Surrogate-based Autotuning for Randomized Sketching Algorithms in Regression Problems

Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different than those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP) based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 4x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

Channel Knowledge Map (CKM)-Assisted Multi-UAV Wireless Network: CKM Construction and UAV Placement

Channel knowledge map (CKM) has recently emerged to facilitate the placement and trajectory optimization for unmanned aerial vehicle (UAV) communications. This paper investigates a CKM-assisted multi-UAV wireless network, by focusing on the construction and utilization of CKMs for multi-UAV placement optimization. First, we consider the CKM construction problem when data measurements for only a limited number of points are available. Towards this end, we exploit a data-driven interpolation technique to construct CKMs to characterize the signal propagation environments. Next, we study the multi-UAV placement optimization problem by utilizing the constructed CKMs, in which the multiple UAVs aim to optimize their placement locations to maximize the weighted sum rate with their respectively associated ground base stations (GBSs). However, the rate function based on the CKMs is generally non-differentiable. To tackle this issue, we propose a novel iterative algorithm based on derivative-free optimization, in which a series of quadratic functions are iteratively constructed to approximate the objective function under a set of interpolation conditions, and accordingly, the UAVs' placement locations are updated by maximizing the approximate function subject to a trust region constraint. Finally, numerical results are presented to validate the proposed design achieves near-optimal performance, but with much lower implementation complexity.