# DTN: A Learning Rate Scheme with Convergence Rate of $\mathcal{O}(1/t)$ for SGD

## TL;DR

This paper discusses a learning rate scheme for SGD claiming an $(1/t)$ convergence rate, but later acknowledges errors in the proofs and invalidates the main convergence claims due to incorrect use of the test criterion.

## Contribution

Proposes a learning rate scheme for SGD with a claimed convergence rate, but the main theoretical results are invalidated due to proof errors.

## Key findings

- Original convergence claims are invalidated.
- The paper admits mistakes in the proof of key lemmas.
- No validated convergence rate is established due to errors.

## Abstract

This paper has some inconsistent results, i.e., we made some failed claims because we did some mistakes for using the test criterion for a series. Precisely, our claims on the convergence rate of $\mathcal{O}(1/t)$ of SGD presented in Theorem 1, Corollary 1, Theorem 2 and Corollary 2 are wrongly derived because they are based on Lemma 5. In Lemma 5, we do not correctly use the test criterion for a series. Hence, the result of Lemma 5 is not valid. We would like to thank the community for pointing out this mistake!

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Source: https://tomesphere.com/paper/1901.07634