arXiv subjects

Junji Yan

Publications and source records attributed to Junji Yan.

3 recordsLinked to original sources

arXiv2026

Horizon-Independent Contraction for Continuous-Time Discounted Regularized Mean-Field Games

We study contraction properties of non-stationary continuous-time mean-field games (MFGs) under discounting and entropy regularization. The state of the representative agent evolves according to a controlled continuous-time Markov chain, and both the state and action spaces are finite. In contrast to the undiscounted case, we show that, under a sufficiently large discount rate, finite-horizon MFGs admit a horizon-independent contraction condition, which also coincides with the corresponding infinite-horizon non-stationary contraction condition. As a byproduct, we obtain an explicit convergence rate between finite- and infinite-horizon mean-field equilibria. For each finite horizon, we further derive a refined contraction criterion from the spectral radius of a positive operator that majorizes the propagation of policy errors, and show that its large-horizon limit agrees with the horizon-independent contraction factor. Finally, we provide an explicit error bound between discounted and undiscounted finite-horizon regularized equilibria.

cs.GT↗

arXiv2026

A Stackelberg Game Framework with Drainability Guardrails for Pricing and Scaling in Multi-Tenant GPU Cloud Platforms

Modern Graphics Processing Unit (GPU)-backed services must satisfy strict latency service-level objectives (SLOs) while controlling spare-capacity costs. In multi-tenant GPU cloud platforms, this trade-off is inherently dynamic because workload demand is endogenous; specifically, pricing shapes the submissions of heterogeneous tenants, which subsequently impact congestion and delay. We formulate the joint pricing-and-scaling problem as a large-population Stackelberg game problem, and we derive an explicit equilibrium demand map. The resulting closed-loop model reveals a structural failure mode in which delay-insensitive workloads sustain a residual demand floor, making the backlog undrainable under bounded price and service capacity. This observation motivates a computable drainability guardrail that certifies uniformly negative backlog drift in the residual-demand regime. For any fixed price-capacity pair satisfying the drainability guardrail, we establish global convergence to a unique operating point under a checkable step-size condition. Building on this fixed-pair analysis, we further develop an optimizer-agnostic action shield that provides a negative-drift certificate for shielded execution in the residual regime of the dynamic problem and show empirically that it improves safety and robustness for model-free reinforcement learning (RL) in this setting.

cs.GT↗

arXiv2022

Graphon Mean-Field Control for Cooperative Multi-Agent Reinforcement Learning

The marriage between mean-field theory and reinforcement learning has shown a great capacity to solve large-scale control problems with homogeneous agents. To break the homogeneity restriction of mean-field theory, a recent interest is to introduce graphon theory to the mean-field paradigm. In this paper, we propose a graphon mean-field control (GMFC) framework to approximate cooperative multi-agent reinforcement learning (MARL) with nonuniform interactions and show that the approximate order is of $\mathcal{O}(\frac{1}{\sqrt{N}})$, with $N$ the number of agents. By discretizing the graphon index of GMFC, we further introduce a smaller class of GMFC called block GMFC, which is shown to well approximate cooperative MARL. Our empirical studies on several examples demonstrate that our GMFC approach is comparable with the state-of-art MARL algorithms while enjoying better scalability.

cs.MA↗