Individual Professional Practice in the Company

Bakalářská práce popisuje absolvování odborné praxe ve společnosti ISSA CZECH s. r. o. Má odborná praxe byla zaměřena na vývoj webových stránek a informačních systémů. V práci si dávám za cíl seznámit čtenáře s jednotlivými projekty, řešením a také s technologiemi, které jsem k projektům použil. Zmíním se také o mých zkušenostech a vědomostech, které jsem za celou praxi získal.The Bachelor’s thesis describes the completion of professional practice at the ISSA CZECH Company. My professional practice was focused on front-end web development and development of information systems. My main goal is to introduce reader with projects, its solution and technologies used in the projects. I will also mention my experience and knowledge, which I gained during whole practice.460 - Katedra informatikyvýborn

Simple Complexity Analysis of Simplified Direct Search

We consider the problem of unconstrained minimization of a smooth function in the derivative-free setting using. In particular, we propose and study a simplified variant of the direct search method (of direction type), which we call simplified direct search (SDS). Unlike standard direct search methods, which depend on a large number of parameters that need to be tuned, SDS depends on a single scalar parameter only. Despite relevant research activity in direct search methods spanning several decades, complexity guarantees---bounds on the number of function evaluations needed to find an approximate solution---were not established until very recently. In this paper we give a surprisingly brief and unified analysis of SDS for nonconvex, convex and strongly convex functions. We match the existing complexity results for direct search in their dependence on the problem dimension ($n$) and error tolerance ($\epsilon$), but the overall bounds are simpler, easier to interpret, and have better dependence on other problem parameters. In particular, we show that for the set of directions formed by the standard coordinate vectors and their negatives, the number of function evaluations needed to find an $\epsilon$-solution is $O(n^2 /\epsilon)$ (resp. $O(n^2 \log(1/\epsilon))$) for the problem of minimizing a convex (resp. strongly convex) smooth function. In the nonconvex smooth case, the bound is $O(n^2/\epsilon^2)$, with the goal being the reduction of the norm of the gradient below $\epsilon$.Comment: 21 pages, 5 algorithms, 1 tabl

Randomized Distributed Mean Estimation: Accuracy vs Communication

We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any statistical assumptions about the source of the vectors. This problem arises as a subproblem in many applications, including reduce-all operations within algorithms for distributed and federated optimization and learning. We propose a flexible family of randomized algorithms exploring the trade-off between expected communication cost and estimation error. Our family contains the full-communication and zero-error method on one extreme, and an $\epsilon$-bit communication and ${\cal O}\left(1/(\epsilon n)\right)$ error method on the opposite extreme. In the special case where we communicate, in expectation, a single bit per coordinate of each vector, we improve upon existing results by obtaining $\mathcal{O}(r/n)$ error, where $r$ is the number of bits used to represent a floating point value.Comment: 19 pages, 1 figur