661 research outputs found
Optimized Algorithms for Prediction within Robotic Tele-Operative Interfaces
Robonaut, the humanoid robot developed at the Dexterous Robotics Laboratory at NASA Johnson Space Center serves as a testbed for human-robot collaboration research and development efforts. One of the primary efforts investigates how adjustable autonomy can provide for a safe and more effective completion of manipulation-based tasks. A predictive algorithm developed in previous work was deployed as part of a software interface that can be used for long-distance tele-operation. In this paper we provide the details of this algorithm, how to improve upon the methods via optimization, and also present viable alternatives to the original algorithmic approach. We show that all of the algorithms presented can be optimized to meet the specifications of the metrics shown as being useful for measuring the performance of the predictive methods. Judicious feature selection also plays a significant role in the conclusions drawn
Exploiting higher order smoothness in derivative-free optimization and continuous bandits
We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order smoothness properties of the function on the optimization error and on the cumulative regret. To solve this problem we consider a randomized approximation of the projected gradient descent algorithm. The gradient is estimated by a randomized procedure involving two function evaluations and a smoothing kernel. We derive upper bounds for this algorithm both in the constrained and unconstrained settings and prove minimax lower bounds for any sequential search method. Our results imply that the zero-order algorithm is nearly optimal in terms of sample complexity and the problem parameters. Based on this algorithm, we also propose an estimator of the minimum value of the function achieving almost sharp oracle behavior. We compare our results with the state-of-the-art, highlighting a number of key improvements
Phase transitions in Ising model induced by weight redistribution on weighted regular networks
In order to investigate the role of the weight in weighted networks, the
collective behavior of the Ising system on weighted regular networks is studied
by numerical simulation. In our model, the coupling strength between spins is
inversely proportional to the corresponding weighted shortest distance.
Disordering link weights can effectively affect the process of phase transition
even though the underlying binary topological structure remains unchanged.
Specifically, based on regular networks with homogeneous weights initially,
randomly disordering link weights will change the critical temperature of phase
transition. The results suggest that the redistribution of link weights may
provide an additional approach to optimize the dynamical behaviors of the
system.Comment: 6 pages, 5 figure
Efficient Rank Reduction of Correlation Matrices
Geometric optimisation algorithms are developed that efficiently find the
nearest low-rank correlation matrix. We show, in numerical tests, that our
methods compare favourably to the existing methods in the literature. The
connection with the Lagrange multiplier method is established, along with an
identification of whether a local minimum is a global minimum. An additional
benefit of the geometric approach is that any weighted norm can be applied. The
problem of finding the nearest low-rank correlation matrix occurs as part of
the calibration of multi-factor interest rate market models to correlation.Comment: First version: 20 pages, 4 figures Second version [changed content]:
21 pages, 6 figure
Minimum Enclosing Circle with Few Extra Variables
Asano et al. [JoCG 2011] proposed an open problem of computing the minimum enclosing circle of a set of n points in R^2 given in a read-only array in sub-quadratic time. We show that Megiddo\u27s prune and search algorithm for computing the minimum radius circle enclosing the given points can be tailored to work in a read-only environment in O(n^{1+epsilon}) time using O(log n) extra space, where epsilon is a positive constant less than 1. As a warm-up, we first solve the same problem in an in-place setup in linear time with O(1) extra space
Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits
We study the problem of zero-order optimization of a strongly convex
function. The goal is to find the minimizer of the function by a sequential
exploration of its values, under measurement noise. We study the impact of
higher order smoothness properties of the function on the optimization error
and on the cumulative regret. To solve this problem we consider a randomized
approximation of the projected gradient descent algorithm. The gradient is
estimated by a randomized procedure involving two function evaluations and a
smoothing kernel. We derive upper bounds for this algorithm both in the
constrained and unconstrained settings and prove minimax lower bounds for any
sequential search method. Our results imply that the zero-order algorithm is
nearly optimal in terms of sample complexity and the problem parameters. Based
on this algorithm, we also propose an estimator of the minimum value of the
function achieving almost sharp oracle behavior. We compare our results with
the state-of-the-art, highlighting a number of key improvements
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