2,157 research outputs found
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
Minimum-Information LQG Control - Part I: Memoryless Controllers
With the increased demand for power efficiency in feedback-control systems,
communication is becoming a limiting factor, raising the need to trade off the
external cost that they incur with the capacity of the controller's
communication channels. With a proper design of the channels, this translates
into a sequential rate-distortion problem, where we minimize the rate of
information required for the controller's operation under a constraint on its
external cost. Memoryless controllers are of particular interest both for the
simplicity and frugality of their implementation and as a basis for studying
more complex controllers. In this paper we present the optimality principle for
memoryless linear controllers that utilize minimal information rates to achieve
a guaranteed external-cost level. We also study the interesting and useful
phenomenology of the optimal controller, such as the principled reduction of
its order
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