Gauss quadrature for matrix inverse forms with applications

We present a framework for accelerating a spectrum of machine learning algorithms that require computation of bilinear inverse forms u[superscript T] A[superscript −1]u, where A is a positive definite matrix and u a given vector. Our framework is built on Gauss-type quadrature and easily scales to large, sparse matrices. Further, it allows retrospective computation of lower and upper bounds on u[superscript T] > A[superscript −1]u, which in turn accelerates several algorithms. We prove that these bounds tighten iteratively and converge at a linear (geometric) rate. To our knowledge, ours is the first work to demonstrate these key properties of Gauss-type quadrature, which is a classical and deeply studied topic. We illustrate empirical consequences of our results by using quadrature to accelerate machine learning tasks involving determinantal point processes and submodular optimization, and observe tremendous speedups in several instances.Google (Research Award)National Science Foundation (U.S.) (CAREER Award 1553284

Efficient Serverless Function Scheduling at the Network Edge

Serverless computing is a promising approach for edge computing since its inherent features, e.g., lightweight virtualization, rapid scalability, and economic efficiency. However, previous studies have not studied well the issues of significant cold start latency and highly dynamic workloads in serverless function scheduling, which are exacerbated at the resource-limited network edge. In this paper, we formulate the Serverless Function Scheduling (SFS) problem for resource-limited edge computing, aiming to minimize the average response time. To efficiently solve this intractable scheduling problem, we first consider a simplified offline form of the problem and design a polynomial-time optimal scheduling algorithm based on each function's weight. Furthermore, we propose an Enhanced Shortest Function First (ESFF) algorithm, in which the function weight represents the scheduling urgency. To avoid frequent cold starts, ESFF selectively decides the initialization of new function instances when receiving requests. To deal with dynamic workloads, ESFF judiciously replaces serverless functions based on the function weight at the completion time of requests. Extensive simulations based on real-world serverless request traces are conducted, and the results show that ESFF consistently and substantially outperforms existing baselines under different settings