When we train our model on datasets, we need the error to converge to a minimum for efficient analysis. Choosing a good optimizer out of the plethora of options is one of the most important decisions that will after this process. A good optimizer will make sure that we get the required accuracy after few epochs of training. The best optimizer for training varies from problem to problem and dataset to dataset. Another important aspect of faster convergence is the learning rate of the optimizer. Since, an optimizer can proceed with many different learning rates, it is important to identify a learning rate that works best for the problem we have. Too high a learning rate might lead to lack of convergence and too low a learning rate will slow down the training process. So, it is essential to test different learning rates to find the best one which converges faster. It has been observed that having a high learning rate initially is better for faster searching of the loss landscape. Subsequently, it has also been observed that reducing the learning rate as the number of epochs increases helps the optimizer to not make sudden jumps out of a minimum it is approaching, thus helping it to reach a minimum. So, we use different learning rate schedulers to see which one will work best with the optimizer to reach a minimum faster, if at all it does aid the optimizers.

The Dataset we have is that of Cardiac MRI Segmentation. The dataset contains around 4k images for training. We are dividing the dataset into 80% as training and 20% as validation sets. We are creating a U-Net model to train the dataset as given in the paper. (Chuckyee, 2017)

We are not use data augmentation methods given in the paper for training. We used Weighted categorical Cross entropy as our loss function which we call as pixel loss. Mean Intersection-Over-Union was used along with Accuracy as a metric for evaluation as our task is semantic image segmentation Dice loss was also computed as an evaluation metric.

We use the following 7 different optimizers for our experiment.

• SGD
• RMSprop
• Adagrad
• Adadelta
• Adam
• Adamax
• Nadam

We are going to train the data using each of the above optimizers with 4 different learning rates

• 0.1
• 0.01
• 0.001
• 0.0001 to find out how fast the loss converges to a minimum. We find the minimum number of epochs needed for the validation error to converge to a minimum as measure of convergence. The training was run for 100 epochs to check the convergence for high learning rates and to 700 epochs for low learning rates.

After finding the best learning rate for each of the optimizers from the results of the first experiment, we vary the data available for training and see how that affects the rate of convergence for each of the optimizers. For this experiment, we are only training at the best learning rates we found for each optimizer. So, from the result we can know if availability of data affects the behaviour of the optimizer. We train the model using

• 20%
• 40%
• 60%
• 80%
• 100% of available training data.