# Learning Optimal Admission Control in Partially Observable Queueing Networks

arXiv: https://arxiv.org/abs/2308.02391 · HTML: https://mlsanity.com/paper/2308.02391/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 4 Aug 2023.

## Builds on (most cited first, 11 of 11)

- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximation](https://mlsanity.com/paper/1806.02450/) (2018)
- [Model-free Reinforcement Learning in Infinite-horizon Average-reward Markov Decision Processes](https://mlsanity.com/paper/1910.07072/) (2019)
- [Efficient Bias-Span-Constrained Exploration-Exploitation in Reinforcement Learning](https://mlsanity.com/paper/1802.04020/) (2018)
- [Sample-Efficient Reinforcement Learning of Undercomplete POMDPs](https://mlsanity.com/paper/2006.12484/) (2020)
- [Learning Unknown Markov Decision Processes: A Thompson Sampling Approach](https://mlsanity.com/paper/1709.04570/) (2017)
- [Reinforcement Learning of POMDPs using Spectral Methods](https://mlsanity.com/paper/1602.07764/) (2016)
- [A PAC RL Algorithm for Episodic POMDPs](https://mlsanity.com/paper/1605.08062/) (2016)
- [Near-optimal Optimistic Reinforcement Learning using Empirical Bernstein Inequalities](https://mlsanity.com/paper/1905.12425/) (2019)
- [Reinforcement Learning in a Birth and Death Process: Breaking the Dependence on the State Space](https://mlsanity.com/paper/2302.10667/) (2023)

## Abstract (arXiv)

We present an efficient reinforcement learning algorithm that learns the optimal admission control policy in a partially observable queueing network. Specifically, only the arrival and departure times from the network are observable, and optimality refers to the average holding/rejection cost in infinite horizon. While reinforcement learning in Partially Observable Markov Decision Processes (POMDP) is prohibitively expensive in general, we show that our algorithm has a regret that only depends sub-linearly on the maximal number of jobs in the network, S. In particular, in contrast with existing regret analyses, our regret bound does not depend on the diameter of the underlying Markov Decision Process (MDP), which in most queueing systems is at least exponential in S. The novelty of our approach is to leverage Norton's equivalent theorem for closed product-form queueing networks and an efficient reinforcement learning algorithm for MDPs with the structure of birth-and-death processes.