What common optimization algorithms are used in deep learning?
Deep learning is the subfield of machine learning, which is used to perform complex tasks. A deep learning model consists of input, hidden and output layers, and activation and loss functions. The model has some parameters like weights and biases that are required for its training. The model learns these parameters during its training.
While training our model, we aim to minimize the error i.e. reduce the value of the loss function, which is also known as the cost function. Here’s where the optimization algorithms come to work. An optimization algorithm aims to adjust the parameters, like weights, the learning rate alpha, and the bias so as to minimize the cost function and improve the accuracy of the model.
Now that we know what an optimization algorithm is, let’s dive deeper into some common optimization algorithms used in deep learning models.
Gradient descent
Gradient descent is an iterative technique that begins from a random location on a function and descends gradually until it reaches the function's lowest point.
It begins with certain coefficients and calculates their cost and looks for cost values that are less expensive than they are right now. It then shifts in the direction of the lighter weight while updating the coefficient values until it reaches the local minimum.
The algorithm for gradient descent is as follows:
We just explored gradient descent, let's move on to another variant of gradient descent i.e. stochastic gradient descent.
Stochastic gradient descent
Stochastic gradient descent (SGD) is an extension to the gradient descent. The stochastic gradient descent overcomes the limitations of the gradient descent. It iteratively updates the model's parameters based on the gradients computed on individual training examples or small subsets of examples called mini-batches. Therefore, it requires more iterations than gradient descent to attain the minimum and also has more noise.
The equation for SGD is as follows:
Adagrad
The adaptive gradient descent (Adagrad) algorithm is slightly different from other gradient descent algorithms. This is because it uses different learning rates for each iteration. The change in learning rate depends upon the difference in the parameters during training.
The Adagrad algorithm uses the below formula to update the weights.
Adagrad is effective for handling sparse real-world datasets with heterogeneous gradients, but it may decrease the learning rate too aggressively over time.
RMSProp
Root mean square propagation (RMSProp) addresses the limitations of fixed learning rates by adapting the learning rate for each parameter based on the magnitude of the historical gradients.
Root mean squared rop outperforms Adagrad. RMSProp uses the exponential moving average as opposed to AdaGrad's cumulative sum of squared gradients. Both AdaGrad and RMSProp begin with the same step. The learning rate is simply divided by an average with exponential decline in RMSProp.
This technique enables speedy convergence and a stable and efficient training of deep neural networks.
The equation for RMSProp is as follows:
Adam Optimizer
The Adam optimizer offers the benefits of adaptive learning rates and momentum to achieve efficient and effective optimization. Adam maintains adaptive learning rates for each parameter by utilizing both the first moment (the mean) and the second moment (the uncentered variance) of the gradients. This allows it to handle sparse gradients and noisy updates effectively. By incorporating momentum, which accumulates past gradients, Adam accelerates convergence and improves the optimization process.
The Adam optimizer equation is as follows:
Adam has become popular due to its robustness, fast convergence, and ease of use. It is widely applied in various deep learning tasks, including image recognition, natural language processing, and reinforcement learning.
Now, that we had an overview of the common optimizers used in deep learning let's summarize their benefits, limitations, and applications in a table, as shown below:
Summary
Optimizer | Benefits | Limitations | Applications |
Gradient descent | Guaranteed convergence for convex functions | Computationally expensive for large datasets | Linear regression, Logistic regression |
Stochastic Gradient descent | Efficient computation with mini-batches of training data | Noisy updates can lead to slower convergence | Large-scale machine learning |
RMSProp | Provides stable and efficient convergence | May decrease the learning rate too aggressively | Reinforcement learning |
Adagrad | Effective for sparse data and diverse feature spaces | Learning rate can become too small over time | Recommender systems |
Adam | Combines benefits of AdaGrad and RMSProp | Requires more memory due to the storage of past gradients | NLP, deep learning, computer vision |
Conclusion
In conclusion, optimization techniques are essential for effectively and efficiently training deep learning models. Each algorithm has its own strengths and limitations, making them suitable for different scenarios.
The best optimization algorithm depends on the amount of the dataset, the complexity of the model, and the features of the problem. Therefore, it is important to select the best optimization technique for your particular requirement.
