619 research outputs found
The Separation Principle in Stochastic Control, Redux
Over the last 50 years a steady stream of accounts have been written on the
separation principle of stochastic control. Even in the context of the
linear-quadratic regulator in continuous time with Gaussian white noise, subtle
difficulties arise, unexpected by many, that are often overlooked. In this
paper we propose a new framework for establishing the separation principle.
This approach takes the viewpoint that stochastic systems are well-defined maps
between sample paths rather than stochastic processes per se and allows us to
extend the separation principle to systems driven by martingales with possible
jumps. While the approach is more in line with "real-life" engineering thinking
where signals travel around the feedback loop, it is unconventional from a
probabilistic point of view in that control laws for which the feedback
equations are satisfied almost surely, and not deterministically for every
sample path, are excluded.Comment: 23 pages, 6 figures, 2nd revision: added references, correction
Optimal Policy with Partial Information in a Forward-Looking Model: Certainty-Equivalence Redux
This paper proves a certainty equivalence result for optimal policy under commitment with symmetric partial information about the state of the economy in a model with forward-looking variables. This result is used in our previous paper, Indicator Variables for Optimal Policy,' which synthesizes what is known about the case of symmetric partial information, and derives useful general formulas for computation of the optimal policy response coefficients and efficient estimates of the state of the economy in the context of a fairly general forward-looking rational-expectations model. In particular, our proof takes into account that, under commitment, the policymaker can affect the future evolution of the observable variables, and thereby potentially affect the future information available.
Steering state statistics with output feedback
Consider a linear stochastic system whose initial state is a random vector
with a specified Gaussian distribution. Such a distribution may represent a
collection of particles abiding by the specified system dynamics. In recent
publications, we have shown that, provided the system is controllable, it is
always possible to steer the state covariance to any specified terminal
Gaussian distribution using state feedback. The purpose of the present work is
to show that, in the case where only partial state observation is available, a
necessary and sufficient condition for being able to steer the system to a
specified terminal Gaussian distribution for the state vector is that the
terminal state covariance be greater (in the positive-definite sense) than the
error covariance of a corresponding Kalman filter.Comment: 10 pages, 2 figure
Optimal control of the state statistics for a linear stochastic system
We consider a variant of the classical linear quadratic Gaussian regulator
(LQG) in which penalties on the endpoint state are replaced by the
specification of the terminal state distribution. The resulting theory
considerably differs from LQG as well as from formulations that bound the
probability of violating state constraints. We develop results for optimal
state-feedback control in the two cases where i) steering of the state
distribution is to take place over a finite window of time with minimum energy,
and ii) the goal is to maintain the state at a stationary distribution over an
infinite horizon with minimum power. For both problems the distribution of
noise and state are Gaussian. In the first case, we show that provided the
system is controllable, the state can be steered to any terminal Gaussian
distribution over any specified finite time-interval. In the second case, we
characterize explicitly the covariance of admissible stationary state
distributions that can be maintained with constant state-feedback control. The
conditions for optimality are expressed in terms of a system of dynamically
coupled Riccati equations in the finite horizon case and in terms of algebraic
conditions for the stationary case. In the case where the noise and control
share identical input channels, the Riccati equations for finite-horizon
steering become homogeneous and can be solved in closed form. The present paper
is largely based on our recent work in arxiv.org/abs/1408.2222,
arxiv.org/abs/1410.3447 and presents an overview of certain key results.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1410.344
The modularity of action and perception revisited using control theory and active inference
The assumption that action and perception can be investigated independently is entrenched in theories, models and experimental approaches across the brain and mind sciences. In cognitive science, this has been a central point of contention between computationalist and 4Es (enactive, embodied, extended and embedded) theories of cognition, with the former embracing the “classical sandwich”, modular, architecture of the mind and the latter actively denying this separation can be made. In this work we suggest that the modular independence of action and perception strongly resonates with the separation principle of control theory and furthermore that this principle provides formal criteria within which to evaluate the implications of the modularity of action and perception. We will also see that real-time feedback with the environment, often considered necessary for the definition of 4Es ideas, is not however a sufficient condition to avoid the “classical sandwich”. Finally, we argue that an emerging framework in the cognitive and brain sciences, active inference, extends ideas derived from control theory to the study of biological systems while disposing of the separation principle, describing non-modular models of behaviour strongly aligned with 4Es theories of cognition
COINSTAC: A Privacy Enabled Model and Prototype for Leveraging and Processing Decentralized Brain Imaging Data
The field of neuroimaging has embraced the need for sharing and collaboration. Data sharing mandates from public funding agencies and major journal publishers have spurred the development of data repositories and neuroinformatics consortia. However, efficient and effective data sharing still faces several hurdles. For example, open data sharing is on the rise but is not suitable for sensitive data that are not easily shared, such as genetics. Current approaches can be cumbersome (such as negotiating multiple data sharing agreements). There are also significant data transfer, organization and computational challenges. Centralized repositories only partially address the issues. We propose a dynamic, decentralized platform for large scale analyses called the Collaborative Informatics and Neuroimaging Suite Toolkit for Anonymous Computation (COINSTAC). The COINSTAC solution can include data missing from central repositories, allows pooling of both open and ``closed'' repositories by developing privacy-preserving versions of widely-used algorithms, and incorporates the tools within an easy-to-use platform enabling distributed computation. We present an initial prototype system which we demonstrate on two multi-site data sets, without aggregating the data. In addition, by iterating across sites, the COINSTAC model enables meta-analytic solutions to converge to ``pooled-data'' solutions (i.e. as if the entire data were in hand). More advanced approaches such as feature generation, matrix factorization models, and preprocessing can be incorporated into such a model. In sum, COINSTAC enables access to the many currently unavailable data sets, a user friendly privacy enabled interface for decentralized analysis, and a powerful solution that complements existing data sharing solutions
Strong experimental guarantees in ultrafast quantum random number generation
We describe a methodology and standard of proof for experimental claims of
quantum random number generation (QRNG), analogous to well-established methods
from precision measurement. For appropriately constructed physical
implementations, lower bounds on the quantum contribution to the average
min-entropy can be derived from measurements on the QRNG output. Given these
bounds, randomness extractors allow generation of nearly perfect
"{\epsilon}-random" bit streams. An analysis of experimental uncertainties then
gives experimentally derived confidence levels on the {\epsilon} randomness of
these sequences. We demonstrate the methodology by application to
phase-diffusion QRNG, driven by spontaneous emission as a trusted randomness
source. All other factors, including classical phase noise, amplitude
fluctuations, digitization errors and correlations due to finite detection
bandwidth, are treated with paranoid caution, i.e., assuming the worst possible
behaviors consistent with observations. A data-constrained numerical
optimization of the distribution of untrusted parameters is used to lower bound
the average min-entropy. Under this paranoid analysis, the QRNG remains
efficient, generating at least 2.3 quantum random bits per symbol with 8-bit
digitization and at least 0.83 quantum random bits per symbol with binary
digitization, at a confidence level of 0.99993. The result demonstrates
ultrafast QRNG with strong experimental guarantees.Comment: 11 pages, 9 figure
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