We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning. Metaphorically, the adaptation allows us to find needles in haystacks in the form of very predictive but rarely seen features. Our paradigm stems from recent advances in stochastic optimization and online learning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. We give several efficient algorithms for empirical risk minimization problems with common and important regularization functions and domain constraints. We experimentally study our theoretical analysis and show that adaptive subgradient methods outperform state-of-the-art, yet non-adaptive, subgradient algorithms.

Adaptive Subgradient Methods for Online Learning and Stochastic Optimization.

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Adaptive Subgradient Methods for Online Learning and Stochastic Optimization

https://sci2s.ugr.es/sites/default/files/files/Teaching/GraduatesCourses/Metaheuristicas/Bibliography/VNS.pdf

Variable neighborhood search

Variable Neighborhood Search.

Network function virtualization (NFV) has drawn significant attention from both industry and academia as an important shift in telecommunication service provisioning. By decoupling network functions (NFs) from the physical devices on which they run, NFV has the potential to lead to significant reductions in operating expenses (OPEX) and capital expenses (CAPEX) and facilitate the deployment of new services with increased agility and faster time-to-value. The NFV paradigm is still in its infancy and there is a large spectrum of opportunities for the research community to develop new architectures, systems and applications, and to evaluate alternatives and trade-offs in developing technologies for its successful deployment. In this paper, after discussing NFV and its relationship with complementary fields of software defined networking (SDN) and cloud computing, we survey the state-of-the-art in NFV, and identify promising research directions in this area. We also overview key NFV projects, standardization efforts, early implementations, use cases, and commercial products.

/pdf/network-function-virtualization-state-of-the-art-and-29gg3feprt.pdf

Network Function Virtualization: State-of-the-Art and Research Challenges

When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become significantly easier to solve The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property We show that Monge-array results for two sum-of-edge-costs shortest-path problems can likewise be extended to a general algebraic setting, provided the problems' ordered commutative semigroup satisfies one additional restriction In addition to this general result, we also show how our algorithms can be modified to solve certain bottleneck shortestpath problems, even though the ordered commutative semigroup naturally associated with bottleneck problems does not satisfy our additional restriction We show how our bottleneck shortest-path techniques can be used to obtain fast algorithms for a variant of Hirschberg and Larmore's optimal paragraph formation problem, and a special case of the bottleneck traveling-salesman problem

Fast Algorithms with Algebraic Monge Properties

Meggido [1974] showed that the maximum flow through sets of sources in a multiple sink flow network is a polymatroidal function. Recently, Federgruen and Groenevelt [1985], [1986] have considered polymatroids that can be represented by a multiple source flow network and have improved the runnung time of an important scheduling application. We give a characterization of network representability and relate representable polymatroids to the theory of gammoids.

Peter Brucker

Papers

Fast Algorithms with Algebraic Monge Properties

A characterization of network representable polymatroids