Graph neural networks (GNN) have recently emerged as a vehicle for applying deep network architectures to graph and relational data. However, given the increasing size of industrial datasets, in many practical situations the message passing computations required for sharing information across GNN layers are no longer scalable. Although various sampling methods have been introduced to approximate full-graph training within a tractable budget, there remain unresolved complications such as high variances and limited theoretical guarantees. To address these issues, we build upon existing work and treat GNN neighbor sampling as a multi-armed bandit problem but with a newly-designed reward function that introduces some degree of bias designed to reduce variance and avoid unstable, possibly-unbounded pay outs. And unlike prior bandit-GNN use cases, the resulting policy leads to near-optimal regret while accounting for the GNN training dynamics introduced by SGD.

GCNGAT Algorithmγη Tγη T Thanos 0.4 0.01 1000 0.4 0.01 1000 BanditSampler 0.4 0.01 N/A 0.4 0.01 N/A Table 5: The detailed sampling hyperparameters for Squirrel.

However, in practice, the environment is typically time-varying and nonstationary .

We consider a general adversarial multi-armed blocking bandit setting where each played arm can be blocked (unavailable) for some time periods and the reward per arm is given at each time period adversarially without obeying any distribution. The setting models scenarios of allocating scarce limited supplies (e.g., arms) where the supplies replenish and can be reused only after certain time periods. We first show that, in the optimization setting, when the blocking durations and rewards are known in advance, finding an optimal policy (e.g., determining which arm per round) that maximises the cumulative reward is strongly NP-hard, eliminating the possibility of a fully polynomial-time approximation scheme (FPTAS) for the problem unless P = NP. To complement our result, we show that a greedy algorithm that plays the best available arm at each round provides an approximation guarantee that depends on the blocking durations and the path variance of the rewards. In the bandit setting, when the blocking durations and rewards are not known, we design two algorithms, RGA and RGA-META, for the case of bounded duration an path variation.

In this work, we propose three efficient restart paradigms for model-free non-stationary reinforcement learning (RL). We identify two core issues with the restart design of Mao et al. (2022)'s RestartQ-UCB algorithm: (1) complete forgetting, where all the information learned about an environment is lost after a restart, and (2) scheduled restarts, in which restarts occur only at predefined timings, regardless of the incompatibility of the policy with the current environment dynamics. We introduce three approaches, which we call partial, adaptive, and selective restarts to modify the algorithms RestartQ-UCB and RANDOMIZEDQ (Wang et al., 2025). We find near-optimal empirical performance in multiple different environments, decreasing dynamic regret by up to $91$% relative to RestartQ-UCB.

However, in practice, the environment is typically time-varying and nonstationary .