Restless bandits with imperfect binary feedback: PCL-indexability analysis and computation
This paper studies restless bandits with binary latent states and imperfect binary feedback, motivated by opportunistic spectrum access with sensing errors. The authors develop a partial conservation laws (PCL)-based analytical and computational framework for establishing indexability and computing the Whittle index. Using deterministic skeleton, renewal decompositions, and combinatorics on words, they obtain tractable expressions in several threshold regimes, fully verifying PCL-indexability. For the remaining regime, efficient numerical schemes are derived for computing the marginal productivity index. Experiments show that the MP index policy typically outperforms standard benchmarks.
[2606.11192] Restless bandits with imperfect binary feedback: PCL-indexability analysis and computation
[Submitted on 27 Mar 2026]
Title:Restless bandits with imperfect binary feedback: PCL-indexability analysis and computation
View a PDF of the paper titled Restless bandits with imperfect binary feedback: PCL-indexability analysis and computation, by Jos\'e Ni\~no-Mora
View PDF HTML (experimental)
Abstract:We study restless bandits with binary latent states and imperfect binary feedback, motivated by opportunistic spectrum access with sensing errors. For the associated belief-state model, we develop a partial conservation laws (PCL)-based analytical and computational framework for establishing indexability and evaluating the Whittle index, building on a verification theorem for real-state discounted restless bandits. The framework analyzes the stochastic dynamics via an associated deterministic skeleton, renewal decompositions, and combinatorics on words. It yields tractable expressions for discounted reward and resource metrics in several threshold regimes, enabling full verification of the PCL-indexability conditions there. For the remaining regime, where a complete analytic verification is not achieved in this paper, we derive efficient numerical schemes for computing the relevant marginal metrics and the marginal productivity (MP) index, which equals the Whittle index when those conditions hold. Extensive computational experiments provide strong evidence that these conditions also hold in that regime across broad parameter ranges and without the stringent parameter restrictions imposed in prior work. The experiments further show that theMP index policy typically outperforms standard benchmark policies, often by a substantial margin.
Comments: 59 pages, 12 figures, submitted 27/3/2026
Subjects:
Machine Learning (cs.LG); Optimization and Control (math.OC)
MSC classes: 90B36 (Primary) 90C40, 90B15 (Secondary)
Cite as: arXiv:2606.11192 [cs.LG]
(or arXiv:2606.11192v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.11192
arXiv-issued DOI via DataCite
Submission history
From: José Niño-Mora [view email] [v1] Fri, 27 Mar 2026 17:34:37 UTC (1,867 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Restless bandits with imperfect binary feedback: PCL-indexability analysis and computation, by Jos\'e Ni\~no-Mora
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-06
Change to browse by:
cs math math.OC
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender (What is IArxiv?)
Author
Venue
Institution
Topic
About arXivLabs
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?)