[2206.04547v2] Value Iteration is Optic Composition
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Category Theory

arXiv:2206.04547v2 (math)
[Submitted on 9 Jun 2022 (v1), last revised 31 Jul 2023 (this version, v2)]

Title:Value Iteration is Optic Composition

Authors:Jules Hedges (University of Strathclyde), Riu Rodríguez Sakamoto (University of Strathclyde)
View PDF
Abstract:Dynamic programming is a class of algorithms used to compute optimal control policies for Markov decision processes. Dynamic programming is ubiquitous in control theory, and is also the foundation of reinforcement learning. In this paper, we show that value improvement, one of the main steps of dynamic programming, can be naturally seen as composition in a category of optics, and intuitively, the optimal value function is the limit of a chain of optic compositions. We illustrate this with three classic examples: the gridworld, the inverted pendulum and the savings problem. This is a first step towards a complete account of reinforcement learning in terms of parametrised optics.
Comments: In Proceedings ACT 2022, arXiv:2307.15519
Subjects: Category Theory (math.CT); Optimization and Control (math.OC)
Cite as: arXiv:2206.04547 [math.CT]
  (or arXiv:2206.04547v2 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2206.04547
Journal reference: EPTCS 380, 2023, pp. 417-432
Related DOI: https://doi.org/10.4204/EPTCS.380.24

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Thu, 9 Jun 2022 14:52:07 UTC (35 KB)
[v2] Mon, 31 Jul 2023 10:32:59 UTC (28 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.CT
< prev   |   next >
new | recent | 2022-06
Change to browse by:
math
math.OC

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)