Relax and Localize: From Value to Algorithms

We show a principled way of deriving online learning algorithms from a minimax analysis. Various upper bounds on the minimax value, previously thought to be non-constructive, are shown to yield algorithms. This allows us to seamlessly recover known methods and to derive new ones. Our framework also captures such "unorthodox" methods as Follow the Perturbed Leader and the R^2 forecaster. We emphasize that understanding the inherent complexity of the learning problem leads to the development of algorithms. We define local sequential Rademacher complexities and associated algorithms that allow us to obtain faster rates in online learning, similarly to statistical learning theory. Based on these localized complexities we build a general adaptive method that can take advantage of the suboptimality of the observed sequence. We present a number of new algorithms, including a family of randomized methods that use the idea of a "random playout". Several new versions of the Follow-the-Perturbed-Leader algorithms are presented, as well as methods based on the Littlestone's dimension, efficient methods for matrix completion with trace norm, and algorithms for the problems of transductive learning and prediction with static experts

A High-Throughput Solver for Marginalized Graph Kernels on GPU

We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned conjugate gradient (PCG) method to compute the solution to a generalized Laplacian equation associated with the tensor product of two graphs. To cope with the gap between the instruction throughput and the memory bandwidth of current generation GPUs, our solver forms the tensor product linear system on-the-fly without storing it in memory when performing matrix-vector dot product operations in PCG. Such on-the-fly computation is accomplished by using threads in a warp to cooperatively stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. Besides, we propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to improve the efficiency of the sparse format.We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales

A connection-level call admission control using genetic algorithm for MultiClass multimedia services in wireless networks

Call admission control in a wireless cell in a personal communication system (PCS) can be modeled as an M/M/C/C queuing system with m classes of users. Semi-Markov Decision Process (SMDP) can be used to optimize channel utilization with upper bounds on handoff blocking probabilities as Quality of Service constraints. However, this method is too time-consuming and therefore it fails when state space and action space are large. In this paper, we apply a genetic algorithm approach to address the situation when the SMDP approach fails. We code call admission control decisions as binary strings, where a value of “1” in the position i (i=1,…m) of a decision string stands for the decision of accepting a call in class-i; a value of “0” in the position i of the decision string stands for the decision of rejecting a call in class-i. The coded binary strings are feed into the genetic algorithm, and the resulting binary strings are founded to be near optimal call admission control decisions. Simulation results from the genetic algorithm are compared with the optimal solutions obtained from linear programming for the SMDP approach. The results reveal that the genetic algorithm approximates the optimal approach very well with less complexity

Parallelizing RRT on distributed-memory architectures

This paper addresses the problem of improving the performance of the Rapidly-exploring Random Tree (RRT) algorithm by parallelizing it. For scalability reasons we do so on a distributed-memory architecture, using the message-passing paradigm. We present three parallel versions of RRT along with the technicalities involved in their implementation. We also evaluate the algorithms and study how they behave on different motion planning problems