{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import torch\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Differentiable Agent-Based Models\n", "\n", "In previous notebooks we learned how automatic differentiation (AD) can be used to obtain gradients from stochastic computer programs. Next, we will use what we have learned to implement several differentiable programs, including a differentiable agent-based model (ABM).\n", "\n", "\n", "\n", "## The Random Walk\n", "\n", "To begin let's implement a one-dimensonal random walk. Recall that a one-dimensional random walk is given by the following recursion:\n", "\n", "$$\n", "x_{t+1} = x_t + \\begin{cases}1 &\\mathrm{if} &\\xi = 1 \\\\ -1 &\\mathrm{if} &\\xi = 0\\end{cases}, \\quad \\xi \\sim \\mathrm{Bern}({\\theta})\n", "$$\n", "\n", "where $\\text{Bern}$ denotes the Bernoulli distribution, $x_{t}$ denotes the position observed after $t$ steps, and $\\theta$ denotes a parameter determining the probability of moving in the positive direction. Let's use PyTorch to implement this model as a stochastic program called `random_walk`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def random_walk(theta, n_timesteps):\n", " x = torch.tensor([0.])\n", " for i in range(n_timesteps-1):\n", " xi = torch.distributions.Bernoulli(theta).sample()\n", " if xi == 1:\n", " next_x = x[-1] + 1\n", " else:\n", " next_x = x[-1] - 1\n", " x = torch.hstack((x, next_x))\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's forward simulate our stochastic program to make sure everything is working correclty!" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = 0.2\n", "n_timesteps = 100\n", "x = random_walk(theta, n_timesteps)\n", "plt.plot(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we are confident the model is correclty implemented, let's check whether PyTorch can compute a gradient. Since `random_walk` returns a time series and has one parameter the Jacobian,\n", "\n", "$$\n", "(J)_t = \\frac{\\partial {x_t}}{\\partial \\theta},\n", "$$\n", "\n", "will be a row vector. Let's plot the Jacobian at $\\theta = 0.2$ by using the `torch.autograd` module." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dx_dtheta = torch.autograd.functional.jacobian(\n", " lambda x: random_walk(theta=x, n_timesteps=n_timesteps), torch.tensor(theta)\n", ")\n", "plt.plot(dx_dtheta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We immediately see that all entries of the Jacobian are zero! This is happening for two reasons. Firstly, as we saw in the previous notebook, the Bernoulli distribution is not differentiable by default and we need to a use technique like the Gumbel-Softmax trick to differentiate through it. We can implement the Gumbel-Sofxmax trick in ``random walk`` by replacing\n", "\n", "```python\n", " xi = torch.distributions.Bernoulli(theta).sample()\n", "``` \n", "\n", "with \n", "\n", "```python\n", "logits = torch.hstack((theta, 1 - theta)).log()\n", "xi = torch.nn.functional.gumbel_softmax(logits, tau=tau, hard=True)[0]\n", "```\n", "\n", "There is also an issue with control flow. Under the hood, PyTorch builds a **static computational graph**. This means that the structure of the computational graph cannot change at run-time based on the outcome of control flow statements. As a result, the gradient will not correctly flow backwards through `if` statements that depend on the parameters we want to differentiate with respect to. Analysing the code of `random_walk` we find the following control flow statement:\n", "\n", "```python\n", "xi = torch.distributions.Bernoulli(theta).sample()\n", "if xi == 1:\n", " next_x = x[-1] + 1\n", "else:\n", " next_x = x[-1] - 1\n", "```\n", "\n", "Since the `if` statement predicate depends on `xi` which in turn depends on `theta`, the gradient will not flow backwards properly. To fix this issue, we can reimplement the `if` statement using **masking**.\n", "\n", "```python\n", "xi = torch.distributions.Bernoulli(theta)\n", "next_x = xi * (x[-1] + 1) + (1-xi) * (x[-1] - 1)\n", "```\n", "\n", "Note that if `xi = 1` then `next_x` will be equal to `x[-1] +1` as `(1-xi)` will be equal to zero. That is, the `else` output of the original `if` statement is *masked out*. Likewise, if `xi = 0` then `next_x` will be equal to `x[-1] - 1` as the output `(x[-1] + 1)` is masked out by its multiplier `xi`. In other words, the code above is completely equivalent to the previous `if` statement. Moreover this code will play nicely with the static compuational graph generated by PyTorch as it contains no control flow statements.\n", "\n", "Let's rewrite `random_walk` to implement both masking and the Gumbel-Softmax trick!\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def random_walk(theta, n_timesteps, tau=0.1):\n", " x = torch.tensor([0.0])\n", " for i in range(n_timesteps - 1):\n", " logits = torch.hstack((theta, 1 - theta)).log()\n", " xi = torch.nn.functional.gumbel_softmax(logits, tau=tau, hard=True)[0]\n", " next_x = x[-1] + 2 * xi - 1\n", " x = torch.hstack((x, next_x))\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's run a simulation to check our model runs properly." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = torch.tensor(0.4)\n", "n_timesteps = 100\n", "x = random_walk(theta, n_timesteps)\n", "plt.plot(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both implementations of `random_walk` behave identically. Any difference observed between simulation outputs is caused by the randomness of the Bernoulli distribution. This is because we set `hard=True` when employing the Gumbel-Softmax trick, ensuring that the Bernoulli distribution is only replaced by a continuous relaxation when applying the chain rule during the backwards pass. If the previous sentence is confusing, you should review the previous notebook. Let's check the Jacobian again!\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dx_dtheta = torch.autograd.functional.jacobian(\n", " lambda x: random_walk(theta=x, n_timesteps=n_timesteps, tau=1.0), theta\n", ")\n", "plt.plot(dx_dtheta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PyTorch is now giving us non-zero derivatives thanks to our changes. Recall that the bias-variance trade-off of the Gumbel-Softmax trick is controlled implicitly by setting the temperatrue $\\tau$. Let's investigate this trade-off in the context of the random walk. Thankfully, the exact analytical gradient is easy to derive for the random walk:\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{\\partial}{\\partial \\theta} \\mathbb E[x_t] & = \\frac{\\partial}{\\partial \\theta} \\mathbb E\\left[ \\sum_{j=1}^{t} 2 \\mathrm{Bern(\\theta)} - 1 \\right]\\\\\n", " & = \\frac{\\partial}{\\partial \\theta} (2 t \\theta - t) \\\\\n", " & = 2t\n", "\\end{align}\n", "$$\n", "\n", "This means we can compare the gradients output by PyTorch against the analytical gradient for different temperature settings!\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "taus = [0.1, 0.5, 1.0]\n", "n_gradient_samples = 50\n", "n_timesteps = 50\n", "gradients_per_tau = {tau: [] for tau in taus}\n", "for tau in taus:\n", " for i in range(n_gradient_samples):\n", " dx_dtheta = torch.autograd.functional.jacobian(\n", " lambda x: random_walk(theta=x, n_timesteps=n_timesteps, tau=tau),\n", " theta,\n", " vectorize=True,\n", " )\n", " gradients_per_tau[tau].append(dx_dtheta)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "for i, tau in enumerate(gradients_per_tau):\n", " for grad in gradients_per_tau[tau]:\n", " ax.plot(grad, color=f\"C{i}\", alpha=0.2)\n", " ax.plot(\n", " sum(gradients_per_tau[tau]) / n_gradient_samples,\n", " color=f\"C{i}\",\n", " linestyle=\"--\",\n", " label=rf\"$\\tau$ = {tau} [mean]\",\n", " lw=3\n", " )\n", " ax.plot([], [], color=f\"C{i}\", label=rf\"$\\tau$ = {tau}\")\n", "ax.plot(\n", " range(n_timesteps),\n", " 2 * np.array(range(n_timesteps)),\n", " color=\"black\",\n", " linestyle=\"--\",\n", " label=\"true gradient\",\n", ")\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Unsurprisingly, as $\\tau$ decreases, the mean of each gradient estimate gets closer to the analytical gradient, whilst the variance increases significantly. In this case, it may be more reasonable to use $\\tau=0.5$ rather than $\\tau=0.1$, since a small increase in bias is compensated by a large reduction in variance.\n", "\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "In this notebook, we used the tools we have learned so far to build a simple differenitable program. In the next notebook, we will see how the same tools can be applied to build a differentiable economic ABM. Moreover, we will finally highlight the advantages of differentiability when it comes to calibration!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "torch2", "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": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 2 }