{ "cells": [ { "cell_type": "markdown", "id": "e89f81f1", "metadata": {}, "source": [ "# Parallel (associative-scan) solvers\n", "\n", "The Riccati recursion in LQR is sequential: step $t$ needs step $t+1$. However, the recursion can\n", "be rewritten as an **associative** combination of per-step elements, which\n", "`jax.lax.associative_scan` evaluates in $O(\\log T)$ parallel depth (Särkkä & García-Fernández,\n", "2023). diffilqrax provides parallel counterparts of every solver:\n", "\n", "| sequential | parallel |\n", "|---|---|\n", "| `lqr.solve_lqr` | `plqr.solve_plqr` |\n", "| `ilqr.ilqr_solver` | `parallel_ilqr.pilqr_solver` |\n", "| `diff_lqr.dlqr` | `parallel_dlqr.pdlqr` |\n", "| `diff_ilqr.dilqr` | `parallel_dilqr.pdilqr` |\n", "\n", "The parallel versions take the same arguments and converge to the same solutions. This notebook\n", "checks that on a long-horizon iLQR problem and shows how run time scales with the horizon.\n", "\n", "The parallel solvers do more total work, so on a **CPU** you should not expect a speed-up; at\n", "best they roughly match the sequential solver. The benefit appears on a **GPU** with long\n", "horizons, where the sequential solver is limited by its $O(T)$ depth." ] }, { "cell_type": "code", "execution_count": 1, "id": "00ecd3b6", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:41:27.642118Z", "iopub.status.busy": "2026-10-14T22:41:27.641821Z", "iopub.status.idle": "2026-10-14T22:41:28.278938Z", "shell.execute_reply": "2026-10-14T22:41:28.278341Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "device: TFRT_CPU_0\n" ] } ], "source": [ "import time as timer\n", "\n", "import jax\n", "import jax.numpy as jnp\n", "import jax.random as jr\n", "import matplotlib.pyplot as plt\n", "\n", "from diffilqrax.ilqr import ilqr_solver\n", "from diffilqrax.parallel_ilqr import pilqr_solver, dynamics_defects\n", "from diffilqrax.diff_ilqr import dilqr\n", "from diffilqrax.parallel_dilqr import pdilqr\n", "from diffilqrax.typs import System, ModelDims, iLQRParams, Theta\n", "\n", "jax.config.update(\"jax_enable_x64\", True)\n", "print(\"device:\", jax.devices()[0])" ] }, { "cell_type": "markdown", "id": "e5101561", "metadata": {}, "source": [ "## A long-horizon problem\n", "\n", "A stable tanh RNN, $x_{t+1} = \\tanh(U_h x_t + W_h u_t)$, tracks a slow sine wave in every state." ] }, { "cell_type": "code", "execution_count": 2, "id": "4b600865", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:41:28.282832Z", "iopub.status.busy": "2026-10-14T22:41:28.282597Z", "iopub.status.idle": "2026-10-14T22:41:28.861235Z", "shell.execute_reply": "2026-10-14T22:41:28.860597Z" } }, "outputs": [], "source": [ "N, M = 8, 3\n", "k1, k2 = jr.split(jr.PRNGKey(0))\n", "theta = Theta(Uh=0.8 * jr.normal(k1, (N, N)) / jnp.sqrt(N), Wh=jr.normal(k2, (N, M)) / jnp.sqrt(N), sigma=0.0, Q=None)\n", "\n", "\n", "def make_model(horizon):\n", " def cost(t, x, u, th):\n", " return jnp.sum((x - 0.5 * jnp.sin(t / 50.0)) ** 2) + 0.1 * jnp.sum(u**2)\n", "\n", " def costf(x, th):\n", " return jnp.sum(x**2)\n", "\n", " def dynamics(t, x, u, th):\n", " return jnp.tanh(th.Uh @ x + th.Wh @ u)\n", "\n", " return System(cost, costf, dynamics, ModelDims(n=N, m=M, horizon=horizon, dt=0.1))\n", "\n", "\n", "params = iLQRParams(x0=jnp.zeros(N), theta=theta)" ] }, { "cell_type": "markdown", "id": "9200c22c", "metadata": {}, "source": [ "## Same solution\n", "\n", "`pilqr_solver` has two ways to roll out a candidate step:\n", "\n", "- `rollout=\"feedback\"` (default) runs the parallel Riccati scan, then a sequential non-linear\n", " rollout under the feedback policy, exactly like `ilqr_solver`. Every iterate is a feasible\n", " trajectory.\n", "- `rollout=\"parallel\"` uses **multiple shooting**. The states are also optimisation variables, the\n", " dynamics defects $d_t = f(x_t, u_t) - x_{t+1}$ enter the local LQR, and the whole step is\n", " computed with associative scans. Iterates are feasible only at convergence, so we report the\n", " largest defect." ] }, { "cell_type": "code", "execution_count": 3, "id": "ec3abdaf", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:41:28.864605Z", "iopub.status.busy": "2026-10-14T22:41:28.864372Z", "iopub.status.idle": "2026-10-14T22:41:58.620285Z", "shell.execute_reply": "2026-10-14T22:41:58.619475Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ilqr J = 745.6031498673\n", "pilqr feedback J = 745.6031498673 max|ΔU| = 1.2e-15\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "pilqr parallel J = 745.6031498673 max|ΔU| = 7.0e-13 max defect = 3.3e-16\n" ] } ], "source": [ "T = 1000\n", "model = make_model(T)\n", "Us_init = jnp.zeros((T, M))\n", "\n", "(Xs, Us, _), J, _ = ilqr_solver(model, params, Us_init, max_iter=200)\n", "(Xf, Uf, _), Jf, _ = pilqr_solver(model, params, Us_init, max_iter=200, rollout=\"feedback\")\n", "(Xp, Up, _), Jp, _ = pilqr_solver(model, params, Us_init, max_iter=200, rollout=\"parallel\")\n", "\n", "print(f\"ilqr J = {float(J):.10f}\")\n", "print(f\"pilqr feedback J = {float(Jf):.10f} max|ΔU| = {jnp.max(jnp.abs(Uf - Us)):.1e}\")\n", "print(f\"pilqr parallel J = {float(Jp):.10f} max|ΔU| = {jnp.max(jnp.abs(Up - Us)):.1e} \"\n", " f\"max defect = {jnp.max(jnp.abs(dynamics_defects(model, params, Xp, Up))):.1e}\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "673b7f96", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:41:58.623605Z", "iopub.status.busy": "2026-10-14T22:41:58.623341Z", "iopub.status.idle": "2026-10-14T22:42:00.473076Z", "shell.execute_reply": "2026-10-14T22:42:00.472513Z" }, "tags": [ "thumbnail" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "time = jnp.arange(T + 1)\n", "fig, axes = plt.subplots(2, 1, figsize=(9, 4.5), sharex=True, layout=\"constrained\")\n", "axes[0].plot(time, 0.5 * jnp.sin(time / 50.0), \"k\", lw=0.8, label=\"target\")\n", "for (X, U), style, label in [((Xs, Us), \"-\", \"ilqr\"), ((Xf, Uf), \"--\", \"pilqr feedback\"), ((Xp, Up), \":\", \"pilqr parallel\")]:\n", " axes[0].plot(time, X[:, 0], style, label=label)\n", " axes[1].plot(time[:-1], U[:, 0], style)\n", "axes[0].set(ylabel=\"$x_0$\")\n", "axes[1].set(ylabel=\"$u_0$\", xlabel=\"t\")\n", "axes[0].legend(ncol=4, fontsize=8);" ] }, { "cell_type": "markdown", "id": "b6d81305", "metadata": {}, "source": [ "## Gradients agree too\n", "\n", "`pdilqr` is the parallel counterpart of `dilqr`. Both the forward solve and the adjoint LQR in the\n", "reverse pass use associative scans." ] }, { "cell_type": "code", "execution_count": 5, "id": "dc1f9eea", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:42:00.475802Z", "iopub.status.busy": "2026-10-14T22:42:00.475609Z", "iopub.status.idle": "2026-10-14T22:42:25.829062Z", "shell.execute_reply": "2026-10-14T22:42:25.828568Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dL/dUh: relative difference 9.8e-15\n", "dL/dWh: relative difference 7.1e-15\n" ] } ], "source": [ "Ts = 200\n", "model_s = make_model(Ts)\n", "U0 = jnp.zeros((Ts, M))\n", "\n", "\n", "def loss(solver, th):\n", " return jnp.sum(solver(model_s, iLQRParams(params.x0, th), U0, max_iter=200) ** 2)\n", "\n", "\n", "g_seq = jax.grad(lambda th: loss(dilqr, th))(theta)\n", "g_par = jax.grad(lambda th: loss(pdilqr, th))(theta)\n", "for name in (\"Uh\", \"Wh\"):\n", " a, b = getattr(g_par, name), getattr(g_seq, name)\n", " print(f\"dL/d{name}: relative difference {jnp.linalg.norm(a - b) / jnp.linalg.norm(b):.1e}\")" ] }, { "cell_type": "markdown", "id": "92d6b7b2", "metadata": {}, "source": [ "## Scaling with the horizon\n", "\n", "We time one jitted solve at several horizons. The absolute numbers depend on your hardware. On a\n", "CPU, all three scale linearly and take similar time. On a GPU, the `\"parallel\"` rollout should\n", "scale best." ] }, { "cell_type": "code", "execution_count": 6, "id": "dbe0f994", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:42:25.831830Z", "iopub.status.busy": "2026-10-14T22:42:25.831644Z", "iopub.status.idle": "2026-10-14T22:44:05.648237Z", "shell.execute_reply": "2026-10-14T22:44:05.647467Z" } }, "outputs": [], "source": [ "def time_solver(solve, model, n_repeat=3):\n", " Us0 = jnp.zeros((model.dims.horizon, M))\n", " f = jax.jit(lambda p, u: solve(model, p, u, max_iter=200))\n", " jax.block_until_ready(f(params, Us0)) # compile\n", " start = timer.perf_counter()\n", " for _ in range(n_repeat):\n", " jax.block_until_ready(f(params, Us0))\n", " return (timer.perf_counter() - start) / n_repeat\n", "\n", "\n", "solvers = {\n", " \"ilqr\": ilqr_solver,\n", " \"pilqr feedback\": lambda m, p, u, **kw: pilqr_solver(m, p, u, rollout=\"feedback\", **kw),\n", " \"pilqr parallel\": lambda m, p, u, **kw: pilqr_solver(m, p, u, rollout=\"parallel\", **kw),\n", "}\n", "horizons = [250, 500, 1000, 2000]\n", "timings = {name: [time_solver(s, make_model(h)) for h in horizons] for name, s in solvers.items()}" ] }, { "cell_type": "code", "execution_count": 7, "id": "820e7827", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:44:05.651392Z", "iopub.status.busy": "2026-10-14T22:44:05.651150Z", "iopub.status.idle": "2026-10-14T22:44:06.058304Z", "shell.execute_reply": "2026-10-14T22:44:06.057586Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(5, 3.5), layout=\"constrained\")\n", "for name, ts in timings.items():\n", " ax.loglog(horizons, ts, \"o-\", label=name)\n", "ax.set(xlabel=\"horizon T\", ylabel=\"wall time per solve (s)\", title=f\"device: {jax.devices()[0].platform}\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "77d3d7a3", "metadata": {}, "source": [ "## How to adapt\n", "\n", "- **Switching solver:** replace `ilqr_solver` with `pilqr_solver` (or `dilqr` with `pdilqr`). The\n", " model, parameters and initial inputs are unchanged.\n", "- **Choosing a rollout:** use `\"feedback\"` when you need every iterate to be feasible, for example\n", " when stopping early. Use `\"parallel\"` for the most parallelism on a GPU.\n", "- **Non-convex costs:** `make_psd=\"R\"` or `\"full\"` projects the local problem to be convex, which\n", " makes every scan element valid without regularisation retries.\n", "- **Gradient adjoint:** `pdilqr(..., adjoint=\"sequential\")` solves the reverse LQR sequentially.\n", " This is useful for checking results or on a CPU.\n", "- **Benchmarking on a GPU:** install a CUDA build of JAX and re-run this notebook. For a script\n", " version, see `examples/long_horizon.py` in the repository." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.11.11" } }, "nbformat": 4, "nbformat_minor": 5 }