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math.PR2025
On the instability of local learning algorithms: Q-learning can fail in infinite state spaces
Urtzi Ayesta, Sergey Foss, Matthieu Jonckheere +1
We investigate the challenges of applying model-free reinforcement learning algorithms, like online Q-learning, to infinite state space Markov Decision Processes (MDPs). We first i…
math.PR2025
On Recurrence of the Infinite Server Queue
Sergey Foss, Peter Glynn
This paper concerns the recurrence structure of the infinite server queue, as viewed through the prism of the maximum dater sequence, namely the time to drain the current work in t…
math.PR2025
Heavy-tail asymptotics for the length of a busy period in a Generalised Jackson Network
Sergey Foss, Masakiyo Miyazawa, Linglong Yuan
We consider a Generalised Jackson Network with finitely many servers, a renewal input and service times at each queue. We assume the network to be stable and, in addition,…