Now, we'll see how inequality minimization TAML works step by step:

1. Let's say we have a model parameterized by a parameter and we've a distribution over tasks . First, we randomly initialize the model parameter .
2. We sample a batch of tasks from a distribution of tasks—that is, . Say, we've sampled three tasks, then .
3. Inner loop: For each task in tasks , we sample k data points and prepare our train and test datasets:

Then, we calculate the loss on the our training set , minimize the loss using gradient descent, and get the optimal parameters:

So, for each of the tasks, we sample k data points, prepare the train dataset, minimize the loss, and get the optimal parameters. Since we sampled three tasks, we'll have three optimal parameters—that is, .

4. Outer loop: Now, we perform meta optimization. Here, we try to minimize the loss on our training set, . We minimize the loss by calculating the gradient with respect to our optimal parameter and update our randomly initialized parameter ; along with this, we'll add the entropy term. So, our final meta objective becomes the following:

5. We repeat steps 2 to 4 for n number of iterations.