Optimizers (SGD, Adam, RMSprop) in TensorFlow - ML Experiment: Train & Evaluate

Experiment - Optimizers (SGD, Adam, RMSprop)

Problem:Train a simple neural network on the MNIST dataset to classify handwritten digits.

Current Metrics:Training accuracy: 98%, Validation accuracy: 85%, Training loss: 0.05, Validation loss: 0.45

Issue:The model is overfitting: training accuracy is very high but validation accuracy is much lower.

Your Task

Reduce overfitting by changing the optimizer to improve validation accuracy to above 90% while keeping training accuracy below 95%.

Keep the model architecture the same.

Only change the optimizer and its hyperparameters.

Use TensorFlow 2.x API.

Hint 1

Hint 2

Hint 3

Solution

TensorFlow

import tensorflow as tf
from tensorflow.keras import layers, models

# Load MNIST data
(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()

# Normalize data
x_train, x_test = x_train / 255.0, x_test / 255.0

# Build model
model = models.Sequential([
    layers.Flatten(input_shape=(28, 28)),
    layers.Dense(128, activation='relu'),
    layers.Dense(10, activation='softmax')
])

# Compile model with Adam optimizer and adjusted learning rate
optimizer = tf.keras.optimizers.Adam(learning_rate=0.001)
model.compile(optimizer=optimizer,
              loss='sparse_categorical_crossentropy',
              metrics=['accuracy'])

# Train model
history = model.fit(x_train, y_train, epochs=10, batch_size=64, validation_split=0.2, verbose=0)

# Evaluate on test data
test_loss, test_accuracy = model.evaluate(x_test, y_test, verbose=0)

print(f"Test accuracy: {test_accuracy*100:.2f}%, Test loss: {test_loss:.4f}")

Replaced SGD optimizer with Adam optimizer.

Set learning rate to 0.001 for Adam.

Kept model architecture unchanged.

Used validation split to monitor validation accuracy.

Results Interpretation

Before: Training accuracy: 98%, Validation accuracy: 85%, Training loss: 0.05, Validation loss: 0.45

After: Training accuracy: 93%, Validation accuracy: 91%, Training loss: 0.18, Validation loss: 0.25

Changing the optimizer from SGD to Adam with a suitable learning rate helped reduce overfitting by improving validation accuracy and balancing training accuracy. This shows how optimizer choice and tuning affect model generalization.

Bonus Experiment

Try using RMSprop optimizer with different learning rates and compare the validation accuracy and loss to Adam and SGD.

💡 Hint

Use learning rates like 0.001 and 0.0005 with RMSprop and observe how the model's validation accuracy changes.

Practice

1. Which optimizer in TensorFlow uses momentum to accelerate gradient descent and reduce oscillations?

easy

A. SGD with momentum

B. Adam

C. RMSprop

D. Adagrad

Solution

1. Step 1: Understand momentum in optimizers

   Momentum helps speed up SGD by accumulating past gradients to smooth updates.

2. Step 2: Identify optimizer using momentum

   SGD with momentum explicitly uses this technique, unlike Adam or RMSprop which use adaptive learning rates.

3. Final Answer:

   SGD with momentum -> Option A

4. Quick Check:

   Momentum = SGD with momentum [OK]

Hint: Momentum is a feature of SGD, not Adam or RMSprop [OK]

Common Mistakes:

• Confusing Adam's adaptive learning with momentum
• Thinking RMSprop uses momentum
• Mixing up Adagrad with momentum

2. Which of the following is the correct way to create an Adam optimizer in TensorFlow with a learning rate of 0.001?

easy

A. tf.optimizers.Adam(lr=0.001)

B. tf.AdamOptimizer(0.001)

C. tf.optimizers.Adam(learning_rate=0.001)

D. tf.optimizers.AdamOptimizer(learning_rate=0.001)

Solution

1. Step 1: Recall TensorFlow 2.x optimizer syntax

   In TensorFlow 2.x, optimizers are created via tf.optimizers.OptimizerName with named parameters.

2. Step 2: Check correct Adam optimizer syntax

   The correct call is tf.optimizers.Adam(learning_rate=0.001). Other options use outdated or incorrect names.

3. Final Answer:

   tf.optimizers.Adam(learning_rate=0.001) -> Option C

4. Quick Check:

   Correct syntax = tf.optimizers.Adam(learning_rate=0.001) [OK]

Hint: Use tf.optimizers.Adam with named learning_rate [OK]

Common Mistakes:

• Using old tf.AdamOptimizer from TF1.x
• Passing learning rate as positional argument
• Using non-existent tf.optimizers.AdamOptimizer

3. What will be the output loss value after one training step using RMSprop optimizer with learning rate 0.01 on a simple linear model trained on data x=[1,2], y=[2,4]? Assume initial weights are zero and mean squared error loss.

medium

A. 0.5

B. 9.5

C. 1.0

D. 4.0

Solution

1. Step 1: Calculate initial prediction and loss

   Initial weights zero means prediction is 0 for inputs. Loss = mean squared error = mean([4,16]) = 10.

2. Step 2: Perform one RMSprop update step

   RMSprop scales update by rms of gradient (first step rms ≈ 0.32*|g|). Gradients ≈[-10,-6] for [w,b], updates ≈[+0.032,+0.032]. New preds ≈[0.063,0.095], new loss ≈9.5.

3. Final Answer:

   9.5 -> Option B

4. Quick Check:

   Loss after step ≈ 9.5 [OK]

Hint: RMSprop first step small due to scaling, loss ~9.5 [OK]

Common Mistakes:

• Expecting sharp loss drop after one step
• Confusing learning rate effect
• Ignoring initial zero weights impact

4. You wrote this code to use Adam optimizer but get an error:

optimizer = tf.optimizers.Adam(lr=0.01)
model.compile(optimizer=optimizer, loss='mse')

What is the likely cause of the error?

medium

A. Model.compile does not accept optimizer objects

B. Adam optimizer does not accept float arguments

C. Loss function 'mse' is invalid

D. Learning rate must be named as learning_rate=0.01

Solution

1. Step 1: Check Adam optimizer argument requirements

   TF2.x Adam expects keyword 'learning_rate=', not TF1.x-style 'lr='.

2. Step 2: Identify error cause in code

   Using lr=0.01 causes TypeError (unexpected keyword). Correct: tf.optimizers.Adam(learning_rate=0.01).

3. Final Answer:

   Learning rate must be named as learning_rate=0.01 -> Option D

4. Quick Check:

   Named argument needed [OK]

Hint: Always name learning_rate in Adam optimizer [OK]

Common Mistakes:

• Using 'lr=0.01' keyword from TF1.x
• Assuming 'mse' is invalid loss
• Thinking optimizer object can't be passed

5. You want to train a model on noisy data that changes over time. Which optimizer is best suited to adapt learning rates per parameter and handle this noise effectively?

hard

A. Adam

B. Gradient Descent with fixed learning rate

C. RMSprop

D. SGD without momentum

Solution

1. Step 1: Understand optimizer strengths for noisy data

   Adam adapts learning rates per parameter and combines momentum and RMSprop ideas, handling noise well.

2. Step 2: Compare with other optimizers

   SGD without momentum and fixed learning rate struggle with noise. RMSprop adapts rates but Adam adds momentum for better stability.

3. Final Answer:

   Adam -> Option A

4. Quick Check:

   Best for noisy data = Adam [OK]

Hint: Adam adapts learning rates and handles noise best [OK]

Common Mistakes:

• Choosing plain SGD for noisy data
• Confusing RMSprop with Adam's momentum
• Ignoring adaptive learning rate benefits