31,087 research outputs found
Approximating the Held-Karp Bound for Metric TSP in Nearly Linear Time
We give a nearly linear time randomized approximation scheme for the
Held-Karp bound [Held and Karp, 1970] for metric TSP. Formally, given an
undirected edge-weighted graph on edges and , the
algorithm outputs in time, with high probability, a
-approximation to the Held-Karp bound on the metric TSP instance
induced by the shortest path metric on . The algorithm can also be used to
output a corresponding solution to the Subtour Elimination LP. We substantially
improve upon the running time achieved previously
by Garg and Khandekar. The LP solution can be used to obtain a fast randomized
-approximation for metric TSP which improves
upon the running time of previous implementations of Christofides' algorithm
Distributed Tree Kernels
In this paper, we propose the distributed tree kernels (DTK) as a novel
method to reduce time and space complexity of tree kernels. Using a linear
complexity algorithm to compute vectors for trees, we embed feature spaces of
tree fragments in low-dimensional spaces where the kernel computation is
directly done with dot product. We show that DTKs are faster, correlate with
tree kernels, and obtain a statistically similar performance in two natural
language processing tasks.Comment: ICML201
Feature Reinforcement Learning: Part I: Unstructured MDPs
General-purpose, intelligent, learning agents cycle through sequences of
observations, actions, and rewards that are complex, uncertain, unknown, and
non-Markovian. On the other hand, reinforcement learning is well-developed for
small finite state Markov decision processes (MDPs). Up to now, extracting the
right state representations out of bare observations, that is, reducing the
general agent setup to the MDP framework, is an art that involves significant
effort by designers. The primary goal of this work is to automate the reduction
process and thereby significantly expand the scope of many existing
reinforcement learning algorithms and the agents that employ them. Before we
can think of mechanizing this search for suitable MDPs, we need a formal
objective criterion. The main contribution of this article is to develop such a
criterion. I also integrate the various parts into one learning algorithm.
Extensions to more realistic dynamic Bayesian networks are developed in Part
II. The role of POMDPs is also considered there.Comment: 24 LaTeX pages, 5 diagram
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