In this session we will discuss about various methods to optimise a machine learning model and, how we can adjust the hyper-parameters to minimise the cost function.

1. Presented By: Aayush Srivastava
& Divyank Saxena
Methods of
Optimization in
Machine Learning

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3. Our Agenda
01 What is Optimization in
Machine Learning
02 What is Gradient Descent
03
What is Minibatch Stochastic
Gradient
04
What is Adam optimization
05
Demo
05
06
What is Stochastic Gradient
Descent

4. .
What is Optimization in ML
● Optimization in Machine Learning is a technique used to find the best set of parameters for a given
model to minimize a loss function and improve its performance. It is an essential step in the training
process of a machine learning model.
● The goal of optimization is to find the best weights and biases for the model, so that it can make
accurate predictions.
● Optimization is used in machine learning because models typically have many parameters, and finding
the best values for those parameters can be a challenging task.
● With optimization techniques, the model can automatically search for the best parameters, rather than
relying on manual tuning by the user.

5. .
What is Cost Function
● A cost function is a function which measures the error between predictions and their actual values
across the whole dataset.
● Minimizing the cost function helps the learning algorithm find the optimal set of parameters, such as
weights and biases, that produce the best predictions.
● Cost function is a measure of how wrong the model is in estimating the relationship between X(input)
and Y(output) Parameter
- m is the number of samples
- Sum from i to m,
- The actual calculation is just the hypothesis value for h(x)
minus the actual value of y. Then you square whatever you get.

6. .
What is Cost Function
● Let’s run through the calculation for best_fit_1.
1.The hypothesis is 0.50. This is the h_the ha(x(i)) part
what we think is the correct value.
2.The actual value for the sample data is 1.00.
So we are left with (0.50 — 1.00)^2 , which is 0.25.
3.Let’s add this result to an array called results and do the same for all three points
4.Results = [0.25, 2.25, 4.00]
5.Finally, we add them all up and multiply by ⅙ .We get the cost for best_fit1 = 1.083

7. .
What is Cost Function
● COST: best_fit_1: 1.083
best_fit_2: 0.083
best_fit_3: 0.25
● A low costs represents a smaller difference.

8. .
What is Loss Function
● A loss function, also known objective function, is a mathematical measure of how well a model is able
to make predictions that match the true values.
● A loss function measures the error between a single prediction and the corresponding actual value.
● Loss and cost functions are methods of measuring the error in machine learning predictions. Loss
functions measure the error per observation, whilst cost functions measure the error over all
observations.
Types:
1.Mean Squared Error (MSE): This loss function measures the average squared difference between the
predicted values and the true values.
2.Mean Absolute Error (MAE): This loss function measures the average absolute difference between the
predicted values and the true values.

9. ● Gradient, in plain terms means slope or slant of a surface. So gradient descent literally means
descending a slope to reach the lowest point on that surface
● Gradient descent enables a model to learn the gradient or direction that the model should take in
order to reduce errors (differences between actual y and predicted y).
● This algorithm that tries to find a minimum of a function iteratively
What is Gradient Descent

10. .
What is Learning Rate
● Learning Rate:
The learning rate is a hyperparameter in machine learning that determines the step size at which the
optimization algorithm updates the model's parameters. It is used to control the speed at which the
model learns.

11. .
Limitation of Gradient Descent
● Some limitations and drawbacks that can affect its performance and efficiency.
● Local Minima: Gradient Descent can get stuck in a local minimum, which may not be the global
minimum, and therefore, the optimization will not produce the best result.
● Vanishing gradient: When training deep neural networks, the gradients can become very small,
leading to the vanishing gradient problem, which can slow down or prevent convergence.

12. ● Stochastic Gradient Descent (SGD) is a variant of Gradient Descent optimization algorithm, that is
used to update the parameters of a model in a more efficient and faster way.
● “Stochastic” in plain terms means “random”
● In SGD, at each step, the algorithm calculates the gradient for one observation picked at random,
instead of calculating the gradient for the entire dataset..
● So, let’s have a dataset that contains 1000 rows, and when we apply SGD it will update the model
parameters 1000 times in one complete cycle of a dataset instead of one time as in Gradient Descent.
What is Stochastic Gradient Descent

13. ● In the left diagram of the above picture, we have SGD (where 1 per step time) we take a Gradient
Descent step for each example and on the right diagram is GD(1 step per entire training set).
● This represents a significant performance improvement, when the dataset contains millions of
observations.
What is Stochastic Gradient Descent

14. Advantages of Stochastic Gradient Descent
● It is easier to fit into memory due to a single training sample being processed by the network
● For larger datasets it can converge faster as it causes updates to the parameters more frequently
● Due to frequent updates the steps taken towards the minima of the loss function have oscillations
which can help getting out of local minimums of the loss function
What is Stochastic Gradient Descent

15. ● So far we encountered two extremes in the approach to gradient-based learning:
● First Gradient Descent uses the full dataset to compute gradients and to update parameters, one
pass at a time. And Conversely, Stochastic Gradient Descent processes one training example at a
time to make progress. Either of them has its own drawbacks.
● Gradient descent is not particularly data efficient whenever data is very similar. Stochastic gradient
descent is not particularly computationally efficient since CPUs and GPUs cannot exploit the full
power of vectorization.
● This suggests that there might be something in between, and in fact, that is what we have been using
so far in the examples we discussed.
What is Minibatch Stochastic Gradient

16. ● Mini Batch Gradient Descent is considered to be the cross-over between GD and SGD. In this
approach instead of iterating through the entire dataset or one observation, we split the dataset into
small subsets (batches) and compute the gradients for each batch.
● Steps involved in Mini-batch stochastic gradient:
1. Pick a mini-batch
2. Feed it to Neural Network
3. Calculate the mean gradient of the mini-batch
4. Use the mean gradient we calculated in step 3 to update the weights
5. Repeat steps 1–4 for the mini-batches we created
What is Minibatch Stochastic Gradient

17. ● Minibatch stochastic gradient descent is able to trade-off convergence speed and computation
efficiency. A minibatch size of 10 is more efficient than stochastic gradient descent; a minibatch size
of 100 even outperforms GD in terms of runtime.
What is Minibatch Stochastic Gradient

18. Advantages of Mini-Batch Gradient Descent:
● Reduces variance of the parameter update and hence lead to stable convergence
● Speeds the learning
● Helpful to estimate the approximate location of the actual minimum
Disadvantages of Mini Batch Gradient Descent:
● Loss is computed for each mini batch and hence total loss needs to be accumulated across all mini
batches
Advantages and Disadvantages

19. The Adam optimization algorithm is an extension to stochastic gradient descent that has recently
seen broader adoption for deep learning applications in computer vision and natural language
processing.
The method is really efficient when working with large problem involving a lot of data or parameters.
Adam is an adaptive learning rate method, which means, it computes individual learning rates for
different parameters. Its name is derived from adaptive moment estimation
What is Adam Optimizer

20. The method computes individual adaptive learning rates for different parameters from estimates of
first and second moments of the gradients.
Adam optimizer involves a combination of two gradient descent methodologies:
1. Momentum:
This algorithm is used to accelerate the gradient descent algorithm by taking into consideration
the ‘exponentially weighted average’ of the gradients. Using averages makes the algorithm
converge towards the minima in a faster pace.
2. Root Mean Square Propagation (RMSP):
It maintains per-parameter learning rates that are adapted based on the average of recent
magnitudes of the gradients for the weight (e.g. how quickly it is changing). This means the
algorithm does well on online and non-stationary problems (e.g. noisy).
How Adam Optimizer Work

21. List of attractive benefits of using Adam, as follows:
● Straightforward to implement.
● Computationally efficient.
● Less memory requirements.
● Well suited for problems that are large in terms of data and/or parameters.
● Appropriate for problems with very noisy/or sparse gradients.
● Hyper-parameters have intuitive interpretation and typically require little tuning.
Benefits of Adam Optimizer

22. Demo

23. Thank You !
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