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arXiv · 2506.23303

On the boundedness of the sequence generated by minibatch stochastic gradient descent

Heinz H. Bauschke·Tran Thanh Tung
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Abstract

Stochastic Gradient Descent (SGD) with Polyak's stepsize has recently gained renewed attention in stochastic optimization. Recently, Orvieto, Lacoste-Julien, and Loizou introduced a decreasing variant of Polyak's stepsize, where convergence relies on a boundedness assumption of the iterates. They established that this assumption holds under strong convexity. In this paper, we extend their result by proving that boundedness also holds for a broader class of objective functions, including coercive functions. We also present a case in which boundedness may or may not hold.

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Heinz H. Bauschke, Tran Thanh Tung. 2025-06-29. On the boundedness of the sequence generated by minibatch stochastic gradient descent. https://arxiv.org/abs/2506.23303

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