Stochastic Approximation

• Record Nr.: UNINA9910831015103321
• Autore: Borkar Vivek S
• Pubbl/distr/stampa: Singapore : , : Springer, , 2024; ©2023
• ISBN: 981-9982-77-4
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (280 pages)
• Collana: Texts and Readings in Mathematics Series ; ; v.48
• Soggetti: Anàlisi estocàstica; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- (Expanded from the 1st edition) -- Contents -- About the Author -- 1 Introduction -- References -- 2 Convergence Analysis -- 2.1 The o.d.e. Limit -- 2.2 Extensions and Variations -- References -- 3 Finite Time Bounds and Traps -- 3.1 Estimating the Lock-in Probability -- 3.2 Sample Complexity -- 3.3 Extensions -- 3.4 Avoidance of Traps -- References -- 4 Stability Criteria -- 4.1 Introduction -- 4.2 Stability Through a Scaling Limit -- 4.3 Stability by Comparison -- 4.4 Stabilizability by Stepsize Selection -- 4.5 Stabilizability by Resetting -- 4.6 Convergence for Tight Iterates -- References -- 5 Stochastic Recursive Inclusions -- 5.1 Introduction -- 5.2 The Differential Inclusion Limit -- 5.3 An Alternative Representation -- 5.4 Applications -- 5.5 Projected Stochastic Approximation -- 5.6 Extensions -- References -- 6 Asynchronous Schemes -- 6.1 Introduction -- 6.2 Asymptotic Behaviour -- 6.3 Effect of Delays -- 6.4 Convergence -- References -- 7 A Limit Theorem for Fluctuations -- 7.1 Introduction -- 7.2 A Tightness Result -- 7.3 The Functional Central Limit Theorem -- 7.4 The Convergent Case -- References -- 8 Multiple Timescales -- 8.1 Two Timescales -- 8.2 Controlled Markov Noise -- 8.3 Averaging the Natural Timescale -- 8.4 Other Multiscale Algorithms -- References -- 9 Constant Stepsize Algorithms -- 9.1 Introduction -- 9.2 Asymptotic Behaviour -- 9.3 Tracking -- 9.4 Refinements -- References -- 10 General Noise Models ; -- 10.1 The Problem -- 10.2 Preliminaries -- 10.3 Moment Estimates -- 10.4 Main Results -- 10.5 Extensions and Variations -- References -- 11 Stochastic Gradient Schemes -- 11.1 Introduction -- 11.2 The Basic Stochastic Gradient Descent -- 11.3 Approximate Gradient Schemes -- 11.4 Some Important Variants -- 11.5 Langevin Algorithm and Simulated Annealing -- 11.6 Simulation-Based Optimization.; 11.7 SGD for Machine Learning -- 11.7.1 Empirical Risk Minimiziation -- 11.7.2 Variance Reduction Techniques -- 11.7.3 Error Bounds -- References -- 12 Liapunov and Related Systems -- 12.1 Introduction -- 12.2 Primal-Dual Algorithms -- 12.3 Stochastic Fixed Point Iterations -- 12.4 Collective Phenomena -- 12.5 Miscellaneous Applications -- References -- Appendix A Topics in Analysis -- A.1 Continuous Functions -- A.2 Square-Integrable Functions -- A.3 Lebesgue's Theorem -- A.4 Set-Valued Maps -- Appendix B Ordinary Differential Equations -- B.1 Basic Theory -- B.2 Linear Systems -- B.3 Asymptotic Behaviour -- Appendix C Topics in Probability -- C.1 Martingales -- C.2 Spaces of Probability Measures -- C.3 Fernique's Inequality -- C.4 Stochastic Differential Equations -- References -- Index.