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Optimal variance-reduced stochastic approximation in Banach spaces
[article]
2022
arXiv
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Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic approximation scheme, and establish non-asymptotic bounds for both the operator ...
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. ...
Acknowledgements This work was supported in part by NSF-FODSI grant 202350, and the DOD-ONR Office of Naval Research N00014-21-1-2842 as well as NSF-DMS grant 2015454 and NSF-IIS grant 1909365 to MJW and ...
arXiv:2201.08518v2
fatcat:enz2q4gwcnbybmfmwnixadarzi
Optimal variance-reduced stochastic approximation in Banach spaces
[article]
2022
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic approximation scheme, and establish non-asymptotic bounds for both the operator ...
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. ...
Acknowledgements This work was supported in part by NSF-FODSI grant 202350, and the DOD-ONR Office of Naval Research N00014-21-1-2842 as well as NSF-DMS grant 2015454 and NSF-IIS grant 1909365 to MJW and ...
doi:10.48550/arxiv.2201.08518
fatcat:roth26co4rcapnwlxgfiqkw66y
Page 5389 of Mathematical Reviews Vol. , Issue 82m
[page]
1982
Mathematical Reviews
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“It is, however, in the Banach space duality framework that the concept enjoys its greatest utility. ...
“In this note we indicate how the decomposability of sets in a dual Banach space can be incorporated into the basic results of conjugate duality for optimization problems in order to yield sufficient conditions ...
Page 6289 of Mathematical Reviews Vol. , Issue 89K
[page]
1989
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Let X(t) be a stochastic process taking values in a separable Banach space E and adapted to a filtration ¥ (t) which satisfies the usual hypotheses. ...
In optimal stopping problems discounted value functions are in turn approximated by continuous solutions of a suitable family of penalty equations. ...
Projection and discretization methods in stochastic programming
1994
Journal of Computational and Applied Mathematics
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Stochastic programs with recourse are equivalent to a special extremum problems in function spaces. ...
For the approximate solution of a problem in an infinite dimensional space some projection method is usually suggested. ...
The results obtained rely on the general stability analysis of parametric optimization problems in Banach spaces. ...
doi:10.1016/0377-0427(94)90379-4
fatcat:6gpl6f5zbna7rltenttzz3cspq
Page 1337 of Mathematical Reviews Vol. 56, Issue 4
[page]
1978
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Assuming that the trajectories of sto- chastic processes realized in the system are elements of a separable Banach space, we may regard them as random variables taking values in a Banach space, and the ...
a Banach space, and to apply that theory to some identification problems. ...
Page 5853 of Mathematical Reviews Vol. , Issue 87j
[page]
1987
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Nowak (Katowice)
Berger, Erich (D-GTN)
Asymptotic behaviour of a class of stochastic
approximation procedures.
Probab. Theory Relat. Fields 71 (1986), no. 4, 517-552. Let B be a real Banach space. ...
A problem arising
in portfolio theory is illustrated as an example of possible applica- tions.”
Lai, T. L. (1-CLMB) 87j:62160 Stochastic approximation and sequential search for optimum. ...
Page 2478 of Mathematical Reviews Vol. , Issue 80F
[page]
1980
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The
result is obtained by reducing the problem to an abstract maximi-
zation problem with side constraints in a Banach space. P. ...
Expanding the solution in a system of eigenfunctions of the operator A,, they propose approximate methods of solving the problem by reducing it to a system of ordinary differential equations involving ...
Page 1529 of Mathematical Reviews Vol. , Issue 2003B
[page]
2003
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Furthermore, by means of a Banach fixed point approach, we prove that the standard finite element approximation applied to this system is quasi-optimally accurate in L*.”
2003b:93094 93E20 60G40 60565 ...
The approach applied allows us to reduce problems of asymptotic stability in probability and mean-square exponential stability of stochastic systems to the study of the stability of corresponding deterministic ...
Page 3126 of Mathematical Reviews Vol. , Issue 98E
[page]
1998
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In the second paper cited above he introduced the notion of the Gaussian measure in a p-adic Banach space as a Haar probability measure on a compact submodule. ...
Let Z be a p-stable random measure defined on ([0, 1], @[0, 1]) and with values in a q-smoothable Banach space, where g < p<2 or q =p =2 (Gaussian case). ...
Stochastic Halpern iteration in normed spaces and applications to reinforcement learning
[article]
2024
arXiv
pre-print
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We analyze the oracle complexity of the stochastic Halpern iteration with variance reduction, where we aim to approximate fixed-points of nonexpansive and contractive operators in a normed finite-dimensional ...
space. ...
This stepsize is easy to handle and, more importantly, leads to optimal residual estimations in the noiseless case in the Hilbert setting, and near-optimal for general Banach spaces. ...
arXiv:2403.12338v2
fatcat:fgrhkwq5jvew5dfj7s3y5r4n2q
Page 2020 of Mathematical Reviews Vol. , Issue 2000c
[page]
2000
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Banach spaces (171-190). ...
Duncan, Solv- able infinite time horizon stochastic control problems in noncom- pact symmetric spaces (373-389); Robert J. ...
Page 2057 of Mathematical Reviews Vol. , Issue 91D
[page]
1991
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Using stochastic calcu- lus, the problem is reduced to a nonlinear programming problem, and then optimization arguments are invoked. Special cases and examples are presented. Stavros A. ...
For instance, a considerable amount of effort and paper could have been saved if it had been realized that any Banach space with separable dual must be separable itself; hence, such a space must be a Suslin ...
Measurements of Generalisation Based on Information Geometry
[chapter]
1997
Operations Research/Computer Science Interfaces Series
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This uni es the majority of error measures currently in use. The optimal estimators also reveal some intricate interrelationships among information geometry, Banach spaces and su cient statistics. ...
In this paper a theory for measuring generalisation is developed by combining Bayesian decision theory with information geometry. ...
We would like to thank many people in the Neural Computing Research Group, especially C. Williams, for useful comments and practical help. This work was partially supported by EPSRC grant (GR/J17814). ...
doi:10.1007/978-1-4615-6099-9_69
fatcat:nfw23gzsh5afjezqhqypln65wy
Page 4389 of Mathematical Reviews Vol. , Issue 84j
[page]
1984
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Noise and observation are Gaussian random elements taking values in Banach spaces, while signals take values in a translation-quasi-invariant Hilbert space. ...
We also obtain optimality conditions for the usual stochastic two-person zero-sum game with hidden choice of actions, introduced by Shapley, by reducing it to the case described above.” ...
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