TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: Fully connected network has been widely used in deep learning, and its computation efficiency is highly benefited from the matrix multiplication algorithm with cuBLAS on GPU. However, We found that, there exist some drawbacks of cuBLAS in calculating matrix A multiplies the transpose of matrix B (i.e., NT operation). To reduce the impact of NT operation by cuBLAS, we exploit the out-of-place transpose of matrix B to avoid using NT operation, and then we apply our method to Caffe, which is a popular deep learning tool. Our contribution is two-fold. First, we propose a naive method (TNN) and model-based method (MTNN) to increase the performance in calculating A B , and it achieves about 4.7 times performance enhancement in our tested cases on GTX1080 card. Second, we integrate MTNN method into Caffe to enhance the efficiency in training fully connected networks, which achieves about 70% speedup compared to the original Caffe in our configured fully connected networks on GTX1080 card.

SOLUTION: Improving the Performance of Fully Connected Neural Networks by Out-of-Place Matrix Transpose

PROBLEM: We propose an efficient technique for multilabel classification based on calibration, a term we use to mean learning a link function that maps independent predictions to joint predictions. Though a naive implementation of our proposal would require training individual classifiers for each label, we show that for natural datasets and linear classifiers we can sidestep this by leveraging techniques from randomized linear algebra. Moreover, our algorithm applies equally well to multiclass classification. The end result is an algorithm that scales to very large multilabel and multiclass problems, and offers state of the art accuracy on many datasets.

SOLUTION: Multilabel Prediction via Calibration

PROBLEM: Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for general-sum stochastic games by Filar and Vrieze [2004]. However, the optimization problem there has a non-linear objective and non-linear constraints with special structure. Since gradients of both the objective as well as constraints of this optimization problem are well defined, gradient based schemes seem to be a natural choice. We discuss a gradient scheme tuned for two-player stochastic games. We show in simulations that this scheme indeed converges to a Nash equilibrium, for a simple terrain exploration problem modelled as a general-sum stochastic game. However, it turns out that only global minima of the optimization problem correspond to Nash equilibria of the underlying general-sum stochastic game, while gradient schemes only guarantee convergence to local minima. We then provide important necessary conditions for gradient schemes to converge to Nash equilibria in general-sum stochastic games.

SOLUTION:
A Study of Gradient Descent Schemes for General-Sum Stochastic Games