# A Linear Interpolation and Curvature-Controlled Gradient Optimization Strategy Based on [PERSON]
## 3 Experimental Design and Analysis of Results
### Experimental Results and Analysis
In Figures 1 and 2, the performance of the LCMAdam algorithm is shown for different combinations of hyperparameter settings on the MNIST and CIFAR10 datasets. The algorithm's performance varies depending on the values of _initial_lr_ and min_lr, max_lr_change_ and _period_ (when validating a dataset, the best performance parameter value is taken for the other dataset). The minimum learning rate parameter, min_lr, is held constant at 0.001. Based on the observations in Figure 1, the LCMAdam algorithm performs best when the learning rate parameter range is increased from 0.001 to 0.005. When the maximum learning rate parameter was set to 0.05 and 0.01, the program lagged behind the maximum learning rate parameter of 0.005 in the later stages of training, although it slightly outperformed the maximum learning rate parameter of 0.005 in the early stages of training. This phenomenon may be due to the learning rate range being set too large, which can result in an inappropriate value of the learning rate during later training phases, ultimately affecting \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & **Optimization** & \multirow{2}{*}{**Accuracy**} & \multirow{2}{*}{**Loss**} \\  & **Algorithm** & & \\ \hline \multirow{8}{*}{MNIST} & SGD & 97.18\% & 0.092 \\  & Adagrad & 98.68\% & 0.067 \\  & Adalelta & 96.42\% & 0.1297 \\  & Adam & 98.64\% & 0.060 \\  & NAdam & 98.44\% & 0.0638 \\  & StochGradAdam & 98.11\% & 0.0695 \\  & LCMAdam & 98.49\% & **0.060** \\ \hline \multirow{8}{*}{CIFAR10} & SGD & 48.32\% & 1.466 \\  & Adagrad & 29.87\% & 1.95 \\  & Adalelta & 25.97\% & 1.973 \\  & Adam & 68.49\% & 1.22 \\  & NAdam & 69.85\% & 1.685 \\  & StochGradAdam & 69.06\% & 1.032 \\  & LCMAdam & **75.20\%** & 1.28 \\ \hline \multirow{8}{*}{Stomach} & SGD & 57.60\% & 1.171 \\  & Adagrad & 69.99\% & 0.9581 \\ \cline{1-1}  & Adalelta & 56.00\% & 1.665 \\ \cline{1-1}  & Adam & 74.20\% & 0.883 \\ \cline{1-1}  & NAdam & 74.80\% & 0.817 \\ \cline{1-1}  & StochGradAdam & 70.20\% & 0.9307 \\ \cline{1-1}  & LCMAdam & **76.80\%** & **0.66** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of experimental results of different optimization algorithms. the search for the local optimal solution. The initial learning rate value remains unchanged at 0.001, and by combining the calculated values of some formulas in this algorithm, the minimum learning rate is set to 0.001 without any other changes. The variation in the maximum variation in the learning rate max_lr_change_ and the cycle length _period_ in Figure 2 also affects the performance of the LCMAdam algorithm. The experimental results indicate that the LCMAdam algorithm performs best when the learning rate maximum variation parameter and the cycle length parameter are set to 1.1 and 0.001, respectively. However, changing the maximum amount of change in the learning rate parameter to 0.01 results in a good performance in the early stages of training, but a decrease in performance in the later stages. When adjusting these two parameters simultaneously, the performance is still not as good as when they are set to 1.1 and 0.001. This phenomenon may be due to improper parameter settings resulting in a large variation in _lr_ in the final calculation. Figure 1: Performance comparison of the MNIST dataset for different learning rate variation intervals: (**a**) comparison of accuracy; (**b**) comparison of loss values. Figure 2: Comparison of the performance of the CIFAR10 dataset for different learning rates in terms of maximum change and cycle length: (**a**) comparison of accuracy; (**b**) comparison of loss values. For training, the hyperparameters are set to the set of data on which the LCMAdam algorithm performs best on the three datasets. Figure 3 shows the performance comparison of various algorithms for the MNIST dataset.