Almost Sure Convergence and Non-Asymptotic Concentration Bounds for Stochastic Mirror Descent Algorithm

This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the assumption of diminishing bias. Furthermore, we derive...

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Vydané v:IEEE control systems letters Ročník 8; s. 2397 - 2402
Hlavní autori: Paul, Anik Kumar, Mahindrakar, Arun D., Kalaimani, Rachel K.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: IEEE 2024
Predmet:
almost sure convergence
concentration inequality
Convergence
Filtration
Mirror descent algorithm
Mirrors
Noise
Noise measurement
Optimization
Random variables
Signal processing algorithms
sub-gaussian random vectors
Vectors
ISSN:2475-1456, 2475-1456
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Shrnutí:This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the assumption of diminishing bias. Furthermore, we derive concentration bounds for the discrepancy between the iterates' function values and the optimal value, based on standard assumptions. Subsequently, leveraging the assumption of Sub-Gaussian noise in stochastic subgradients, we present refined concentration bounds for this discrepancy.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2024.3482148