125,459 research outputs found
Optimal extension to Sobolev rough paths
We show that every -valued Sobolev path with regularity
and integrability can be lifted to a Sobolev rough path in the
sense of T. Lyons provided . Moreover, we prove the existence of
unique rough path lifts which are optimal w.r.t. strictly convex functionals
among all possible rough path lifts given a Sobolev path. As examples, we
consider the rough path lift with minimal Sobolev norm and characterize the
Stratonovich rough path lift of a Brownian motion as optimal lift w.r.t. to a
suitable convex functional. Generalizations of the results to Besov spaces are
briefly discussed.Comment: Typos fixed. To appear in Potential Analysi
Sample Efficient Optimization for Learning Controllers for Bipedal Locomotion
Learning policies for bipedal locomotion can be difficult, as experiments are
expensive and simulation does not usually transfer well to hardware. To counter
this, we need al- gorithms that are sample efficient and inherently safe.
Bayesian Optimization is a powerful sample-efficient tool for optimizing
non-convex black-box functions. However, its performance can degrade in higher
dimensions. We develop a distance metric for bipedal locomotion that enhances
the sample-efficiency of Bayesian Optimization and use it to train a 16
dimensional neuromuscular model for planar walking. This distance metric
reflects some basic gait features of healthy walking and helps us quickly
eliminate a majority of unstable controllers. With our approach we can learn
policies for walking in less than 100 trials for a range of challenging
settings. In simulation, we show results on two different costs and on various
terrains including rough ground and ramps, sloping upwards and downwards. We
also perturb our models with unknown inertial disturbances analogous with
differences between simulation and hardware. These results are promising, as
they indicate that this method can potentially be used to learn control
policies on hardware.Comment: To appear in International Conference on Humanoid Robots (Humanoids
'2016), IEEE-RAS. (Rika Antonova and Akshara Rai contributed equally
Algorithmic Complexity in Cosmology and Quantum Gravity
In this article we use the idea of algorithmic complexity (AC) to study
various cosmological scenarios, and as a means of quantizing the gravitational
interaction. We look at 5D and 7D cosmological models where the Universe begins
as a higher dimensional Planck size spacetime which fluctuates between
Euclidean and Lorentzian signatures. These fluctuations are governed by the AC
of the two different signatures. At some point a transition to a 4D Lorentzian
signature Universe occurs, with the extra dimensions becoming ``frozen'' or
non-dynamical. We also apply the idea of algorithmic complexity to study
composite wormholes, the entropy of blackholes, and the path integral for
quantum gravity.Comment: 15 page
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