What question did this study set out to answer?

This research aims to explore deterministic properties of random algorithms, particularly focusing on boundedness and convergence rates.

June 28, 2026Open Access

On some deterministic properties of stochastic gradient descent and random projection sequences

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TTThanh Tung Tran

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Implication

This thesis investigates boundedness and convergence properties in finite and infinite-dimensional Hilbert spaces, indicating new results for random algorithms.

Key Points

This research aims to explore deterministic properties of random algorithms, particularly focusing on boundedness and convergence rates.
Revisited classical stochastic gradient descent methods assuming coercivity to establish boundedness.
Extended results for boundedness of random projection algorithms to polyhedral sets in infinite-dimensional spaces.
Introduced the innate regularity assumption to ensure boundedness for affine subspaces.
Demonstrated that the iterates of stochastic gradient descent remain bounded under coercivity assumption.
Enabled generalization of boundedness for random projection algorithms, applicable to polyhedral cones.
Illustrated the sharpness of results by providing examples that validate the importance of the innate regularity assumption.

Cite This Study

Thanh Tung Tran (2026) studied this question.

synapsesocial.com/papers/6a40ba8861bb0a67205c65a3 https://doi.org/10.14288/1.0452822

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Implication

This thesis investigates boundedness and convergence properties in finite and infinite-dimensional Hilbert spaces, indicating new results for random algorithms.

On some deterministic properties of stochastic gradient descent and random projection sequences

Discussion

Member takes

Implication

Key Points

Cite This Study

On some deterministic properties of stochastic gradient descent and random projection sequences

Discussion

Member takes

Implication

Key Points

Cite This Study

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