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Approximate Markovian abstractions for linear stochastic systems
2012
2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
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We derive the exact bound of the approximation error and an explicit expression for its growth over time. ...
In this paper, we present a method to generate a finite Markovian abstraction for a discrete time linear stochastic system evolving in a full dimensional polytope. ...
ACKNOWLEDGEMENTS The authors would like to thank Boyan Yordanov from Microsoft Research, Cambridge, UK for his help with polyhedral operations and refinement algorithms. ...
doi:10.1109/cdc.2012.6426184
dblp:conf/cdc/LahijanianAB12
fatcat:534u4ikrybdandf654bon2frpy
Page 4024 of Mathematical Reviews Vol. , Issue 97F
[page]
1997
Mathematical Reviews
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Daniel (1-WI-E; Madison, W1) A characterization of bounded-input bounded-output stability for linear time-invariant systems with distributional inputs. (English summary) SIAM J. ...
Summary: “We consider linear time-invariant operators defined on the space of distributions with left-bounded support. ...
Moment Propagation of Discrete-Time Stochastic Polynomial Systems using Truncated Carleman Linearization
[article]
2021
arXiv
pre-print
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2019 pre-print arXiv:1911.12683v1 fatcat:lyh5f263lfam7kxwxqmy6qvvim
We provide upper bounds on the approximation error for each moment and show that, for large enough truncation limits, the proposed method precisely computes moments for sufficiently small degrees and numbers ...
We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. ...
to compute even higher moments and more time steps in the future. ...
arXiv:1911.12683v2
fatcat:2k2tuzae4vhz3av76sszjmkana
Balanced Truncation for a Class of Stochastic Jump Linear Systems and Model Reduction for Hidden Markov Models
2008
IEEE Transactions on Automatic Control
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The approximation error, which is captured by means of the stochastic 2 gain, is bounded from above by twice the sum of singular numbers associated to the truncated states, similar to the case of linear ...
Index Terms-Balanced truncation, error bound, finite state machines, hidden Markov models, jump systems, model reduction, reduced order systems, stochastic automata, stochastic hybrid systems, stochastic ...
ACKNOWLEDGMENT The authors would like to thank the reviewers for valuable comments and suggestions and V. Blondel for [14] . ...
doi:10.1109/tac.2008.2006931
fatcat:kxvip3rnxjbplezvx6cs2sgvdy
Error Analysis for the Linear Feedback Particle Filter
[article]
2017
arXiv
pre-print
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It is shown that the error converges to zero even with finite number of particles. The paper also presents propagation of chaos estimates for the finite-N linear filter. ...
In this paper, the equations for empirical mean and covariance are derived for the finite-N linear FPF. ...
We begin by presenting the McKean-Vlasov stochastic differential equation (sde) for the linear FPF algorithm. For these models, the state at time t is denoted as Xt . ...
arXiv:1710.11008v1
fatcat:454fw3di5fcsvdemoh2ngklmum
Finite-Time Error Bounds for Biased Stochastic Approximation with Applications to Q-Learning
2020
International Conference on Artificial Intelligence and Statistics
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The resultant finite-time error bound for Q-learning is the first of its kind, in the sense that it holds: i) for the unmodified version (i.e., without making any modifications to the updates), and ii) ...
For direct comparison with past works, we also demonstrate these bounds by applying them to Qlearning with linear function approximation, under the realistic Markov chain observation model. ...
Hence, our finite-time error bound in Thm. 2 also holds for Q-learning with linear approximation. ...
dblp:conf/aistats/WangG20a
fatcat:khgtq2rwhrhppfywqkl2jc4ewm
Moment Propagation Through Carleman Linearization with Application to Probabilistic Safety Analysis
[article]
2022
arXiv
pre-print
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We provide efficient online computation methods for this propagation scheme with several error bounds for the approximation. ...
We then truncate this deterministic system to obtain a finite-dimensional linear system, and use it for moment approximation by iteratively propagating the moments along the finite-dimensional linear dynamics ...
Moment approximations for stochastic logistic map.
1 Fig. 4. Error bound on moment approximations. ...
arXiv:2201.08648v1
fatcat:d2smmzabkzag7lanzcww4huuba
Finite-Time Error Bounds For Linear Stochastic Approximation and TD Learning
[article]
2019
arXiv
pre-print
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We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm ...
As a by-product of our analysis, we also solve the open problem of obtaining finite-time bounds for the performance of temporal difference learning algorithms with linear function approximation and a constant ...
FINITE-TIME ERROR BOUNDS FOR LINEAR STOCHASTIC APPROXIMATION AND TD LEARNING
Appendix E. ...
arXiv:1902.00923v3
fatcat:uqupnpuqq5gorluylrpjakepse
State-Based Confidence Bounds for Data-Driven Stochastic Reachability Using Hilbert Space Embeddings
[article]
2021
arXiv
pre-print
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In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. ...
We present finite sample bounds for point-based approximations of the safety probabilities through construction of probabilistic confidence bounds that are state- and input-dependent. ...
Conclusion We provided state-and input-based finite sample bounds for the stochastic reachability probability constructed via conditional distribution embeddings. ...
arXiv:2010.08036v2
fatcat:b72shw3wb5dpbdzcgnywk5erxu
Optimal, Robust Predictive Control of Nonlinear Systems under Probabilistic Uncertainty using Particles
2007
American Control Conference (ACC)
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The method extends a previous approach for linear systems that approximates the distribution of the predicted system state using a finite number of particles. ...
Any solution returned by the algorithm is guaranteed to be -close to a local optimum of the nonlinear stochastic control problem. ...
Linearization approximates the system dynamics and cost function, but since the linearization region is known and bounded, the approximation error can be bounded using standard results. ...
doi:10.1109/acc.2007.4282699
dblp:conf/acc/BlackmoreW07
fatcat:vupvswykrrfolfzxaz6cjmgv6e
Stochastic Galerkin reduced basis methods for parametrized linear elliptic partial differential equations
[article]
2020
arXiv
pre-print
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We propose residual-corrected estimates of the parameter-dependent expectation and variance of linear functional outputs and provide respective computable error bounds. ...
For a given value of the deterministic paremeter, a stochastic Galerkin finite element (SGFE) method can estimate the corresponding expectation and variance of a linear output at the cost of a single solution ...
An MCRB method for linear elliptic problems with error bounds for the expectation and variance of a linear functional output is derived in [4] . Improved error bounds are provided by [5] . ...
arXiv:1812.08519v2
fatcat:2jz55plj5bepzdu3oetv2zuvuy
A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter
2009
Communications in Computational Physics
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certain conditions also in a bounded error in time. ...
It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under ...
The bounded errorε(ϕ,a) as function of phase ϕ also results in a bounded error ε(t,a) in time for the Unsteady Adaptive Stochastic Finite Elements method l 1 based on first degree Newton-Cotes quadrature ...
doi:10.4208/cicp.2009.v6.p403
fatcat:e6yrcoixhrfzlmrra4camv77we
Finite-Time Error Bounds For Linear Stochastic Approximation andTD Learning
2019
Annual Conference Computational Learning Theory
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We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm ...
As a by-product of our analysis, we also solve the problem of obtaining finite-time bounds for the performance of temporal difference learning algorithms with linear function approximation and a constant ...
stochastic approximation can be converted to finite-time bounds on TD algorithms. ...
dblp:conf/colt/SrikantY19
fatcat:kniymjourrgvde5ztie644vrbm
Finite Abstractions of Stochastic Max-Plus-Linear Systems
[chapter]
2014
Lecture Notes in Computer Science
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This work investigates the use of finite abstractions to study the finite-horizon probabilistic invariance problem over Stochastic Max-Plus-Linear (SMPL) systems. ...
SMPL systems are probabilistic extensions of discrete-event MPL systems that are widely employed in the engineering practice for timing and synchronisation studies. ...
M ij = λ ij for all i, j ∈ IN n . By Theorem 3 and Proposition 4, the bound of the approximation error is then E = N δ(n + 1) i,j λ ij . ...
doi:10.1007/978-3-319-10696-0_7
fatcat:d5m7noumcjdqti5ycdwpisz7f4
Page 7175 of Mathematical Reviews Vol. , Issue 96k
[page]
1996
Mathematical Reviews
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An approximate finite-dimensional discrete-time model for a distributed parameter system of parabolic type is constructed. ...
Under certain controllability and observability conditions and conditions on initial error, noise and smoothness of the nonlinear map featuring in the signal model, error bounds for the linearized, undriven ...
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