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Linear Quadratic Gaussian (LQG) online learning
No full textOptimal control theory and machine learning techniques are combined to propose and solve in closed form an optimal control formulation of online learning from supervised examples. The connections with the classical Linear Quadratic Gaussian (LQG) optimal control problem, of which the proposed learning paradigm is a non trivial variation as it involves random matrices, are investigated. The obtained optimal solutions are compared with the Kalman-filter estimate of the parameter vector to be learned. It is shown that the former enjoys larger smoothness and robustness to outliers, thanks to the presence of a regularization term. The basic formulation of the proposed online-learning framework refers to a discrete time setting with a finite learning horizon and a linear model. Various extensions are investigated, including the infinite learning horizon and, via the so-called "kernel trick", the case of nonlinear models.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1606.04272 [math.OC]
(or arXiv:1606.04272v2 [math.OC] for this version
On the approximation of the optimal control functions in stochastic optimal control problems
No full textComputation of the Structured Singular Value via Moment LMI Relaxations
No full textThe Structured Singular Value (SSV) provides a powerful tool to test robust stability and performance of feedback systems subject to structured uncertainties. Unfortunately, computing the SSV is an NP-hard problem, and the polynomial-time algorithms available in the literature are only able to provide, except for some special cases, upper and lower bounds on the exact value of the SSV. In this work, we present a new algorithm to compute an upper bound on the SSV in case of mixed real/complex uncertainties. The underlying idea of the developed approach is to formulate the SSV computation as a (nonconvex) polynomial optimization problem, which is relaxed into a sequence of convex optimization problems through moment-based relaxation techniques. Two heuristics to compute a lower bound on the SSV are also discussed. The analyzed numerical examples show that the developed approach provides tighter bounds than the ones computed by the algorithms implemented in the Robust Control Toolbox in Matlab, and it provides, in most of the cases, coincident lower and upper bounds on the structured singular value
Reversibility in the higher-order -calculus
No full textThe notion of reversible computation is attracting increasing interest because of its applications in diverse fields, in particular the study of programming abstractions for reliable systems. In this paper, we continue the study undertaken by Danos and Krivine on reversible CCS by defining a reversible higher-order π -calculus, called rhoπ. We prove that reversibility in our calculus is causally consistent and that the causal information used to support reversibility in rhoπ is consistent with the one used in the causal semantics of the π -calculus developed by Boreale and Sangiorgi. Finally, we show that one can faithfully encode rhoπ into a variant of higher-order π, substantially improving on the result we obtained in the conference version of this paper
When Neuroscience 'Touches' Architecture: From Hapticity to a Supramodal Functioning of the Human Brain.
No full textIn the last decades, the rapid growth of functional brain imaging methodologies allowed cognitive neuroscience to address open questions in philosophy and social sciences. At the same time, novel insights from cognitive neuroscience research have begun to influence various disciplines, leading to a turn to cognition and emotion in the fields of planning and architectural design. Since 2003, the Academy of Neuroscience for Architecture has been supporting 'neuro-architecture' as a way to connect neuroscience and the study of behavioral responses to the built environment. Among the many topics related to multisensory perceptual integration and embodiment, the concept of hapticity was recently introduced, suggesting a pivotal role of tactile perception and haptic imagery in architectural appraisal. Arguments have thus risen in favor of the existence of shared cognitive foundations between hapticity and the supramodal functional architecture of the human brain. Precisely, supramodality refers to the functional feature of defined brain regions to process and represent specific information content in a more abstract way, independently of the sensory modality conveying such information to the brain. Here, we highlight some commonalities and differences between the concepts of hapticity and supramodality according to the distinctive perspectives of architecture and cognitive neuroscience. This comparison and connection between these two different approaches may lead to novel observations in regard to people-environment relationships, and even provide empirical foundations for a renewed evidence-based design theory
Detecting early signs of the 2007–2008 crisis in the world trade
No full textSince 2007, several contributions have tried to identify early-warning signals of the financial crisis. However, the vast majority of analyses has focused on financial systems and little theoretical work has been done on the economic counterpart. In the present paper we fill this gap and employ the theoretical tools of network theory to shed light on the response of world trade to the financial crisis of 2007 and the economic recession of 2008–2009. We have explored the evolution of the bipartite World Trade Web (WTW) across the years 1995–2010, monitoring the behavior of the system both before and after 2007. Our analysis shows early structural changes in the WTW topology: since 2003, the WTW becomes increasingly compatible with the picture of a network where correlations between countries and products are progressively lost. Moreover, the WTW structural modification can be considered as concluded in 2010, after a seemingly stationary phase of three years. We have also refined our analysis by considering specific subsets of countries and products: the most statistically significant early-warning signals are provided by the most volatile macrosectors, especially when measured on developing countries, suggesting the emerging economies as being the most sensitive ones to the global economic cycles
Rotation-Invariant Restricted Boltzmann Machine Using Shared Gradient Filters
No full textFinding suitable features has been an essential problem in computer vision. We focus on Restricted Boltzmann Machines (RBMs), which, despite their versatility, cannot accommodate transformations that may occur in the scene. As a result, several approaches have been proposed that consider a set of transformations, which are used to either augment the training set or transform the actual learned filters. In this paper, we propose the Explicit Rotation-Invariant Restricted Boltzmann Machine, which exploits prior information coming from the dominant orientation of images. Our model extends the standard RBM, by adding a suitable number of weight matrices, associated with each dominant gradient. We show that our approach is able to learn rotation-invariant features, comparing it with the classic formulation of RBM on the MNIST benchmark dataset. Overall, requiring less hidden units, our method learns compact features, which are robust to rotations
Passive control of wave propagation in periodic anti-tetrachiral meta-materials
No full textPeriodic anti-tetrachiral materials are strongly characterized by a marked auxeticity,
the unusual and fascinating mechanical property mathematically expressed by negative values
of the Poisson’s ratio. The auxetic behavior is primarily provided by pervasive rolling-up mechanisms
developed by the doubly-symmetric micro-structure of the periodic cell, composed by a
regular pattern of rigid rings connected by tangent flexible ligaments. Adopting a beam-lattice
model to describe the linear free dynamics of the elementary cell, the planar wave propagation
along the bi-dimensional material domain can be studied according to the Floquet-Bloch
theory. Parametric analyses of the dispersion curves, carried out with numerical or asymptotic
tools, typically reveal a highly-dense spectrum, with persistent absence of total band-gaps in the
low-frequency range. The paper analyses the wave propagation in the meta-material developed
by introducing rigid massive inserts, locally housed by all the rings and working as undamped
linear oscillators with assigned inertia and/or stiffness properties. The elastic coupling between
the cell microstructure and the oscillators, if properly tuned (inertial resonators), is found to
significantly modify the Floquet-Bloch spectrum of the material. The effects of the resonator
parameters (tuning frequency and mass ratio) on the low-frequency band structure of the metamaterial
are discussed, with focus on the valuable possibility to (i) open total band gaps, by
either the widening of an existing partial band gap or the avoidance of a crossing point between
adjacent dispersion curves, (ii) finely control the total band-gap amplification, in order to assess
the maximum achievable performance of the meta-material against the vibration propagatio
The price of complexity in financial networks
No full textFinancial institutions form multilayer networks by engaging in contracts with each other and by holding exposures to common assets. As a result, the default probability of one institution depends on the default probability of all of the other institutions in the network. Here, we show how small errors on the knowledge of the network of contracts can lead to large errors in the probability of systemic defaults. From the point of view of financial regulators, our findings show that the complexity of financial networks may decrease the ability to mitigate systemic risk, and thus it may increase the social cost of financial crises
Central limit theorems for a hypergeometric randomly reinforced urn
No full textWe consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracted balls of a certain color given the past is assumed to be hypergeometric. We prove some central limit theorems in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution. The proven results provide asymptotic confidence intervals for the limit proportion, whose distribution is generally unknown. Moreover, we also consider the case of more urns subjected to some random common factors