The cross entropy (CE) method is a model based search method to solve optimization problems where the objective function has minimal structure. The Monte-Carlo version of the CE method employs the naive sample averaging technique which is inefficient, both computationally and space wise. We provide a novel stochastic approximation version of the CE method, where the sample averaging is replaced...

We consider regularized stochastic learning and online optimization problems, where the objective function is the sum of two convex terms: one is the loss function of the learning task, and the other is a simple regularization term such as l1-norm for promoting sparsity. We develop a new online algorithm, the regularized dual averaging (RDA) method, that can explicitly exploit the regularizatio...

A manipulator with free joints is a class of underactuated mechanisms. Control of such systems is one of major topics in robotics and control engineering. In this paper, we apply the averaging method to manipulators connected by free joints and describe their behaviors in response to periodic inputs. We analyze 2R and 3R free-joint manipulators and show that each system has invariant manifolds ...

Acknowledgements: I would like to thank E. Sonnendrücker for the stimulating discussions we had together and from which the problem treated in this paper emerged. Abstract: we show that the solution to an oscillatory-singularly perturbed ordinary differential equation may be asymptotically expanded into a sum of oscillating terms. Each of those terms writes as an oscillating operator acting on ...

We introduce a weighted averaging method for improving the inevitable error induced by theGibbs phenomenon appearing in a spectral approximation for a discontinuous function. In the result we have a family of filters generalizing the well known Fejer filter. In addition, for high resolution recovery, we propose an adaptive filter which is competitive with the existing exponentially convergent a...

In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computational burden placed on the subsequent numerical evaluation. For short-medium t...

In this paper, we address the problem of distributed learning over a decentralized network, arising from scenarios including distributed sensors or geographically separated data centers. We propose a fully distributed algorithm called random walk distributed dual averaging (RW-DDA) that only requires local updates. Our RW-DDA method, improves the existing distributed dual averaging (DDA) method...

In this paper, we address the problem of distributed learning over a large number of distributed sensors or geographically separated data centers, which suffer from sampling biases across nodes. We propose an algorithm called random walk distributed dual averaging (RW-DDA) method that only requires local updates and is fully distributed. Our RW-DDA method is robust to the change in network topo...

This short communication concerns a class of Nash games in which the participants share some of the decision variables. An averaging method is developed in order to transform these games into standard Nash games. This technique is successfully applied to solve an example multileader, single-follower game described by Pang and Fukushima.

in this paper, a novel approach for ranking fuzzy numbers based on the angle measure is introduced. several left and right spreads at each chosen levels of fuzzy numbers is used to determine center of mass points(cmps) and then, the angels between the cmps and the horizontal axis is calculated. the total angle is determined by averaging the computed angles and finally, the novel method is compa...