Distributed asynchronous stochastic approximation algorithms with unbounded stochastic information delays - theory and applications / Adrian Redder ; Advisors: Prof. Dr. Holger Karl, Prof. Dr. Arunselvan Ramaswamy. Paderborn, 2024
Inhalt
- Acknowledgement
- Abstract
- Notation and Definitions
- Introduction
- Motivation
- Stochastic approximation algorithms
- Age of Information (AoI)
- AoI processes driven by event processes with dependency decay
- How AoI arises from asynchronous computing
- Contributions and thesis structure
- Part I: Distributed Asynchronous Stochastic Approximation Algorithms
- Stability of Distributed Asynchronous Stochastic Approximations
- Assumption, main statements and preliminaries
- Traditional Borkar-Meyn theorem
- Recursive structure of stochastic approximation errors caused by AoI
- Creation of rescaled trajectories
- A discrete Gronwall-type inequality for varying lower time-horizons
- Distributed Borkar-Meyn Theorem
- Recursive L2 structure and L2 Bounds
- Stability of the recalled trajectory
- Distributed BMT proof
- Further extensions
- Stability of stochastic approximations with momentum
- Discussion and related work
- Proofs of Chapter 2
- Distributed Asynchronous Stochastic Gradient Descent Methods
- Assumptions and main statements
- Analysis
- Numerical verification
- Discussion and related work
- Proofs of Chapter 3
- Distributed Asynchronous Reinforcement Learning
- Part II: Age of Information Processes
- Stochastic Information Delays
- AoI processes: A definition
- Deterministic growth properties from AoI moment bounds
- Convergence of accumulated stepsizes over AoI horizons
- Proofs of Chapter 5
- AoI arising from strongly mixing event processes
- Main statements
- Strong mixing and assumptions
- Moment bounds, mixing rates, and strong law
- Discussion and related work
- Proofs of Chapter 6
- AoI from asynchronous computing modeled as parallel renewal processes
- Asychronous computing models
- System Models
- Main Results
- Numerical Verification
- Applications
- Discussion and related work
- Proofs for Chapter 7
- AoI in wireless networks
- Numerical Experiments
- Conclusions and Future Directions
- Appendix
- Bibliography