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@tomasiser
Last active June 11, 2024 07:12
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Plateau-reduced optimization using pure NumPy
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Plateau-reduced optimization using pure NumPy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The **plateau-reduced optimization** paper (see the [project page](https://mfischer-ucl.github.io/prdpt/) and [GitHub](https://github.com/mfischer-ucl/prdpt/) by Michael Fischer and Tobias Ritschel) shows how to apply gradient-descent optimization even if:\n",
"\n",
"1) we do not know the function derivatives, and/or\n",
"2) the function contains plateaus that would otherwise give a zero derivative, and/or\n",
"3) the function is highly-dimensional.\n",
"\n",
"The trick is in estimating the partial derivatives (gradient) with a smooth blur kernel, which, surprisingly, leads to a mathematical formulation that does not even need the function derivatives in the first place.\n",
"\n",
"Michael and Tobias were very kind and published their example implementation in PyTorch and Mitsuba 3.\n",
"However, using these libraries might obfuscate how simple and genius the approach really is.\n",
"\n",
"In this implementation, I wanted to show how to implement the paper for optimizing an arbitrary function, using a **simple Python code without any libraries except for NumPy**, such that the intention of the algorithm is clear and not obfuscated by unnecessary things.\n",
"Note that I also used matplotlib to visualize the outputs, but that part can be easily removed.\n",
"The code is designed such that you can easily copy-paste the `estimate_gradient` function from this implementation and use it in your own projects.\n",
"\n",
"This Python notebook is split into two sections:\n",
"- a simple **1-dimensional example** (for functions that only have 1 parameter), and\n",
"- a general **n-dimensional example**, where all dimensions are estimated at once.\n",
"\n",
"Each section contains a different implementation of the `estimate_gradient` function.\n",
"\n",
"First, we import NumPy and matplotlib:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And here is a simple implementation of gradient descent that can be replaced by a more sophisticated approach if you want (SGD with Nesterov momentum, Adagrad, RMSProp, Adam, or similar):"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"class GradientDescent:\n",
" def __init__(self, step_size):\n",
" self.step_size = step_size\n",
" def step(self, params, gradient):\n",
" return params - self.step_size * gradient"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Minimizing a 1-dimensional function\n",
"\n",
"In a 1D case, `estimate_gradient(f, params, sigma, N)` is a very simple code that follows Algorithm 1 and Eq. 10 in the original paper:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def estimate_gradient(f, param, sigma, N):\n",
" grad = 0.0\n",
" for _ in range(N//2):\n",
" ksi = np.random.uniform(0.0, 1.0)\n",
" tau = np.sqrt(-2.0 * sigma * sigma * np.log(ksi))\n",
" grad += f(param + tau) - f(param - tau)\n",
" return grad / N"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's try the code on the following function `loss`, which is a piecewise-defined function containing several plateaus:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 700x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def loss(param):\n",
" x = param\n",
" if x < -2.0: return 1.0\n",
" if x < 0.0: return np.power(x/2, 2.0)\n",
" if x < 1.0: return 0.0\n",
" if x < 2.0: return -np.abs((x-1)/2)\n",
" if x < 4.0: return np.power((x-2)/2, 2.0) - 0.5\n",
" return 0.5\n",
"\n",
"def visualize():\n",
" x = np.linspace(-4.0, 5.0, 1000)\n",
" y = [loss(x_) for x_ in x]\n",
" fig, ax = plt.subplots(figsize=(7,3))\n",
" ax.plot(x, y, label=\"Loss function\")\n",
" ax.grid(color=(0.9,0.9,0.9))\n",
" ax.legend(fontsize=9, loc='upper right')\n",
"\n",
"visualize()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's now run the minimization of function `loss` using `estimate_gradient` and `GradientDescent`, starting at `-3.0`:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"initial_param = param = -3.0\n",
"sigma = 1.0\n",
"N = 2\n",
"step_size = 0.1\n",
"max_steps = 250\n",
"\n",
"def visualize(i):\n",
" x = np.linspace(-4.0, 5.0, 1000)\n",
" y = [loss(x_) for x_ in x]\n",
" fig, ax = plt.subplots(figsize=(7,3))\n",
" ax.set_title(f\"Iteration {i}\")\n",
" ax.plot(x, y, label=\"Loss function\")\n",
" ax.scatter(initial_param, loss(initial_param), marker='x', s=75, color='C3', zorder=10, label=\"Initial estimate\")\n",
" ax.scatter(param, loss(param), s=75, color='C3', zorder=10, label=\"Current estimate\")\n",
" ax.grid(color=(0.9,0.9,0.9))\n",
" ax.legend(fontsize=9, loc='upper right')\n",
"\n",
"visualize(0)\n",
"\n",
"np.random.seed(42)\n",
"optimizer = GradientDescent(step_size)\n",
"for i in range(max_steps):\n",
" gradient = estimate_gradient(loss, param, sigma, N)\n",
" param = optimizer.step(param, gradient)\n",
" if (i+1) % 50 == 0: visualize(i+1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Minimizing an n-dimensional function\n",
"\n",
"In the 1-dimensional case above, the `estimate_gradient` function was only 7 lines of code, because most of the mathematical operations were simplified in one dimension.\n",
"Now, in the multidimensional case, the `estimate_gradient` function gets a little bit more complicated.\n",
"Follow the original paper and supplement to understand what's going on.\n",
"\n",
"Note: The parameters `N` (for the gradient estimation) and `dim` (function dimensionality) are not related."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def estimate_gradient(f, params, sigma, N):\n",
" def gaussian(x, mu=0.0, sigma=1.0):\n",
" return 1.0 / (sigma * (2.0 * np.pi)**0.5) * np.exp(-0.5 * ((x - mu) / sigma) ** 2)\n",
"\n",
" def gaussian_gradient(x, sigma):\n",
" return -(x / sigma ** 2) * gaussian(x, mu=0.0, sigma=sigma)\n",
"\n",
" def monte_carlo_estimate(f_xi, p_xi):\n",
" N = f_xi.shape[0]\n",
" estimate = 1. / N * (f_xi / p_xi).sum(axis=0) # average along batch axis, leave dimension axis unchanged\n",
" return estimate\n",
"\n",
" def importance_sample_gaussian_gradient(N, sigma, is_antithetic, dim):\n",
" eps = 0.00001\n",
" randoms = np.random.uniform(0.0, 1.0, (N, dim))\n",
"\n",
" def icdf(x, sigma):\n",
" res = np.zeros_like(x)\n",
" res[mask == 1] = np.sqrt(-2.0 * sigma ** 2 * np.log(2.0 * (1.0 - x[mask == 1])))\n",
" res[mask == -1] = np.sqrt(-2.0 * sigma ** 2 * np.log(2.0 * x[mask == -1]))\n",
" return res\n",
"\n",
" # samples and antithetic samples\n",
" if is_antithetic:\n",
" randoms = np.concatenate([randoms, 1.0 - randoms])\n",
"\n",
" # avoid NaNs because of numerical instabilities in log\n",
" randoms[np.isclose(randoms, np.ones_like(randoms))] -= eps\n",
" randoms[np.isclose(randoms, np.zeros_like(randoms))] += eps\n",
" randoms[np.isclose(randoms, np.full_like(randoms, fill_value=0.5))] += eps\n",
" randoms[np.isclose(randoms, np.full_like(randoms, fill_value=-0.5))] -= eps\n",
"\n",
" mask = np.where(randoms < 0.5, -1.0, 1.0)\n",
" x_i = icdf(randoms, sigma=sigma) * mask\n",
"\n",
" f_xi = np.abs(x_i) * (1.0 / sigma ** 2) * gaussian(x_i, mu=0.0, sigma=sigma)\n",
" f_xi[f_xi == 0] += eps\n",
" p_xi = 0.5 * sigma * (2.0 * np.pi)**0.5 * f_xi\n",
"\n",
" return x_i, p_xi\n",
"\n",
" def convolve(kernel, perturbed_f, importance_fn, theta, sigma, N, is_antithetic):\n",
" # sample, get kernel(samples), get perturbed_f(samples), return Monte Carlo estimate of output\n",
" # expects theta to be of shape [1, n], where n is dimensionality\n",
"\n",
" dim = theta.shape[-1]\n",
"\n",
" # get importance-sampled taus\n",
" tau, pdf = importance_fn(N, sigma, is_antithetic, dim)\n",
"\n",
" # get kernel weight at taus\n",
" weights = kernel(tau, sigma)\n",
"\n",
" # twice as many samples when antithetic\n",
" if is_antithetic: N *= 2\n",
"\n",
" # shift samples around current parameter\n",
" perturbed_theta = np.concatenate([theta] * N, axis=0) - tau\n",
" values = perturbed_f(perturbed_theta) # output shape [N]\n",
"\n",
" # weight output by kernel, Monte Carlo estimate gradient\n",
" output = np.expand_dims(values, -1) * weights\n",
" forward_output = monte_carlo_estimate(output, pdf)\n",
"\n",
" return forward_output\n",
"\n",
" def perturbed_f(perturbed_theta):\n",
" values = []\n",
" for j in range(perturbed_theta.shape[0]): # for each sample\n",
" perturbed_value = f(perturbed_theta[j,:])\n",
" values.append(perturbed_value)\n",
" return np.stack(values)\n",
" \n",
" return convolve(gaussian_gradient, perturbed_f, importance_sample_gaussian_gradient, np.array([params]), sigma, N, True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example\n",
"\n",
"Let's try to optimize the following 3-dimensional problem.\n",
"We want to move (2 dimensions: x,y axes) and rotate (1 dimension) a small square such that it matches the target image."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 300x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"resolution = 300\n",
"square_size = 100\n",
"target_parameters = [resolution*3/4, resolution*3/4, 45.0] # center x, center y, angle (degrees)\n",
"\n",
"def image_with_rotated_square(center_x, center_y, angle):\n",
" def implicit_function(xy):\n",
" x, y = xy[0] - center_x, xy[1] - center_y\n",
" angle_ = np.deg2rad(angle) - np.pi/4.0\n",
" return np.abs(y * np.cos(angle_) - x * np.sin(angle_)) + np.abs(x * np.cos(angle_) + y * np.sin(angle_)) < square_size / 2.0\n",
" image = np.ones((resolution, resolution))\n",
" image[implicit_function(np.meshgrid(range(resolution),range(resolution)))] = 0.0\n",
" return image\n",
"\n",
"target_image = image_with_rotated_square(*target_parameters)\n",
"\n",
"def visualize():\n",
" fig, ax = plt.subplots(figsize=(3,3))\n",
" ax.set_title(\"Target image\")\n",
" ax.imshow(target_image, cmap=\"Greys\")\n",
"\n",
"visualize()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we optimize the 3 parameters (x, y, angle) using `estimate_gradient` on our `loss` function, which is a simple difference metric between the current image and the target image:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x300 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x300 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x300 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x300 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x300 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x300 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x300 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"initial_params = params = [resolution*2/4, resolution*2/4, 0.0] # center x, center y, angle (degrees)\n",
"sigma = 10.0\n",
"N = 4\n",
"step_size = 0.05\n",
"max_steps = 600\n",
"loss_history = []\n",
"\n",
"def loss(params):\n",
" current_image = image_with_rotated_square(*params)\n",
" return np.sum(np.abs(current_image - target_image))\n",
"\n",
"def visualize(i):\n",
" fig, axs = plt.subplots(ncols=2, figsize=(6,3))\n",
" axs[0].set_title(f\"Iteration {i}\")\n",
" axs[1].set_title(\"Target image\")\n",
" axs[0].imshow(image_with_rotated_square(*params), cmap=\"Greys\", vmin=0.0, vmax=1.0)\n",
" axs[1].imshow(target_image, cmap=\"Greys\", vmin=0.0, vmax=1.0)\n",
" plt.show()\n",
"\n",
"visualize(0)\n",
"\n",
"np.random.seed(42)\n",
"optimizer = GradientDescent(step_size)\n",
"for i in range(max_steps):\n",
" gradient = estimate_gradient(loss, np.array(params), sigma, N)\n",
" params = optimizer.step(params, gradient)\n",
" loss_history.append(loss(params))\n",
" if (i+1) % 100 == 0: visualize(i+1)\n",
"\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"ax.set_title(\"Loss\")\n",
"ax.plot(loss_history)\n",
"ax.set_xlabel(\"Iteration\")\n",
"ax.set_ylim(0)\n",
"ax.grid(color=(0.9,0.9,0.9))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## How to further improve the code?\n",
"\n",
"This implementation focuses on simplicity and can be further improved.\n",
"Follow the original paper and PyTorch implementation for inspiration:\n",
"\n",
"- Normalize the parameter space to [0,1]. For example, in the square example, the square position ranges roughly from 0 to 300 pixels, but the meaningful rotation angles are only from 0 to 90 degrees (due to symmetry). Therefore, the parameter ranges are ([0,300], [0,300], [0,90]). If all of them were normalized to [0,1], the proper `sigma` parameter would be easier to find and it would converge better.\n",
"\n",
"- The `sigma` parameter is a constant, but you can make it dynamic (large at the beginning and decreasing towards later iterations, where the parameters should not change that much anymore)."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "env",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.12"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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