1,721,503 research outputs found
Optimization techniques for large scale finite sum problems
Full text linkWith the explosion of machine learning and artificial intelligence applications, the need for optimization methods specialized in the training of such models has been steadily growing for the last 10-20 years. Indeed, given the big data regime and the special structure of the optimization problems to be solved in these settings, a number of new, efficient optimization methods have been developed. A large amount of these new methods strongly rely on the finite sum structure of the objective function to be minimized, where the indices i=1,...,N often refer to the availability of N input-output pairs on which the model should be trained, i.e. the training set. Nevertheless, this is not the only application where a finite sum structure of the objective function appears. Indeed, beyond the training of Neural Networks (NN) and Support Vector Machines (SVM), which depend by definition on a dataset of input-output pairs, a finite sum structure can also be recognized in Reinforcement Learning (RL) applications, due to the need of estimating expected values by sample approximation. In all these cases, N is usually huge, in the order of millions, or even billions, therefore making the exact computation of the function and gradient infeasible for many real life applications. This is one of the reasons why the field has seen a flourishing of publications from the most diverse communities, beyond the operations research one, for example the dynamical control, computer science, stochastic optimization ones. Many new methods have been developed by these communities, both deterministic and stochastic algorithms, although their comparison is made difficult by the different approaches coming from the different communities the new algorithms belong to. Due to the above considerations, the focus of this dissertation is on how to solve optimization problems where the function is structured as a finite sum of component functions. In this finite sum setting, a function fi can be referred to as a component function, and its gradient Ñfi as a component gradient. In particular, a deep investigation of the algorithms developed so far to solve such problems is carried on, with a specific interest in showing the similarities and differences of the convergence analysis when it is developed in the deterministic vs stochastic cases. The target of the investigation is the case when the component gradients are continuously differentiable, and easily computable, like in many machine learning settings (e.g., neural networks training). In this framework, dynamic minibatching schemes are addressed. These are employed to determine the size of the sample to be used during the optimization process, especially in gradient-based methods, when the gradient is estimated by subsampling the component gradients, namely, when it is estimated based on a subset of the indices 1,...,N. The aim of dynamic minibatching schemes is to dynamically test the quality of the gradient approximation, and consequently suggest if the sample size should grow or not. A new technique is proposed, based on statistical analysis of the gradient estimates. The new technique is based on the well-known Analysis of Variance (ANOVA) test, and the convergence of a subsampled gradient-based method is proved when such technique is employed. Numerical experiments are reported on standard machine learning tasks, like (nonlinear) regression and binary classification. Then, the derivative free setting is explored, i.e. the setting where the component functions come from a black-box-like process and the component gradients are not directly available. An example of such setting is policy optimization for reinforcement learning, where only sample approximations of the stochastic reward function are available. Therefore, in literature, Derivative Free Optimization (DFO) methods have been applied to solve this problem, in particular by trying to estimate the gradient by computing only sample approximations of the function. An analysis of the convergence guaran4 tees of stochastic optimization methods in this setting is performed, showing that approximating the gradient by only computing sample-based estimates of the function brings a further approximation error, leading to poorer theoretical results. The special case of policy optimization for reinforcement learning is analysed, showing that such application is even harder, since the sample approximation of the function, in general, does not have continuity guarantees. Finally, a new class of distributed algorithms is introduced to solve linearly constrained, convex problems, with potential application to the dual formulation of the support vector machines training problem. This employs augmented Lagrangian and primal-dual theory to develop a simple, distributable and parallelizable class of algorithms to solve convex problems with simple bound and hard (i.e. coupling all the variables), linear constraints. Such class of algorithms is of particular interest for training support vector machines, since it allows to fully distribute the data, i.e. the input-output pairs, to the available parallel processes, simplifying the (often infeasible) storage of such large amount of data
On sharply vertex-transitive 2-factorizations of the complete graph
No full textWe introduce the concept of a 2-starter in a group G of odd order. We prove that any 2-factorization of the complete graph admitting G as a sharply vertex transitive automorphism group is equivalent to a suitable 2-starter in G. Some classes of 2-starters are studied, with special attention given to those leading to solutions of some Oberwolfach or Hamilton–Waterloo problems
Formulazioni epossidiche per la riparazione delle fessure in manufatti di calcestruzzo
No full textSi riportano i risultati relativi all' utilizzo di diverse formulazioni epossidiche per il rivestimento e la riparazione di calcestruzzi di varie classi di resistenza e composizione. Per l' indurimento a temperatura ambiente della resina epossidica è stato impiegato un indurente poliamminico modificato. Le formulazioni utilizzate presentano buone caratteristiche di permeabilità al vapor d' acqua, un basso valore di viscosità e caratteristiche meccaniche e di adesione al calcestruzzo compatibili con le caratteristiche richieste dalla normativa europea EN 1504
A non-existence result on cyclic cycle decompositions of the cocktail party graph
No full textWe prove that in every cyclic cycle-decomposition of (the cocktail party graph of order 2n) the number of cycle-orbits of odd length must have the same parity of n(n − 1)/2. This gives, as corollaries, some useful non-existence results one of which allows to determine when the two table Oberwolfach Problem OP(3,2l) admits a 1-rotational solution
Problemi di qualità delle acque dei laghi Albano e di Nemi
No full textVengono riportati i risultati di una campagna di analisi condotta nel 2003 relativa alla qualità della acque superficiali dei laghi Albano e di Nemi.La determinazione di pH, conducibilità, alcalinità, azoto e fosforo totale rivelano che tali laghi soffrono di uno stato di eccessiva eutrofia e che la riduzione del loro volume è conseguenza di un sovra sfruttamento della falda idrica albana
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
- …
