Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where global objective is to minimize average local cost functions over a multiagent network using only computation and peer-to-peer communication. In this article, we propose novel compressed gradient tracking algorithm (C-GT) that combines technique wit...

We consider the distributed optimization problem where $n$ agents, each possessing a local cost function, collaboratively minimize average of functions over connected network. Assuming stochastic gradient information is available, we study algorithm, called exact diffusion with adaptive stepsizes (EDAS) adapted from Exact Di...

Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual object recognition tasks has been limited because of the prohibitive cost of the optimization algorithms required to compute the sparse representation. In this w...

We present extensions to Trio for incorporating continuous uncertainty into the system. Data items with uncertain possible values drawn from a continuous domain are represented through a generic set of functions. Our approach enables precise and efficient representation of arbitrary probability distribution functions, along with standard distributions such as Gaussians. We also describe how que...

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

Bandit Convex Optimization (BCO) is a fundamental framework for decision making under uncertainty, which generalizes many problems from the realm of online and statistical learning. While the special case of linear cost functions is well understood, a gap on the attainable regret for BCO with nonlinear losses remains an important open question. In this paper we take a step towards understanding...

emph{ Smooth Projective Hash Functions } ( SPHFs ) as a specific pattern of zero knowledge proof system are fundamental tools to build many efficient cryptographic schemes and protocols. As an application of SPHFs, emph { Password - Based Authenticated Key Exchange } ( PAKE ) protocol is well-studied area in the last few years. In 2009, Katz and Vaikuntanathan described the first lattice-based ...