Random directions stochastic approximation with deterministic perturbations Article Swipe
L. A. Prashanth
,
Shalabh Bhatnagar
,
Nirav Bhavsar
,
Michael C. Fu
,
Steven I. Marcus
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1808.02871
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1808.02871
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order algorithms to incorporate deterministic perturbations. We show that the gradient and/or Hessian estimates in the resulting algorithms with deterministic perturbations are asymptotically unbiased, so that the algorithms are provably convergent. Furthermore, we derive convergence rates to establish the superiority of the first-order and second-order algorithms, for the special case of a convex and quadratic optimization problem, respectively. Numerical experiments are used to validate the theoretical results.
Related Topics
Concepts
Hessian matrix
Convergence (economics)
Mathematics
Stochastic optimization
Quadratic equation
Perturbation (astronomy)
Applied mathematics
Mathematical optimization
Simultaneous perturbation stochastic approximation
Stochastic approximation
Regular polygon
Order (exchange)
Computer science
Stochastic process
Key (lock)
Physics
Statistics
Economics
Finance
Economic growth
Computer security
Geometry
Quantum mechanics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1808.02871
- https://arxiv.org/pdf/1808.02871
- OA Status
- green
- Cited By
- 1
- References
- 24
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2887882632
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W2887882632Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1808.02871Digital Object Identifier
- Title
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Random directions stochastic approximation with deterministic perturbationsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2018Year of publication
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2018-08-08Full publication date if available
- Authors
-
L. A. Prashanth, Shalabh Bhatnagar, Nirav Bhavsar, Michael C. Fu, Steven I. MarcusList of authors in order
- Landing page
-
https://arxiv.org/abs/1808.02871Publisher landing page
- PDF URL
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https://arxiv.org/pdf/1808.02871Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1808.02871Direct OA link when available
- Concepts
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Hessian matrix, Convergence (economics), Mathematics, Stochastic optimization, Quadratic equation, Perturbation (astronomy), Applied mathematics, Mathematical optimization, Simultaneous perturbation stochastic approximation, Stochastic approximation, Regular polygon, Order (exchange), Computer science, Stochastic process, Key (lock), Physics, Statistics, Economics, Finance, Economic growth, Computer security, Geometry, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
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2020: 1Per-year citation counts (last 5 years)
- References (count)
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24Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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