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.

[Q]: The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. A key advantage of the method is that it avoids projections the computational bottleneck in many applications replacing it by a linear optimization step. Despite this advantage, the known convergence rates of the FW method fall behind standard first order methods for most settings of interest. It is an active line of research to derive faster linear optimization-based algorithms for various settings of convex optimization. In this paper we consider the special case of optimization over strongly convex sets, for which we prove that the vanila FW method converges at a rate of 1 t2 . This gives a quadratic improvement in convergence rate compared to the general case, in which convergence is of the order 1t , and known to be tight. We show that various balls induced by `p norms, Schatten norms and group norms are strongly convex on one hand and on the other hand, linear optimization over these sets is straightforward and admits a closed-form solution. We further show how several previous fastrate results for the FW method follow easily from our analysis.
[A]: Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets


[Q]: This paper presents generalized probabilistic models for high-order projective dependency parsing and an algorithmic framework for learning these statistical models involving dependency trees. Partition functions and marginals for high-order dependency trees can be computed efficiently, by adapting our algorithms which extend the inside-outside algorithm to higher-order cases. To show the effectiveness of our algorithms, we perform experiments on three languages— English, Chinese and Czech, using maximum conditional likelihood estimation for model training and L-BFGS for parameter estimation. Our methods achieve competitive performance for English, and outperform all previously reported dependency parsers for Chinese and Czech.
[A]: Probabilistic Models for High-Order Projective Dependency Parsing


[Q]: We study a novel architecture and training procedure for locomotion tasks. A high-frequency, low-level “spinal” network with access to proprioceptive sensors learns sensorimotor primitives by training on simple tasks. This pre-trained module is fixed and connected to a low-frequency, high-level “cortical” network, with access to all sensors, which drives behavior by modulating the inputs to the spinal network. Where a monolithic end-to-end architecture fails completely, learning with a pre-trained spinal module succeeds at multiple high-level tasks, and enables the effective exploration required to learn from sparse rewards. We test our proposed architecture on three simulated bodies: a 16-dimensional swimming snake, a 20-dimensional quadruped, and a 54-dimensional humanoid (see attached video).
[A]:
Learning and Transfer of Modulated Locomotor Controllers