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We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We show that two classes of Maximum Mean Discrepancy (MMD) based tests attain this optimality on Rd, while the quadratictime Kernel Stein Discrepancy (KSD) based tests achieve the maximum exponential decay rate under a relaxed level constraint. Under the same performance metric, we proceed to show that the quadratic-time MMD based two-sample tests are also optimal for general two-sample problems, provided that kernels are bounded continuous and characteristic. Key to our approach are Sanov’s theorem from large deviation theory and the weak metrizable properties of the MMD and KSD. 

Cellular network performance depends heavily on the configuration of its network parameters. Current practice of parameter configuration relies largely on expert experience, which is often suboptimal, time-consuming, and error-prone. Therefore, it is desirable to automate this process to improve the accuracy and efficiency via learning-based approaches. However, such approaches need to address several challenges in real operational networks: the lack of diverse historical data, a limited amount of experiment budget set by network operators, and highly complex and unknown network performance functions. To address those challenges, we propose a collaborative learning approach to leverage data from different cells to boost the learning efficiency and to improve network performance. Specifically, we formulate the problem as a transferable contextual bandit problem, and prove that by transfer learning, one could significantly reduce the regret bound. Based on the theoretical result, we further develop a practical algorithm that decomposes a cell’s policy into a common homogeneous policy learned using all cells’ data and a cell-specific policy that captures each individual cell’s heterogeneous behavior. We evaluate our proposed algorithm via a simulator constructed using real network data and demonstrates faster convergence compared to baselines. More importantly, a live field test is also conducted on a real metropolitan cellular network consisting 1700+ cells to optimize five parameters for two weeks. Our proposed algorithm shows a significant performance improvement of 20%. 

Cellular network configuration is critical for network performance. Current practice is labor-intensive, errorprone, and far from optimal. To automate efficient cellular network configuration, in this work, we propose an onlinelearning-based joint-optimization approach that addresses a few specific challenges: limited data availability, convoluted sample data, highly complex optimization due to interactions among neighboring cells, and the need to adapt to network dynamics. In our approach, to learn an appropriate utility function for a cell, we develop a neural-network-based model that addresses the convoluted sample data issue and achieves good accuracy based on data aggregation. Based on the utility function learned, we formulate a global network configuration optimization problem. To solve this high-dimensional nonconcave maximization problem, we design a Gibbs-sampling-based algorithm that converges to an optimal solution when a technical parameter is small enough. Furthermore, we design an online scheme that updates the learned utility function and solves the corresponding maximization problem efficiently to adapt to network dynamics. To illustrate the idea, we use the case study of pilot power configuration. Numerical results illustrate the effectiveness of the proposed approach. 

Cellular network configuration is critical for network performance. Current practice is labor-intensive, errorprone, and far from optimal. To automate efficient cellular network configuration, in this work, we propose an onlinelearning-based joint-optimization approach that addresses a few specific challenges: limited data availability, convoluted sample data, highly complex optimization due to interactions among neighboring cells, and the need to adapt to network dynamics. In our approach, to learn an appropriate utility function for a cell, we develop a neural-network-based model that addresses the convoluted sample data issue and achieves good accuracy based on data aggregation. Based on the utility function learned, we formulate a global network configuration optimization problem. To solve this high-dimensional nonconcave maximization problem, we design a Gibbs-samplingbased algorithm that converges to an optimal solution when a technical parameter is small enough. Furthermore, we design an online scheme that updates the learned utility function and solves the corresponding maximization problem efficiently to adapt to network dynamics. To illustrate the idea, we use the case study of pilot power configuration. Numerical results illustrate the effectiveness of the proposed approach.