Fix bug in nesterov optimizer

backend/src/optimization_logic.py

@@ -126,7 +126,7 @@ def nesterov_univariate(
         else:
             m = momentum * (x_values[-1] - x_values[-2])
 
-        x_lookahead = x - m
+        x_lookahead = x + m
         x = x_lookahead - learning_rate * f_prime(x_lookahead)
 
         x_values.append(x)
@@ -173,8 +173,8 @@ def nesterov_bivariate(
             mx = momentum * (x_values[-1] - x_values[-2])
             my = momentum * (y_values[-1] - y_values[-2])
 
-        x_lookahead = x - mx
-        y_lookahead = y - my
+        x_lookahead = x + mx
+        y_lookahead = y + my
 
         x = x_lookahead - learning_rate * fx(x_lookahead, y_lookahead)
         y = y_lookahead - learning_rate * fy(x_lookahead, y_lookahead)
@@ -300,7 +300,7 @@ def adagrad_univariate(
     for i in range(steps - 1):
         g = f_prime(x)
         v += g ** 2
-        x = x - (learning_rate / (np.sqrt(v) + epsilon)) * g
+        x = x - (learning_rate / (np.sqrt(v + epsilon))) * g
 
         x_values.append(x)
         y_values.append(f(x))
@@ -347,8 +347,8 @@ def adagrad_bivariate(
         vx += gx ** 2
         vy += gy ** 2
 
-        x = x - (learning_rate / (np.sqrt(vx) + epsilon)) * gx
-        y = y - (learning_rate / (np.sqrt(vy) + epsilon)) * gy
+        x = x - (learning_rate / (np.sqrt(vx + epsilon))) * gx
+        y = y - (learning_rate / (np.sqrt(vy + epsilon))) * gy
 
         x_values.append(x)
         y_values.append(y)
@@ -387,7 +387,7 @@ def rmsprop_univariate(
     for i in range(steps - 1):
         g = f_prime(x)
         v = beta * v + (1 - beta) * g ** 2
-        x = x - (learning_rate / (np.sqrt(v) + epsilon)) * g
+        x = x - (learning_rate / (np.sqrt(v + epsilon))) * g
 
         x_values.append(x)
         y_values.append(f(x))
@@ -435,8 +435,8 @@ def rmsprop_bivariate(
         vx = beta * vx + (1 - beta) * gx ** 2
         vy = beta * vy + (1 - beta) * gy ** 2
 
-        x = x - (learning_rate / (np.sqrt(vx) + epsilon)) * gx
-        y = y - (learning_rate / (np.sqrt(vy) + epsilon)) * gy
+        x = x - (learning_rate / (np.sqrt(vx + epsilon))) * gx
+        y = y - (learning_rate / (np.sqrt(vy + epsilon))) * gy
 
         x_values.append(x)
         y_values.append(y)

dist/assets/{index-BoSq-s5V.js → index-CPl3lL5a.js}

@@ -3843,4 +3843,4 @@ The plot is interactive:
 - Click and drag to pan
 - Scroll to zoom
 - In bivariate mode, click **Update color scale** to rescale the heatmap so that the currently visible minimum and maximum values define the color range
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+`,ij={"Gradient Descent":{learningRate:"0.1",momentum:"0.0"},Nesterov:{learningRate:"0.1",momentum:"0.0"},Adam:{learningRate:"0.1",beta1:"0.9",beta2:"0.999",epsilon:"1e-8"},Adagrad:{learningRate:"0.1",epsilon:"1e-8"},RMSProp:{learningRate:"0.1",beta:"0.9",epsilon:"1e-8"},Adadelta:{beta:"0.9",epsilon:"1e-3"},Newton:{}},$6={"--Custom--":"x^2",Quadratic:"x^2","Local Minima":"x^2 - 0.1cos(20x)",Plateau:"x^4"},J6={"--Custom--":"x^2 + 3y^2",Quadratic:"x^2 + 3y^2",Small:"(0.05x)^2 + 3(0.05y)^2",Ackley:"-20exp(-0.2 sqrt(0.5(x^2 + y^2))) - exp(0.5(cos(2 pi x) + cos(2 pi y))) + e + 20",Rasteringin:"20 + (x^2 - 10cos(2 pi x)) + (y^2 - 10cos(2 pi y))",Rosenbrock:"(1 - x)^2 + 100(y - x^2)^2"};function oj({settings:Ie,setSettings:ht,onRandomInitialPoint:St,trajectoryValues:wt,onReset:lr,onNextStep:vr,onPrevStep:Lr}){const rn=["Settings","Optimize","Usage"],[xn,$r]=up.useState("Settings");function Tn(Ri,Ts){if(Ri==="algorithm"){const Si=ij[Ts];ht({...Ie,algorithm:Ts,...Si})}else 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dist/assets/{pyodide.worker-jb0eIAfr.js → pyodide.worker-DcyL_a_W.js}

@@ -472,7 +472,7 @@ def nesterov_univariate(
         else:
             m = momentum * (x_values[-1] - x_values[-2])
 
-        x_lookahead = x - m
+        x_lookahead = x + m
         x = x_lookahead - learning_rate * f_prime(x_lookahead)
 
         x_values.append(x)
@@ -519,8 +519,8 @@ def nesterov_bivariate(
             mx = momentum * (x_values[-1] - x_values[-2])
             my = momentum * (y_values[-1] - y_values[-2])
 
-        x_lookahead = x - mx
-        y_lookahead = y - my
+        x_lookahead = x + mx
+        y_lookahead = y + my
 
         x = x_lookahead - learning_rate * fx(x_lookahead, y_lookahead)
         y = y_lookahead - learning_rate * fy(x_lookahead, y_lookahead)
@@ -646,7 +646,7 @@ def adagrad_univariate(
     for i in range(steps - 1):
         g = f_prime(x)
         v += g ** 2
-        x = x - (learning_rate / (np.sqrt(v) + epsilon)) * g
+        x = x - (learning_rate / (np.sqrt(v + epsilon))) * g
 
         x_values.append(x)
         y_values.append(f(x))
@@ -693,8 +693,8 @@ def adagrad_bivariate(
         vx += gx ** 2
         vy += gy ** 2
 
-        x = x - (learning_rate / (np.sqrt(vx) + epsilon)) * gx
-        y = y - (learning_rate / (np.sqrt(vy) + epsilon)) * gy
+        x = x - (learning_rate / (np.sqrt(vx + epsilon))) * gx
+        y = y - (learning_rate / (np.sqrt(vy + epsilon))) * gy
 
         x_values.append(x)
         y_values.append(y)
@@ -733,7 +733,7 @@ def rmsprop_univariate(
     for i in range(steps - 1):
         g = f_prime(x)
         v = beta * v + (1 - beta) * g ** 2
-        x = x - (learning_rate / (np.sqrt(v) + epsilon)) * g
+        x = x - (learning_rate / (np.sqrt(v + epsilon))) * g
 
         x_values.append(x)
         y_values.append(f(x))
@@ -781,8 +781,8 @@ def rmsprop_bivariate(
         vx = beta * vx + (1 - beta) * gx ** 2
         vy = beta * vy + (1 - beta) * gy ** 2
 
-        x = x - (learning_rate / (np.sqrt(vx) + epsilon)) * gx
-        y = y - (learning_rate / (np.sqrt(vy) + epsilon)) * gy
+        x = x - (learning_rate / (np.sqrt(vx + epsilon))) * gx
+        y = y - (learning_rate / (np.sqrt(vy + epsilon))) * gy
 
         x_values.append(x)
         y_values.append(y)

dist/index.html

@@ -5,7 +5,7 @@
     <link rel="icon" type="image/svg+xml" href="/vite.svg" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" />
     <title>Optimization</title>
-    <script type="module" crossorigin src="/assets/index-BoSq-s5V.js"></script>
+    <script type="module" crossorigin src="/assets/index-CPl3lL5a.js"></script>
     <link rel="stylesheet" crossorigin href="/assets/index-5gsYPC1K.css">
   </head>
   <body>