LQG Online Learning

Optimal control theory and machine learning techniques are combined to formulate and solve in closed form an optimal control formulation of online learning from supervised examples with regularization of the updates. 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 proposed algorithm is less sensitive to outliers with respect to the Kalman estimate (thanks to the presence of the regularization term), thus providing smoother estimates with respect to time. 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

Linear Quadratic Gaussian (LQG) online learning

Optimal 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

AIRO 2016. 46th Annual Conference of the Italian Operational Research Society. Emerging Advances in Logistics Systems Trieste, September 6-9, 2016 - Abstracts Book

The AIRO 2016 book of abstract collects the contributions from the conference participants. The AIRO 2016 Conference is a special occasion for the Italian Operations Research community, as AIRO annual conferences turn 46th edition in 2016. To reflect this special occasion, the Programme and Organizing Committee, chaired by Walter Ukovich, prepared a high quality Scientific Programme including the first initiative of AIRO Young, the new AIRO poster section that aims to promote the work of students, PhD students, and Postdocs with an interest in Operations Research. The Scientific Programme of the Conference offers a broad spectrum of contributions covering the variety of OR topics and research areas with an emphasis on “Emerging Advances in Logistics Systems”. The event aims at stimulating integration of existing methods and systems, fostering communication amongst different research groups, and laying the foundations for OR integrated research projects in the next decade. Distinct thematic sections follow the AIRO 2016 days starting by initial presentation of the objectives and features of the Conference. In addition three invited internationally known speakers will present Plenary Lectures, by Gianni Di Pillo, Frédéric Semet e Stefan Nickel, gathering AIRO 2016 participants together to offer key presentations on the latest advances and developments in OR’s research