method is computationally expensive for a reasonable size of state and action. This second-order iterative method also faces difficulty in numerical implementation due to the calculation of an exponential function for larger values. In this manuscript, a few first-order iterative schemes have been derived from the second-order method to overcome the above practical problems. All the proposed iterative schemes possess the global convergence property. The proposed iterative schemes take less time to converge to the solution of the Bellman equation than the secondorder method in many cases. These algorithms are efficient and easy to implement. An interesting theoretical comparison is provided between the algorithms. Numerical simulation supports our theoretical results.

Suggested Citation

  • V Anthony Vijesh & Shreyas S R & Mohammed Shahid Abdulla, 2023. "A Note on Generalized Second Order Value Iteration in Markov Decision Processes," Working papers 556, Indian Institute of Management Kozhikode.
  • Handle: RePEc:iik:wpaper:556
    as

    Download full text from publisher

    File URL: https://iimk.ac.in/uploads/publications/IIMKWPS565ITS202304.pdf
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:iik:wpaper:556. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sudheesh Kumar (email available below). General contact details of provider: https://edirc.repec.org/data/iikmmin.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.