update adadelta optimizer question to new format

Author: mavleo96

Problems/X_adadelta_optimizer/solution.py

@@ -0,0 +1 @@
+Implement the Adadelta optimizer update step function. Your function should take the current parameter value, gradient, and moving averages as inputs, and return the updated parameter value and new moving averages. The function should handle both scalar and array inputs, and include proper input validation.

questions/x_adadelta-optimizer/description.md

@@ -0,0 +1,5 @@
+{
+  "input": "parameter = 1.0, grad = 0.1, u = 1.0, v = 1.0, rho = 0.95, epsilon = 1e-6",
+  "output": "(0.89743, 0.9505, 0.95053)",
+  "explanation": "The Adadelta optimizer computes updated values for the parameter, first moment (u), and second moment (v). With input values parameter=1.0, grad=0.1, u=1.0, v=1.0, and rho=0.95, the updated parameter becomes 0.89743."
+}

questions/x_adadelta-optimizer/example.json

@@ -56,8 +56,8 @@ Return tuple: (updated_parameter, updated_v, updated_u)
 # Example usage:
 parameter = 1.0
 grad = 0.1
-v = 0.0
-u = 0.0
+v = 1.0
+u = 1.0
 
 new_param, new_v, new_u = adadelta_optimizer(parameter, grad, v, u)
 ```

Problems/X_adadelta_optimizer/learn.md questions/x_adadelta-optimizer/learn.mdProblems/X_adadelta_optimizer/learn.md renamed to questions/x_adadelta-optimizer/learn.md

@@ -0,0 +1,17 @@
+{
+  "id": "X",
+  "title": "Adadelta Optimizer",
+  "difficulty": "easy",
+  "category": "Deep Learning",
+  "video": "",
+  "likes": "0",
+  "dislikes": "0",
+  "contributor": [
+    {
+      "profile_link": "https://github.com/mavleo96",
+      "name": "Vijayabharathi Murugan"
+    }
+  ],
+  "tinygrad_difficulty": null,
+  "pytorch_difficulty": null
+}

questions/x_adadelta-optimizer/meta.json

@@ -0,0 +1,44 @@
+import numpy as np
+
+def adadelta_optimizer(parameter, grad, u, v, rho=0.95, epsilon=1e-6):
+    """
+    Update parameters using the AdaDelta optimizer.
+    AdaDelta is an extension of AdaGrad that seeks to reduce its aggressive,
+    monotonically decreasing learning rate.
+
+    Args:
+        parameter: Current parameter value
+        grad: Current gradient
+        u: Running average of squared gradients
+        v: Running average of squared parameter updates
+        rho: Decay rate for the moving average (default=0.95)
+        epsilon: Small constant for numerical stability (default=1e-6)
+
+    Returns:
+        tuple: (updated_parameter, updated_u, updated_v)
+    """
+    assert 0 <= rho < 1, "Rho must be between 0 and 1"
+    assert epsilon > 0, "Epsilon must be positive"
+    assert all(u >= 0) if isinstance(u, np.ndarray) else u >= 0, "u must be non-negative"
+    assert all(v >= 0) if isinstance(v, np.ndarray) else v >= 0, "v must be non-negative"
+
+    # Update running average of squared gradients
+    u = rho * u + (1 - rho) * grad**2
+
+    # Compute RMS of gradient
+    RMS_g = np.sqrt(u + epsilon)
+
+    # Compute RMS of parameter updates
+    RMS_dx = np.sqrt(v + epsilon)
+
+    # Compute parameter update
+    dx = -RMS_dx / RMS_g * grad
+
+    # Update running average of squared parameter updates
+    v = rho * v + (1 - rho) * dx**2
+
+    # Update parameters
+    parameter = parameter + dx
+
+    return np.round(parameter, 5), np.round(u, 5), np.round(v, 5)
+

questions/x_adadelta-optimizer/solution.py

@@ -0,0 +1,21 @@
+import numpy as np
+
+def adadelta_optimizer(parameter, grad, u, v, rho=0.95, epsilon=1e-6):
+    """
+    Update parameters using the AdaDelta optimizer.
+    AdaDelta is an extension of AdaGrad that seeks to reduce its aggressive,
+    monotonically decreasing learning rate.
+
+    Args:
+        parameter: Current parameter value
+        grad: Current gradient
+        u: Running average of squared gradients
+        v: Running average of squared parameter updates
+        rho: Decay rate for the moving average (default=0.95)
+        epsilon: Small constant for numerical stability (default=1e-6)
+
+    Returns:
+        tuple: (updated_parameter, updated_u, updated_v)
+    """
+    # Your code here
+    return np.round(parameter, 5), np.round(u, 5), np.round(v, 5)

questions/x_adadelta-optimizer/starter_code.py

@@ -0,0 +1,22 @@
+[
+    {
+        "test": "print(adadelta_optimizer(1., 0.5, 1., 1., 0.95, 1e-6))",
+        "expected_output": "(0.49035, 0.9625, 0.96299)"
+    },
+    {
+        "test": "print(adadelta_optimizer(np.array([1., 2.]), np.array([0.1, 0.2]), np.array([1., 1.]), np.array([1., 1.]), 0.95, 1e-6))",
+        "expected_output": "(array([0.89743, 1.79502]), array([0.9505, 0.952]), array([0.95053, 0.9521]))"
+    },
+    {
+        "test": "print(adadelta_optimizer(np.array([1., 2.]), np.array([0., 0.2]), np.array([0., 1.]), np.array([0., 1.]), 0.95, 1e-6))",
+        "expected_output": "(array([1., 1.79502]), array([0., 0.952]), array([0., 0.9521]))"
+    },
+    {
+        "test": "print(adadelta_optimizer(np.array([1., 1.]), np.array([1., 1.]), np.array([10000., 1.]), np.array([1., 1.]), 0.95, 1e-6))",
+        "expected_output": "(array([0.98974, 0.]), array([9500.05, 1.]), array([0.95001, 1.]))"
+    },
+    {
+        "test": "print(adadelta_optimizer(1., 0.5, 1., 1., 0., 1e-6))",
+        "expected_output": "(0.999, 0.25, 0.0)"
+    }
+]