The algorithm is known for its efficient computational performance for large datasets by approximating the gradient of the cost function on smaller batches. On the other hand, the algorithm adapts the learning rate for each parameter by considering the recent magnitude of the gradients, helping in faster convergence, especially when dealing with data.

It seems like you're referring to two different algorithms but you didn't mention their names. However, based on the descriptions, the first algorithm could be Stochastic Gradient Descent (SGD). SGD is known for its efficiency with large datasets because it approximates the gradient of the cost function using a single random sample which is computationally less expensive.

The second algorithm sounds like Adaptive Moment Estimation (Adam). Adam adapts the learning rate for each parameter by considering the recent magnitudes of the gradients. This helps in faster convergence, especially when dealing with sparse data.

Please confirm if these are the algorithms you're referring to.