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We consider a connection-level model proposed by Massoulié and Roberts for bandwidth sharing among file transfer flows in a communication network. We study weighted proportionally fair sharing policies and establish explicit-form bounds on the weighted sum of the expected numbers of flows on different routes in heavy traffic. The bounds are linear in the number of critically loaded links in the network, and they hold for a class of phase-type file-size distributions; that is, the bounds are heavy-traffic insensitive to the distributions in this class. Our approach is Lyapunov drift based, which is different from the widely used diffusion approximation approach. A key technique we develop is to construct a novel inner product in the state space, which then allows us to obtain a multiplicative type of state-space collapse in steady state. Furthermore, this state-space collapse result implies the interchange of limits as a byproduct for the diffusion approximation of the unweighted proportionally fair sharing policy under phase-type file-size distributions, demonstrating the heavy-traffic insensitivity of the stationary distribution. 

Recent years have witnessed the superior performance of heterogeneous graph neural networks (HGNNs) in dealing with heterogeneous information networks (HINs). Nonetheless, the success of HGNNs often depends on the availability of sufficient labeled training data, which can be very expensive to obtain in real scenarios. Active learning provides an effective solution to tackle the data scarcity challenge. For the vast majority of the existing work regarding active learning on graphs, they mainly focus on homogeneous graphs, and thus fall in short or even become inapplicable on HINs. In this paper, we study the active learning problem with HGNNs and propose a novel meta-reinforced active learning framework MetRA. Previous reinforced active learning algorithms train the policy network on labeled source graphs and directly transfer the policy to the target graph without any adaptation. To better exploit the information from the target graph in the adaptation phase, we propose a novel policy transfer algorithm based on meta-Q-learning termed per-step MQL. Empirical evaluations on HINs demonstrate the effectiveness of our proposed framework. The improvement over the best baseline is up to 7% in Micro-F1. 

This paper presents a model-free reinforcement learning (RL) algorithm for infinite-horizon average-reward Constrained Markov Decision Processes (CMDPs). Considering a learning horizon K, which is sufficiently large, the proposed algorithm achieves sublinear regret and zero constraint violation. The bounds depend on the number of states S, the number of actions A, and two constants which are independent of the learning horizon K.