algos.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finite Horizon Nonlinear Control Algorithms\n",
    "Overall, our problem, in discrete time, can be written as \n",
    "\\begin{align*}\n",
    "\t\\min_{\\substack{u_0, \\ldots, u_{\\tau -1} \\\\ z_0, \\ldots, z_\\tau  } }  & \\sum_{t=0}^{\\tau-1}h_t(z_t) + g_t(u_t)  + h_\\tau(z_\\tau) \n",
    "\t\\\\\n",
    "\t\\text{subject to} \\quad &  z_{t+1} = \\phi_t(z_t, u_t)  \\quad  \\text{for} \\  t \\in \\{0, \\ldots \\tau-1\\} \\\\\n",
    "\t& z_0 = \\bar z_0.\n",
    "\\end{align*} \n",
    "where $h_t, g_t$ are some costs on the state and control variables and $\\phi_t$ are the discrete-time dynamics obtained after discretizing the continuous time dynamics. \n",
    "\n",
    "In the following, we simply present a regularized Gauss-Newton algorithm and a regularized differential dynamic programming approach. \n",
    "The ideal approach for such dynamical problems is dynamic programming, detailed below.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import time\n",
    "import math\n",
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "torch.set_default_dtype(torch.float64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\renewcommand{\\state}{z} \\renewcommand{\\ctrl}{u} \\renewcommand{\\horizon}{\\tau} \\renewcommand{\\cost}{h} \\renewcommand{\\finalcost}{h_{\\tau}} \\renewcommand{\\dyn}{\\phi} \\renewcommand{\\costogo}{c} \\renewcommand{\\auxstate}{y}$\n",
    "<a id='dyn_prog'></a>\n",
    "\n",
    "### Dynamic Programming\n",
    "Consider a generic dynamical problem of the form:\n",
    "\n",
    "\\begin{align}\n",
    "\t\\min_{\\substack{\\ctrl_0, \\ldots, \\ctrl_{\\horizon -1}  \\\\ \\state_0, \\ldots, \\state_\\horizon  } }  & \\sum_{t=0}^{\\horizon-1}\\cost_t(\\state_t, \\ctrl_t)  + \\finalcost(\\state_\\horizon) \\nonumber\n",
    "\t\\\\\n",
    "\t\\text{subject to} \\quad &  \\state_{t+1} = \\dyn_t(\\state_t, \\ctrl_t)  \\quad  \\text{for} \\  t \\in \\{0, \\ldots \\horizon-1\\} \\nonumber \\\\\n",
    "\t& \\state_0 = \\bar \\state_0. \\nonumber\n",
    "\\end{align} \n",
    "\n",
    "The idea of dynamic programming is to decompose dynamical problems as the one above into a sequence of nested sub-problems. Namely, we define the cost-to-go from $ \\state_t$ at time $t \\in \\{0, \\ldots, \\horizon-1\\}$ as \n",
    "\\begin{align}\n",
    "\t\\costogo_t( \\state_t) = \\min_{\\substack{\\ctrl_t,\\ldots, \\ctrl_{\\horizon-1}\\\\\\auxstate_t,\\ldots, \\auxstate_\\horizon}} \\quad & \\sum_{s=t}^{\\horizon-1} \\cost_{s}(\\auxstate_{s}, \\ctrl_{s}) + \\cost_\\horizon(\\auxstate_\\horizon) \\nonumber\n",
    "\t\\\\\n",
    "\t\\text{subject to} \\quad & \\auxstate_{s+1} =  \\dyn_{s}(\\auxstate_{s}, \\ctrl_{s}) \\quad \\text{for} \\ s \\in \\{t, \\ldots, \\horizon-1\\}, \\nonumber \\\\\n",
    "\t& \\auxstate_{t} =  \\state_{t}. \\nonumber\n",
    "\\end{align}\n",
    "The cost-to-go from $\\state_\\horizon$ at time $\\horizon$ is simply the last cost, namely,\n",
    "\\begin{equation}\n",
    "  \\costogo_\\horizon(\\state_\\horizon) = \\cost_\\horizon(\\state_\\horizon),\n",
    "\\end{equation}\n",
    "and the original problem  amounts to compute $\\costogo_0(\\bar \\state_0)$.\n",
    "The cost-to-go functions define nested sub-problems that are linked for $t\\in \\{0, \\ldots, \\horizon-1\\}$ by the Bellman equation\n",
    "\\begin{equation}\n",
    "\t\\costogo_{t}( \\state_t) = \\min_{\\ctrl_t }  \\left\\{ \\cost_t(\\state_t, \\ctrl_t) + \\costogo_{t+1}(\\dyn_t( \\state_t, \\ctrl_t))\\right\\}.\n",
    "\\end{equation}\n",
    "The optimal control variables are naturally derived from the resolution of the Bellman equations. Namely, if one knows the cost-to-go at time $t+1$ from any state, the optimal control at time $t$ from state $\\state_t$ is given by  the policy\n",
    "\\begin{equation}\n",
    "\\pi_t^*( \\state_t) = \\arg\\min_{\\ctrl_t } \\left\\{ \\cost_t(\\state_t, \\ctrl_t) + \\costogo_{t+1}(\\dyn_t( \\state_t, \\ctrl_t))\\right\\}.\n",
    "\\end{equation}\n",
    "Denoting the procedure that back-propagates the cost-to-go functions as\n",
    "$$\n",
    "\\textrm{BP}:\n",
    "\t\\dyn, \\cost, \\costogo_{t+1} \\rightarrow \\left(\\begin{array}{c}\n",
    "\t\t\\costogo_{t}: \\state\\rightarrow\t\\min_{\\ctrl }  \\left\\{ \\cost(\\state, \\ctrl) + \\costogo_{t+1}(\\dyn( \\state, \\ctrl))\\right\\},\\\\\n",
    "\t\t\\pi_t^* :\\state \\rightarrow\t \\arg\\min_{\\ctrl} \\left\\{ \\cost(\\state, \\ctrl) + \\costogo_{t+1}(\\dyn( \\state, \\ctrl))\\right\\}\n",
    "\t\\end{array}\\right),\n",
    "$$\n",
    "this suggests the following approach.\n",
    "\n",
    "1. **Backward pass** Compute recursively the cost-to-go functions $\\costogo_t$ for $t=\\horizon, \\ldots, 0$ using the Bellman starting from $\\costogo_\\horizon$ given by the final cost. Record at each step the optimal policy function $\\pi_t^*$. Namely, compute from $\\costogo_\\horizon= \\cost_\\horizon$, recording at each step $\\pi_t^*$,\n",
    "\n",
    "$$\n",
    "\\costogo_t, \\pi^*_t = \\textrm{BP}(\\dyn_t, \\cost_t, \\costogo_{t+1}) \\quad \\text{for} \\ t \\in \\{\\horizon-1, \\ldots, 0\\}\n",
    "$$\n",
    "    \n",
    "\t\n",
    "2. **Roll-out phase** Unroll the optimal trajectory that starts from time 0 at $\\bar \\state_0$, follows the dynamics $\\dyn_t$, and use at each step the optimal control given by the optimal policy function. Namely, starting from $\\state_0^* = \\bar \\state_0$, compute\n",
    "\n",
    "$$\n",
    "\\ctrl^*_t= \\pi_t^*(\\state_t^*), \\qquad \\state_{t+1}= \\dyn_t(\\state_t^*, \\ctrl^*_t) \\qquad \\text{for $t=0, \\ldots, \\horizon-1$.}\n",
    "$$\n",
    "\n",
    "The output sequence of control $\\ctrl_0^*, \\ldots, \\ctrl_{\\horizon-1}^*$ is then the optimal sequence of control and the trajectory $\\state_0^*, \\ldots, \\state_\\horizon^*$ is the optimal trajectory for the problem. \n",
    "The bottleneck of the approach is the ability to solve the Bellman equation, i.e.,  having access to the procedure $\\textrm{Bell}$ defined above. For most problems, this procedure cannot be computed in closed form. One exception is the case of linear dynamics and quadratic costs. The algorithms presented below use this fact to compute an optimal sequence of controllers iteratively. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\renewcommand{\\diffctrl}{v} \\renewcommand{\\diffstate}{y} \\renewcommand{\\lin}{\\ell} \\renewcommand{\\costogo}{c} \\renewcommand{\\Bell}{\\textrm{Bell}} \\newcommand{\\qua}{q}$\n",
    "<a id='gauss_newton'></a>\n",
    "\n",
    "### Gauss-Newton\n",
    "Although our original  problem is written as a constrained problem, it can be seen just as a problem over the control variables. Namely, define the function $f$ that, given an initial state $z_0$ and a sequence of controls $u = (u_0, \\ldots, u_{\\tau-1})$ output the trajectory $f(u) = (f_0(u), f_1(u), \\ldots, f_\\tau(u))= (z_0, z_1,\\ldots, z_\\tau)$ defined as\n",
    "\n",
    "$$\tf_{t+1}(u)  = \\phi_t(f_t(u),u_t), \\quad \\text{for} \\ t \\in\\{0, \\ldots, \\tau-1\\}$$\n",
    "with $f_0(u) = z_0$. \n",
    "\n",
    "\n",
    "Our problem can then be written as\n",
    "$$\n",
    "\\min_u h(f(u)) + g(u)\n",
    "$$\n",
    "where $h(z) = \\sum_{t=0}^{\\tau} h(z_t)$ for $z = (z_0, \\ldots, z_\\tau)$ and $g(u) = \\sum_{t=0}^{\\tau-1} g_t(u_t)$ for $u = (u_0, \\ldots, u_{\\tau-1})$.\n",
    "\n",
    "A regularized Gauss-Newton step consists of minimizing a linear-quadratic model of the problem with an additional regularization term. Namely, a regularized Gauss-Newton step consists of iterating steps of the form\n",
    "\n",
    "\\begin{align}\n",
    "u^{\\textrm{new}} & = u + \\diffctrl^\\gamma  \\\\\n",
    "\\text{where} \\quad \\diffctrl^\\gamma & = \\arg\\min_{\\diffctrl} q_h^{f(u)}(\\ell_f^u(\\diffctrl)) + q_g^u(u) + \\frac{1}{2\\gamma} \\|\\diffctrl\\|_2^2 \\tag{GN} \n",
    "\\end{align}\n",
    "where for a function $f$, we denote \n",
    "$$\n",
    "\\ell_f^x(y) =\\nabla f(x)^\\top y, \\qquad \n",
    "q_f^x(y)  = \\nabla f(x)^\\top y +\\frac{1}{2} \\nabla^2 f(x)[y, y, \\cdot], $$\n",
    "respectively the linear and quadratic approximations of $f$ such that e.g. $f(x+y) \\approx  f(x) + \\ell_f^x(y)$ and \n",
    " $\\gamma$ acts a step-size: the smaller the gamma, the smaller the $\\diffctrl^\\gamma$.\n",
    "\n",
    "The problem (GN) is a linear quadratic control problem that can be solved exactly by dynamic programming as presented before. Overall, one regularized Gauss-Newton step amounts to the following steps.\n",
    "\n",
    "1. A **forward pass** that records the derivatives of the dynamics and the costs to express  the problem (GN) in terms of the quadratic approximations of the costs $h_t, g_t$ and the linear approximations of the dynamics $\\phi_t$.\n",
    "\n",
    "2. A **backward pass** that computes the optimal policies of the linear-quadratic problem using the fact that the operator $\\textrm{BP}$ can be formulated analytically for linear dynamics and quadratic costs. Namely, the policies are computed as\n",
    "$$\n",
    "\\costogo_t^\\gamma, \\pi_t^\\gamma = \\textrm{BPLQ}_{\\gamma}(\\lin_{\\dyn_t}^{\\state_t, \\ctrl_t}, \\qua_{\\cost_t}^{\\state_t, \\ctrl_t}, \\costogo_{t+1}^\\gamma) \\quad \\text{for} \\ t = \\horizon-1, \\ldots, 0,\n",
    "$$\n",
    "where $\\textrm{BPLQ}_{\\gamma}$ solves the Bellman equation for linear dynamics and quadratic costs with an additional regularization defined by $\\gamma$, and $\\state_t$ are the states corresponding to the current sequence of controls $\\ctrl_t$.\n",
    "\n",
    "3. A **roll-out phase** that computes the solution of the linear-quadratic problem by using the optimal policies computed in the backward pass and apply them step by step on the linearized trajectories, namely the sequence $\\diffctrl^\\gamma$ is computed as \n",
    "\n",
    "$$\n",
    "\t\t\\diffctrl_t^\\gamma= \\pi_t^\\gamma(\\diffstate_t), \\qquad \\diffstate_{t+1} = \\lin_{\\dyn_t}^{\\state_t, \\ctrl_t}(\\state_t + \\diffstate_t, \\ctrl_t + \\diffctrl^\\gamma_t) \\qquad \\text{for $t=0, \\ldots, \\horizon-1$},\n",
    "$$\n",
    "\n",
    "Each step depends on the choice of the step size $\\gamma$ defined above. This step-size is chosen such that \n",
    "\n",
    "$$ h(f(u+ \\diffctrl^\\gamma)) + g(u+ \\diffctrl^\\gamma)  \\leq h(f(u)) + g(u) + q_h^{f(u)}(\\ell_f^u(\\diffctrl^\\gamma)) + q_g^u(\\diffctrl^\\gamma) + \\frac{1}{2\\gamma} \\|\\diffctrl^\\gamma\\|_2^2, $$\n",
    "\n",
    "by decreasing the step size until this criterion is satisfied. The computed step size is kept in memory for the next step. The next sequence of controllers is then $u_{new} = u + \\diffctrl^\\gamma$.\n",
    "\n",
    "The computational scheme of a Gauss-Newton step is illustrated below, the $f_t$ here correspond to the $\\phi_t$ above.\n",
    "\n",
    "<center><img src=\"fig/ilqr_gn.png\" alt=\"Computational Scheme of a Gauss-Newton Oracle\" width=\"900\" /></center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='ddp'></a>\n",
    "\n",
    "\n",
    "### Differential Dynamic Programming \n",
    "\n",
    "The differential dynamic programming approach is very similar to a Gauss-Newton step except that, rather than computing the roll-out phase using the linear approximations of the dynamics, the roll-out phase uses the exact trajectories. The algorithm can be summarized as follows:\n",
    "\n",
    "1. A **forward pass** that records the derivatives of the dynamics and the costs to express  the problem (GN) in terms of the quadratic approximations of the costs $h_t, g_t$ and the linear approximations of the dynamics $\\phi_t$.\n",
    "\n",
    "2. A **backward pass** that computes the optimal policies of the linear-quadratic problem using the fact that the operator $\\textrm{Bell}$ can be formulated analytically for linear dynamics and quadratic costs. Namely, the policies are computed as\n",
    "\n",
    "$$\n",
    "\\costogo_t^\\gamma, \\pi_t^\\gamma = \\mathrm{LQBP}_{\\gamma}(\\lin_{\\dyn_t}^{\\state_t, \\ctrl_t}, q_{\\cost_t}^{\\state_t, \\ctrl_t}, \\costogo_{t+1}^\\gamma) \\quad \\text{for} \\ t = \\horizon-1, \\ldots, 0.\n",
    "$$\n",
    "\n",
    "3. A **roll-out phase** that computes the solution of the linear-quadratic problem by using the optimal policies computed in the backward pass and apply them step by step on the exact trajectories, namely the sequence $\\delta u^\\gamma$ is computed as \n",
    "\n",
    "$$\n",
    "\t\t\\diffctrl_t^\\gamma= \\pi_t^\\gamma( \\diffstate_t), \\qquad \\diffstate_{t+1} =  \\dyn_t(\\state_t + \\diffstate_t, \\ctrl_t + \\diffctrl_t^\\gamma ) - \\dyn_t(\\state_t, \\ctrl_t) \\qquad \\text{for $t=0, \\ldots, \\horizon-1$}\n",
    "$$\n",
    "\n",
    "We use the same line-search as for Gauss-Newton to find the step-size\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='implementation'></a>\n",
    "\n",
    "\n",
    "## Implementation\n",
    "\n",
    "The implementation of these algorithms require to store the derivatives with respect to the dynamics and the costs at each step of the algorithm. In that purpose, we define a generic class as follows. Note that the class implmented in the toolbox can also store quadratic approximations of the dynamics to implement Newton steps or a differential dynamic programming approach with quadratic approximations. See the technical report [Roulet et al 2022]((#refs) for a complete mathematical exposition of these algorithms. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import time\n",
    "from typing import Callable, List\n",
    "\n",
    "from torch.autograd import grad as auto_grad\n",
    "from envs.torch_utils import auto_multi_grad\n",
    "\n",
    "\n",
    "class DiffEnv:\n",
    "    def __init__(self):\n",
    "        super(DiffEnv, self).__init__()\n",
    "        self.dim_ctrl, self.dim_state = None, None\n",
    "        self.dt, self.horizon = None, None\n",
    "        self.state, self.time_iter = None, 0\n",
    "        self.init_state, self.init_time_iter = None, None\n",
    "        self.viewer = None\n",
    "\n",
    "    def discrete_dyn(self, state: torch.Tensor, ctrl: torch.Tensor, time_iter: int) -> torch.Tensor:\n",
    "        raise NotImplementedError\n",
    "\n",
    "    def costs(self, next_state: torch.Tensor, ctrl: torch.Tensor, time_iter: int) -> (torch.Tensor, torch.Tensor):\n",
    "        return torch.tensor(0.), torch.tensor(0.)\n",
    "\n",
    "    def step(self, ctrl: torch.Tensor, approx: str = None) -> (torch.Tensor, torch.Tensor):\n",
    "        if approx == 'linquad':\n",
    "            next_state = diff_discrete_dyn(self.discrete_dyn, self.state, ctrl, self.time_iter)\n",
    "            new_time_iter = self.time_iter + 1\n",
    "            cost = diff_cost(self.costs, next_state, ctrl, new_time_iter)\n",
    "        else:\n",
    "            next_state = self.discrete_dyn(self.state, ctrl, self.time_iter)\n",
    "            new_time_iter = self.time_iter + 1\n",
    "            cost = sum(self.costs(next_state, ctrl, new_time_iter))\n",
    "        self.state, self.time_iter = next_state, new_time_iter\n",
    "        return next_state, cost\n",
    "\n",
    "    def forward(self, cmd: torch.Tensor, approx: str = None, reset: bool = True) \\\n",
    "            -> (List[torch.Tensor], List[torch.Tensor]):\n",
    "        if reset:\n",
    "            self.reset(requires_grad=approx is not None)\n",
    "        dim_state, dim_ctrl, horizon = self.dim_state, self.dim_ctrl, cmd.shape[0]\n",
    "        state = self.state\n",
    "        traj = [state]\n",
    "        init_cost = torch.tensor(0.)\n",
    "        init_cost.hess_state, init_cost.grad_state = torch.zeros(dim_state, dim_state), torch.zeros(dim_state)\n",
    "        costs = [init_cost]\n",
    "        for t in range(horizon):\n",
    "            state, cost = self.step(cmd[t], approx=approx)\n",
    "            traj.append(state)\n",
    "            costs.append(cost)\n",
    "        return traj, costs\n",
    "\n",
    "    def reset(self, requires_grad=False) -> torch.Tensor:\n",
    "        self.time_iter = self.init_time_iter\n",
    "        self.state = self.init_state\n",
    "        self.state.requires_grad = requires_grad\n",
    "        return self.state\n",
    "\n",
    "    def close(self):\n",
    "        if self.viewer:\n",
    "            self.viewer.close()\n",
    "            self.viewer = None\n",
    "\n",
    "    def visualize(self, cmd: torch.Tensor, dt: float =None):\n",
    "        if dt is None:\n",
    "            dt = self.dt\n",
    "        self.reset()\n",
    "        for ctrl in cmd:\n",
    "            self.render()\n",
    "            time.sleep(dt)\n",
    "            self.step(ctrl)\n",
    "        self.render()\n",
    "        self.close()\n",
    "\n",
    "\n",
    "def diff_discrete_dyn(discrete_dyn: Callable, state: torch.Tensor,\n",
    "                      ctrl: torch.Tensor, time_iter: int) -> torch.Tensor:\n",
    "    next_state = discrete_dyn(state, ctrl, time_iter)\n",
    "\n",
    "    grad_dyn_state = auto_multi_grad(next_state, state)\n",
    "    grad_dyn_ctrl = auto_multi_grad(next_state, ctrl)\n",
    "    for attr, val in zip(['grad_dyn_state', 'grad_dyn_ctrl'], [grad_dyn_state, grad_dyn_ctrl]):\n",
    "        val = val.data if val is not None else None\n",
    "        setattr(next_state, attr, val)\n",
    "    return next_state\n",
    "\n",
    "\n",
    "def diff_cost(costs: Callable, next_state: torch.Tensor, ctrl: torch.Tensor, time_iter: int) -> torch.Tensor:\n",
    "    dim_state, dim_ctrl = next_state.shape[0], ctrl.shape[0]\n",
    "\n",
    "    cost_next_state, cost_ctrl = costs(next_state, ctrl, time_iter)\n",
    "    cost = cost_next_state + cost_ctrl\n",
    "\n",
    "    if cost_next_state.grad_fn is not None:\n",
    "        cost_grad_state = auto_grad(cost_next_state, next_state, create_graph=True)[0]\n",
    "        cost.hess_state = auto_multi_grad(cost_grad_state, next_state).data\n",
    "        cost.grad_state = cost_grad_state.data\n",
    "        cost.has_cost_state = True\n",
    "    else:\n",
    "        cost.hess_state, cost.grad_state = torch.zeros(dim_state, dim_state), torch.zeros(dim_state)\n",
    "        cost.has_cost_state = False\n",
    "\n",
    "    if cost_ctrl.grad_fn is not None:\n",
    "        cost_grad_ctrl = auto_grad(cost_ctrl, ctrl, create_graph=True)[0]\n",
    "        cost.hess_ctrl = auto_multi_grad(cost_grad_ctrl, ctrl).data\n",
    "        cost.grad_ctrl = cost_grad_ctrl.data\n",
    "    else:\n",
    "        cost.hess_ctrl, cost.grad_ctrl = torch.zeros(dim_ctrl, dim_ctrl), torch.zeros(dim_ctrl)\n",
    "\n",
    "    return cost\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then instantiate  our previous model of a car within the above class to be able to access the linear approximations of the dynamics and the quadratic approximations of the cost.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-08-01 16:05:31.291 Python[59775:1688755] ApplePersistenceIgnoreState: Existing state will not be touched. New state will be written to /var/folders/pf/znths45963l2918jylv3wzjr0134jq/T/org.python.python.savedState\n"
     ]
    }
   ],
   "source": [
    "import colorsys\n",
    "import math\n",
    "\n",
    "import numpy as np\n",
    "import torch\n",
    "import os\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from envs.discretization import euler, runge_kutta4, runge_kutta4_cst_ctrl\n",
    "from envs import rendering\n",
    "from envs.tracks.tracks import get_track\n",
    "from envs.torch_utils import smooth_relu\n",
    "from envs.car import set_window_viewer, add_car_to_viewer, add_track_to_viewer, plot_track, plot_traj\n",
    "\n",
    "\n",
    "\n",
    "class Car(DiffEnv):\n",
    "    def __init__(self, dt=0.02, discretization='rk4_cst_ctrl', horizon=20,\n",
    "                 track='simple', model='simple',\n",
    "                 reg_ctrl=1e-6, reg_cont=0.1, reg_lag=10., reg_speed=0.1, reg_bar=100., reg_obs=0.,\n",
    "                 cost='contouring', time_penalty='vref_squared',\n",
    "                 vref=3., vinit=1., constrain_angle=math.pi/3, acc_bounds=(-0.1, 1.), seed=0\n",
    "                 ):\n",
    "        super(Car, self).__init__()\n",
    "        if seed != 0:\n",
    "            torch.manual_seed(seed)\n",
    "            vinit = vinit + 1e-2*torch.randn(1).item()\n",
    "            reg_cont, reg_lag, reg_speed = reg_cont + 1e-3 * torch.randn(1).item(), \\\n",
    "                                           reg_lag + 1e-3 * torch.randn(1).item(), \\\n",
    "                                           reg_speed + 1e-3 * torch.randn(1).item()\n",
    "\n",
    "        # dyn parameters\n",
    "        self.dt, self.discretization, self.horizon = dt, discretization, horizon\n",
    "        self.model = model\n",
    "        self.vref, self.constrain_angle, self.acc_bounds = vref, constrain_angle, acc_bounds\n",
    "\n",
    "        # cost parameters\n",
    "        self.reg_ctrl, self.reg_cont, self.reg_lag, self.reg_speed, self.reg_bar, self.reg_obs = \\\n",
    "            reg_ctrl, reg_cont, reg_lag, reg_speed, reg_bar, reg_obs\n",
    "        self.cost_type, self.time_penalty = cost, time_penalty\n",
    "\n",
    "        # track parameters\n",
    "        self.track, self.inner_track, self.outer_track = get_track(track)\n",
    "        dx_ref, dy_ref = self.track.derivative(torch.tensor(0.))\n",
    "        phi_ref = torch.atan2(dy_ref, dx_ref)\n",
    "\n",
    "        if model == 'simple':\n",
    "            self.init_state = torch.tensor([0., 0., phi_ref, vinit, 0., vinit])\n",
    "            self.dim_ctrl, self.dim_state = 3, 6\n",
    "        elif model == 'real':\n",
    "            self.init_state = torch.tensor([0., 0., phi_ref, vinit, 0., 0., 0., vinit])\n",
    "            self.dim_ctrl, self.dim_state = 3, 8\n",
    "        else:\n",
    "            raise NotImplementedError\n",
    "\n",
    "        if self.discretization == 'RK4':\n",
    "            self.dim_ctrl *= 3\n",
    "\n",
    "        self.dyn_csts = pd.read_json(os.path.join('envs/bicycle_model.json'), typ='series')\n",
    "\n",
    "        self.cartrans = None\n",
    "        self.init_time_iter = 0\n",
    "\n",
    "        time_obstacle = max(self.track._t) / 20\n",
    "        self.obstacle = self.track.evaluate(time_obstacle) + torch.tensor([0.2, 0.])\n",
    "\n",
    "    def discrete_dyn(self, state, ctrl, time_iter):\n",
    "        if self.model == 'real':\n",
    "            dyn = self.bicycle_model\n",
    "        elif self.model == 'simple':\n",
    "            dyn = self.simple_model\n",
    "        else:\n",
    "            raise NotImplementedError\n",
    "        if self.discretization == 'euler':\n",
    "            next_state = euler(dyn, state, ctrl, self.dt)\n",
    "        elif self.discretization == 'rk4':\n",
    "            next_state = runge_kutta4(dyn, state, ctrl, self.dt)\n",
    "        elif self.discretization == 'rk4_cst_ctrl':\n",
    "            next_state = runge_kutta4_cst_ctrl(dyn, state, ctrl, self.dt)\n",
    "        else:\n",
    "            raise NotImplementedError\n",
    "        return next_state\n",
    "\n",
    "    def simple_model(self, state, ctrl):\n",
    "        x, y, phi, v, tref, vtref = state\n",
    "        a, delta, atref = ctrl\n",
    "        delta = 2/math.pi*torch.arctan(delta)*self.constrain_angle\n",
    "        carlength = 1.5*self.dyn_csts['car_l']\n",
    "\n",
    "        dx = v * torch.cos(phi)\n",
    "        dy = v * torch.sin(phi)\n",
    "        dv = a\n",
    "        dphi = v * torch.tan(delta)/carlength\n",
    "        dtref = vtref\n",
    "        dvtref = atref\n",
    "        return torch.stack([dx, dy, dphi, dv, dtref, dvtref])\n",
    "\n",
    "    def bicycle_model(self, state, ctrl):\n",
    "        x, y, phi, vx, vy, vphi, tref, vtref = state\n",
    "        a, delta, atref = ctrl\n",
    "        delta = 2/math.pi*torch.arctan(delta)*self.constrain_angle\n",
    "        # hardcode constraints on the acceleration\n",
    "        gap = self.acc_bounds[1] - self.acc_bounds[0]\n",
    "        a = gap*torch.sigmoid(4 * a / gap) + self.acc_bounds[0]\n",
    "\n",
    "\n",
    "        Cm1, Cm2, Cr0, Cr2,\\\n",
    "        Br, Cr, Dr, Bf, Cf, Df,\\\n",
    "        m, Iz, lf, lr = [self.dyn_csts[key] for key in ['Cm1', 'Cm2', 'Cr0', 'Cr2',\n",
    "                                                        'Br', 'Cr', 'Dr', 'Bf', 'Cf', 'Df',\n",
    "                                                        'm', 'Iz', 'lf', 'lr']]\n",
    "        alphaf = delta - torch.atan2(vphi*lf + vy, vx)\n",
    "        alphar = torch.atan2(vphi*lr - vy, vx)\n",
    "        Fry = Dr*torch.sin(Cr*torch.atan(Br*alphar))\n",
    "        Ffy = Df*torch.sin(Cf*torch.atan(Bf*alphaf))\n",
    "        Frx = (Cm1 - Cm2*vx)*a - Cr0 - Cr2*vx**2\n",
    "        dx = torch.cos(phi)*vx - torch.sin(phi)*vy\n",
    "        dy = torch.sin(phi)*vx + torch.cos(phi)*vy\n",
    "        dphi = vphi\n",
    "        dvx = (Frx - Ffy*torch.sin(delta) + m*vy*vphi)/m\n",
    "        dvy = (Fry + Ffy*torch.cos(delta) - m*vx*vphi)/m\n",
    "        dvphi = (Ffy*lf*torch.cos(delta) - Fry*lr)/Iz\n",
    "        dtref = vtref\n",
    "        dvtref = atref\n",
    "        return torch.stack([dx, dy, dphi, dvx, dvy, dvphi, dtref, dvtref])\n",
    "\n",
    "    def costs(self, next_state, ctrl, time_iter):\n",
    "        if self.model == 'simple':\n",
    "            x, y, phi, v, tref, vtref = next_state\n",
    "        else:\n",
    "            x, y, phi, vx, vy, vphi, tref, vtref = next_state\n",
    "\n",
    "        if self.cost_type == 'contouring':\n",
    "            qC, qL, qVs = self.reg_cont, self.reg_lag, self.reg_speed\n",
    "            x_ref, y_ref = self.track.evaluate(tref)\n",
    "            dx_ref, dy_ref = self.track.derivative(tref)\n",
    "            phi_ref = torch.atan2(dy_ref, dx_ref)\n",
    "\n",
    "            cont_err = torch.sin(phi_ref)*(x-x_ref) - torch.cos(phi_ref)*(y-y_ref)\n",
    "            lag_err = -torch.cos(phi_ref)*(x-x_ref) - torch.sin(phi_ref)*(y-y_ref)\n",
    "            cost_next_state = qC*cont_err**2 + qL*lag_err**2\n",
    "            if self.time_penalty == 'tref':\n",
    "                cost_next_state = cost_next_state - qVs*tref\n",
    "            elif self.time_penalty == 'dref':\n",
    "                cost_next_state = cost_next_state - qVs*vtref*self.dt\n",
    "            elif self.time_penalty == 'dref_squared':\n",
    "                cost_next_state = cost_next_state - qVs*vtref*self.dt*tref\n",
    "            elif self.time_penalty == 'vref_squared':\n",
    "                cost_next_state = cost_next_state + qVs*(vtref-self.vref)**2*self.dt**2\n",
    "            else:\n",
    "                raise NotImplementedError\n",
    "        elif self.cost_type == 'exact':\n",
    "            time = torch.tensor(time_iter*self.vref*self.dt)\n",
    "            x_ref, y_ref = self.track.evaluate(time)\n",
    "            cost_next_state = (x - x_ref)**2 + (y - y_ref)**2\n",
    "        else:\n",
    "            raise NotImplementedError\n",
    "\n",
    "        if type(self.reg_ctrl) == tuple:\n",
    "            if self.discretization in ['euler', 'RK4_cst_ctrl']:\n",
    "                a, delta, atref = ctrl\n",
    "                cost_ctrl = self.reg_ctrl[0]*(a**2 + delta**2) + self.reg_ctrl[1]*atref**2\n",
    "            elif self.discretization == 'RK4':\n",
    "                accs, deltas, atrefs = ctrl[::3], ctrl[1::3], ctrl[2::3]\n",
    "                cost_ctrl = self.reg_ctrl[0]*((accs**2).sum() + (deltas**2).sum()) \\\n",
    "                            + self.reg_ctrl[1]*(atrefs**2).sum()\n",
    "            else:\n",
    "                raise NotImplementedError\n",
    "        else:\n",
    "            cost_ctrl = self.reg_ctrl*ctrl.dot(ctrl)\n",
    "\n",
    "        barr_next_state = self.barrier(next_state)\n",
    "        cost_next_state = cost_next_state + barr_next_state\n",
    "\n",
    "        return cost_next_state, cost_ctrl\n",
    "\n",
    "    def barrier(self, next_state):\n",
    "        barr_next_state = -1e-6*torch.log(next_state[-1])\n",
    "\n",
    "        carwidth = 1.5*self.dyn_csts['car_w']\n",
    "\n",
    "        tref = next_state[-2]\n",
    "        x, y = next_state[:2]\n",
    "        point = torch.tensor([x, y])\n",
    "        for i, border in enumerate([self.inner_track, self.outer_track]):\n",
    "            border_point = border.evaluate(tref)\n",
    "            dpos = border.derivative(tref)\n",
    "            v = torch.sqrt(torch.sum(dpos**2))\n",
    "            normal = torch.tensor([dpos[1], -dpos[0]])/v\n",
    "            if i == 0:\n",
    "                # inner\n",
    "                barr_next_state = barr_next_state \\\n",
    "                                  + self.reg_bar * smooth_relu(carwidth / 2 - (point - border_point).dot(normal)) ** 2\n",
    "            else:\n",
    "                # outer\n",
    "                barr_next_state = barr_next_state \\\n",
    "                                  + self.reg_bar * smooth_relu((point - border_point).dot(normal) + carwidth / 2) ** 2\n",
    "        barr_next_state = barr_next_state\n",
    "\n",
    "        if self.reg_obs > 0.:\n",
    "            barr_next_state = barr_next_state \\\n",
    "                              + self.reg_obs * smooth_relu(carwidth ** 2 - torch.sum((point - self.obstacle) ** 2))\n",
    "\n",
    "        return barr_next_state\n",
    "\n",
    "    def set_viewer(self):\n",
    "        nb_points = 500\n",
    "        carlength, carwidth = 1.5 * self.dyn_csts['car_l'], 1.5 * self.dyn_csts['car_w']\n",
    "\n",
    "        time = torch.linspace(0, max(self.track._t), nb_points)\n",
    "        track_points = self.outer_track.evaluate(time).numpy()\n",
    "        min_x, max_x = min(track_points[:, 0]), max(track_points[:, 0])\n",
    "        min_y, max_y = min(track_points[:, 1]), max(track_points[:, 1])\n",
    "\n",
    "        self.viewer = set_window_viewer(min_x, max_x, min_y, max_y, 2*carlength)\n",
    "        add_track_to_viewer(self.viewer, self.track, self.inner_track, self.outer_track)\n",
    "\n",
    "        self.cartrans = add_car_to_viewer(self.viewer, carlength, carwidth)\n",
    "\n",
    "    def plot_track(self, fig=None, ax=None):\n",
    "        fig, ax = plot_track(self.track, self.inner_track, self.outer_track, fig=fig, ax=ax)\n",
    "        return fig, ax\n",
    "\n",
    "    def plot_traj(self, traj, fig, ax, add_colorbar=True):\n",
    "        return plot_traj(traj, fig, ax, model=self.model, add_colorbar=add_colorbar)\n",
    "\n",
    "    def render(self, title=None):\n",
    "        if self.viewer is None:\n",
    "            self.set_viewer()\n",
    "        self.cartrans.set_translation(self.state[0].item(), self.state[1].item())\n",
    "        self.cartrans.set_rotation(self.state[2].item())\n",
    "        return self.viewer.render(title=title)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following code, we compute the trajectory associated to a sequence of controls and display the intermediate approximations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradients of the dynamics at time step 5:\n",
      " tensor([[ 1.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],\n",
      "        [ 0.0000,  1.0000,  0.0000,  0.0000,  0.0000,  0.0000],\n",
      "        [-0.0067,  0.0192,  1.0000,  0.0000,  0.0000,  0.0000],\n",
      "        [ 0.0186,  0.0073,  0.0740,  1.0000,  0.0000,  0.0000],\n",
      "        [ 0.0000,  0.0000,  0.0000,  0.0000,  1.0000,  0.0000],\n",
      "        [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0200,  1.0000]])\n",
      "tensor([[ 1.8629e-04,  7.2784e-05,  7.4028e-04,  2.0000e-02,  0.0000e+00,\n",
      "          0.0000e+00],\n",
      "        [-4.5463e-04,  1.2556e-03,  1.3135e-01,  0.0000e+00,  0.0000e+00,\n",
      "          0.0000e+00],\n",
      "        [ 0.0000e+00,  0.0000e+00,  0.0000e+00,  0.0000e+00,  2.0000e-04,\n",
      "          2.0000e-02]])\n",
      "Quadratic approximation of the state cost at time step 5:\n",
      " tensor([[ 2.0000e+01,  1.9347e-06,  0.0000e+00,  0.0000e+00, -2.0000e+01,\n",
      "          0.0000e+00],\n",
      "        [ 1.9347e-06,  2.0000e-01,  0.0000e+00,  0.0000e+00, -2.5639e-06,\n",
      "          0.0000e+00],\n",
      "        [ 0.0000e+00,  0.0000e+00,  0.0000e+00,  0.0000e+00,  0.0000e+00,\n",
      "          0.0000e+00],\n",
      "        [ 0.0000e+00,  0.0000e+00,  0.0000e+00,  0.0000e+00,  0.0000e+00,\n",
      "          0.0000e+00],\n",
      "        [-2.0000e+01, -2.5639e-06,  0.0000e+00,  0.0000e+00,  2.0000e+01,\n",
      "          0.0000e+00],\n",
      "        [ 0.0000e+00,  0.0000e+00,  0.0000e+00,  0.0000e+00,  0.0000e+00,\n",
      "          8.0959e-05]])\n",
      "tensor([-0.0462,  0.0037,  0.0000,  0.0000,  0.0462, -0.0002])\n"
     ]
    }
   ],
   "source": [
    "car = Car(model='simple', track='simple')\n",
    "horizon = 20\n",
    "\n",
    "accs = torch.linspace(0, 2, horizon) # Linearly increasing acceleration\n",
    "deltas = math.pi/6*torch.ones(horizon) # Constant steering angle\n",
    "accsrefs = accs\n",
    "cmd = torch.stack((accs, deltas, accsrefs), dim=1) # Sequence of controls\n",
    "cmd.requires_grad = True\n",
    "\n",
    "traj, costs = car.forward(cmd, approx='linquad')\n",
    "\n",
    "state = traj[5]\n",
    "print('Gradients of the dynamics at time step 5:\\n {0}\\n{1}'.format(state.grad_dyn_state, state.grad_dyn_ctrl))\n",
    "cost = costs[5]\n",
    "print('Quadratic approximation of the state cost at time step 5:\\n {0}\\n{1}'.format(cost.hess_state, cost.grad_state))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the linear approximations of the dynamics and the quadratic approximations of the costs, we can perform a backward pass that computes the policies. These policies are affine, i.e., of the form\n",
    "\n",
    "$$ \\pi_t(z_t) = K_t z_t + k_t,$$\n",
    "\n",
    "where $K_t$ is called the *gain* and $k_t$ is called the *offset*. The cost-to-go functions are quadratic of the form\n",
    "\n",
    "$$ c_t(x) = \\frac{1}{2} x^\\top J_t x + j_t^\\top x + j_{t, 0}. $$\n",
    "\n",
    "We use $J_t, j_t$ and $j_t$ to parameterize these functions. See e.g. [[Roulet et al, 2022]](#refs) for the mathematical derivations. \n",
    "\n",
    "Finally, the Bellman equation seeks for a minimum in the control variable. Hence, if the sub-problem defining the Bellman equation is not convex we cannot ensure that we have found a minimum. Rather than checking if the sub-problem is convex we simply check whether the rest is negative or not. A negative rest ensures a good descent direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lin_quad_backward(traj, costs, reg_ctrl=1., handle_bad_dir='flag'):\n",
    "    # Compute iteratively the cost-to-go and the policies by going backward in time\n",
    "    horizon = len(traj)-1\n",
    "    \n",
    "    # The first cost-to-go function is defined by the quadratic approximation of the last state\n",
    "    J, j, jcst = costs[-1].hess_state, costs[-1].grad_state, 0.\n",
    "    feasible = True\n",
    "    \n",
    "    # The policies are stored in a list of gains\n",
    "    gains = list()\n",
    "    for t in range(horizon-1, -1, -1):\n",
    "        P, p = costs[t].hess_state, costs[t].grad_state\n",
    "        Q, q = costs[t+1].hess_ctrl, costs[t+1].grad_ctrl\n",
    "        A, B = traj[t+1].grad_dyn_state.t(), traj[t+1].grad_dyn_ctrl.t()\n",
    "\n",
    "        J, j, jcst, K, k, feasible = bell_step(J, j, jcst, P, p, Q, q, A, B, reg_ctrl, handle_bad_dir)\n",
    "        gain = dict(gain_ctrl=K, offset_ctrl=k)\n",
    "        gains.insert(0, gain)\n",
    "        if not feasible:\n",
    "            break\n",
    "    return gains, jcst, feasible\n",
    "\n",
    "def bell_step(J, j, jcst, P, p, Q, q, A, B, reg, handle_bad_dir='flag'):\n",
    "    # Check if the step is good or not by looking at the sign of the rest of the minimization\n",
    "    # If the rest is positive, the subproblem was necessirally not convex and we did not properly solve the Bellman equation\n",
    "    # A rigorous approach would check at if step if the matrix H below was semi-definite positive\n",
    "    # We rather simply check the rest which avoids computing an svd at each step\n",
    "    H = Q + B.t().mm(J.mm(B)) + reg * torch.eye(Q.shape[0])\n",
    "\n",
    "    next_J, next_j, rest, K, k = bell_core(J, j, H, P, p, q, A, B)\n",
    "    if rest > 0:\n",
    "        if handle_bad_dir == 'flag':\n",
    "            next_J = next_j = next_jcst = K = k = None\n",
    "            feasible = False\n",
    "        elif handle_bad_dir == 'modify_hess':\n",
    "            (lam, U) = torch.eig(H, eigenvectors=True)\n",
    "            lam = torch.abs(lam[:, 0])\n",
    "            H = torch.mm(U, torch.mm(torch.diag(lam), U.t()))\n",
    "            next_J, next_j, rest, K, k = bell_core(J, j, H, P, p, q, A, B)\n",
    "            feasible = True\n",
    "            assert rest < 0\n",
    "            next_jcst = jcst + rest\n",
    "        elif handle_bad_dir == 'let_it_be':\n",
    "            feasible = True\n",
    "            next_jcst = jcst + rest\n",
    "        else:\n",
    "            raise NotImplementedError\n",
    "    else:\n",
    "        feasible = True\n",
    "        next_jcst = jcst + rest\n",
    "    return next_J, next_j, next_jcst, K, k, feasible\n",
    "\n",
    "\n",
    "def bell_core(J, j, H, P, p, q, A, B):\n",
    "    # Core algebra manipulations\n",
    "    K = - torch.linalg.solve(H, B.t().mm(J.mm(A)))\n",
    "    k = - torch.linalg.solve(H, q + B.t().mv(j))\n",
    "    next_J = P + A.t().mm(J.mm(A) + J.mm(B.mm(K)))\n",
    "    next_j = p + A.t().mv(j + J.mv(B.mv(k)))\n",
    "    rest = 0.5 * (q + B.t().mv(j)).dot(k)\n",
    "    return next_J, next_j, rest, K, k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the policies have been computed in the form of gains, we can find the next sequence of controllers by either rolling out the policies along the linearized trajectories or along the exact trajectories as coded below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def roll_out_lin(traj, gains):\n",
    "    dim_state, horizon = traj[0].shape, len(traj)-1\n",
    "    dim_ctrl = gains[0]['offset_ctrl'].shape[0]\n",
    "\n",
    "    diff_x = torch.zeros(dim_state)\n",
    "    diff_cmd = torch.zeros(horizon, dim_ctrl)\n",
    "\n",
    "    for t in range(horizon):\n",
    "        A = traj[t + 1].grad_dyn_state.t()\n",
    "        B = traj[t + 1].grad_dyn_ctrl.t() \n",
    "        diff_ctrl = gains[t]['gain_ctrl'].mv(diff_x) + gains[t]['offset_ctrl']\n",
    "        diff_cmd[t] = diff_ctrl\n",
    "        diff_x = A.mv(diff_x) + B.mv(diff_ctrl)\n",
    "    return diff_cmd\n",
    "\n",
    "\n",
    "def roll_out_exact(env, traj, gains, cmd):\n",
    "    dim_state, horizon = traj[0].shape, len(traj) - 1\n",
    "    diff_x, state = torch.zeros(dim_state), env.init_state\n",
    "    diff_cmd = torch.zeros_like(cmd) \n",
    "    diff_cmd.requires_grad = state.requires_grad = False\n",
    "\n",
    "    for t in range(horizon):\n",
    "        diff_ctrl = gains[t]['gain_ctrl'].mv(diff_x) + gains[t]['offset_ctrl']\n",
    "        diff_cmd[t] = diff_ctrl\n",
    "        state = env.discrete_dyn(state, cmd[t].data + diff_ctrl, t)\n",
    "        diff_x = state - traj[t+1].data\n",
    "    return diff_cmd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have now implemented the forward pass, the backward pass, and the roll-out phase. Regularized Gauss-Newton and Differential Dynamic Programming methods can then readily be implemented. We define the oracles associated with each algorithm and wrap them in a backtracking line search."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gn_reg_oracle(env, traj, costs, cmd, handle_bad_dir):\n",
    "    def oracle(stepsize):\n",
    "        gains, opt_step, feasible = lin_quad_backward(traj, costs, 1 / stepsize, handle_bad_dir=handle_bad_dir)\n",
    "        out = (roll_out_lin(traj, gains), opt_step) if feasible else (None, None)\n",
    "        return out\n",
    "    return oracle\n",
    "\n",
    "def ddp_reg_oracle(env, traj, costs, cmd, handle_bad_dir):\n",
    "    def oracle(stepsize):\n",
    "        gains, opt_step, feasible = lin_quad_backward(traj, costs, 1 / stepsize, handle_bad_dir=handle_bad_dir)\n",
    "        out = (roll_out_exact(env, traj, gains, cmd), opt_step) if feasible else (None, None)\n",
    "        return out\n",
    "    return oracle\n",
    "\n",
    "oracles = dict(classic_linquad_reg=gn_reg_oracle, ddp_linquad_reg=ddp_reg_oracle)\n",
    "\n",
    "def min_step(env, traj, costs, cmd, stepsize,\n",
    "             line_search, algo, handle_bad_dir):\n",
    "    def func(cmd):\n",
    "        traj, costs = env.forward(cmd)\n",
    "        cost = sum(costs)\n",
    "        return cost\n",
    "    \n",
    "    oracle = oracles[algo](env, traj, costs, cmd, handle_bad_dir)\n",
    "    if line_search:\n",
    "        diff_cmd, stepsize = backtrack_line_search(func, cmd, oracle, stepsize)\n",
    "    else:\n",
    "        diff_cmd, _ = oracle(stepsize)\n",
    "    if diff_cmd is not None:\n",
    "        next_cmd = cmd + diff_cmd\n",
    "        traj, costs = env.forward(next_cmd, approx='linquad')\n",
    "    else:\n",
    "        next_cmd = traj = costs = None\n",
    "    return next_cmd, traj, costs, stepsize\n",
    "\n",
    "def backtrack_line_search(func, var, oracle, stepsize):\n",
    "    decrease_fac = 0.1\n",
    "    increase_fac = 10.\n",
    "    stepsize *= increase_fac\n",
    "    dir = float(np.sign(stepsize))\n",
    "\n",
    "    curr_val = func(var)\n",
    "    diff_var, dec_obj = oracle(stepsize)\n",
    "\n",
    "    if diff_var is None:\n",
    "        decrease = False\n",
    "        stop = np.abs(stepsize) < 1e-32\n",
    "    else:\n",
    "        new_val = func(var + diff_var)\n",
    "        decrease = dir * (new_val - (curr_val + dec_obj)) < 0\n",
    "        stop = torch.norm(diff_var) < 1e-12\n",
    "\n",
    "    while not decrease and not stop:\n",
    "        stepsize *= decrease_fac\n",
    "\n",
    "        diff_var, dec_obj = oracle(stepsize)\n",
    "\n",
    "        if diff_var is None:\n",
    "            decrease = False\n",
    "            stop = np.abs(stepsize) < 1e-32\n",
    "        else:\n",
    "            new_val = func(var + diff_var)\n",
    "            decrease = dir * (new_val - (curr_val + dec_obj)) < 0\n",
    "            stop = torch.norm(diff_var) < 1e-12\n",
    "\n",
    "    if stop:\n",
    "        print('line-search failed')\n",
    "    return diff_var, stepsize\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We finally define a function that iterates one of the above algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from algorithms.run_min_algo import check_cvg_status\n",
    "from utils_pipeline.optim_helpers import print_info_step\n",
    "\n",
    "def run_min_algo(env, max_iter=10, algo='ddp_linquad_reg', stepsize=1., line_search=True, handle_bad_dir='flag'):\n",
    "    cmd = torch.zeros(env.horizon, env.dim_ctrl)\n",
    "    cmd.requires_grad = True\n",
    "    \n",
    "    traj, costs = env.forward(cmd, approx='linquad')\n",
    "    metrics, iteration, time_start = None, 0, 0.\n",
    "    metrics = collect_info(metrics, env, cmd, costs, iteration, stepsize, algo, time_start)\n",
    "    status = check_cvg_status(metrics)\n",
    "\n",
    "    while status == 'running' and iteration < max_iter:\n",
    "        start_time = time.time()\n",
    "        cmd, traj, costs, stepsize = min_step(env, traj, costs, cmd, stepsize,\n",
    "                                              line_search, algo, handle_bad_dir)\n",
    "        iteration += 1\n",
    "        time_iter = time.time() - start_time\n",
    "        metrics = collect_info(metrics, env, cmd, costs, iteration, stepsize, algo, time_iter)\n",
    "        stop = check_cvg_status(metrics)\n",
    "\n",
    "    return cmd.data, metrics\n",
    "\n",
    "def collect_info(metrics, env, cmd, costs, iteration, stepsize, algo, time_iter):\n",
    "    cumul_time = 0. if iteration == 0 else metrics['time'][-1]\n",
    "    cost = sum(costs) if costs is not None else torch.tensor(float('nan'))\n",
    "    info_step = dict(iteration=iteration, time=cumul_time + time_iter, cost=cost.item(), stepsize=stepsize, algo=algo)\n",
    "    format_types = ['int', 'time', 'scientific', 'scientific', 'string']\n",
    "    print_info_step(info_step, format_types, iteration == 0)\n",
    "    if metrics is None:\n",
    "        metrics = {key: [info_step[key]] for key in info_step.keys()}\n",
    "    else:\n",
    "        for key in info_step.keys():\n",
    "            metrics[key].append(info_step[key])\n",
    "    return metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now test our algorithms and compare their convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run with classic_linquad_reg\n",
      "iteration           time                cost                stepsize            algo                \n",
      "0                   0:00:00             1.12e-01            1.00e+00            classic_linquad_reg \n",
      "1                   0:00:00.699290      6.97e-02            1.00e+01            classic_linquad_reg \n",
      "2                   0:00:01.324002      6.44e-02            1.00e+02            classic_linquad_reg \n",
      "3                   0:00:01.988331      6.27e-02            1.00e+02            classic_linquad_reg \n",
      "4                   0:00:02.654109      6.14e-02            1.00e+02            classic_linquad_reg \n",
      "5                   0:00:03.254764      5.40e-02            1.00e+03            classic_linquad_reg \n",
      "6                   0:00:03.920956      5.04e-02            1.00e+02            classic_linquad_reg \n",
      "7                   0:00:04.522613      4.40e-02            1.00e+03            classic_linquad_reg \n",
      "8                   0:00:05.131332      3.66e-02            1.00e+03            classic_linquad_reg \n",
      "9                   0:00:05.803036      3.31e-02            1.00e+02            classic_linquad_reg \n",
      "10                  0:00:06.405702      2.91e-02            1.00e+03            classic_linquad_reg \n",
      "Run with ddp_linquad_reg\n",
      "iteration           time                cost                stepsize            algo                \n",
      "0                   0:00:00             1.12e-01            1.00e+00            ddp_linquad_reg     \n",
      "1                   0:00:00.615435      6.95e-02            1.00e+01            ddp_linquad_reg     \n",
      "2                   0:00:01.337321      6.43e-02            1.00e+02            ddp_linquad_reg     \n",
      "3                   0:00:02.040562      6.27e-02            1.00e+02            ddp_linquad_reg     \n",
      "4                   0:00:02.728597      6.15e-02            1.00e+02            ddp_linquad_reg     \n",
      "5                   0:00:03.405366      6.03e-02            1.00e+02            ddp_linquad_reg     \n",
      "6                   0:00:04.088491      5.92e-02            1.00e+02            ddp_linquad_reg     \n",
      "7                   0:00:04.759977      5.82e-02            1.00e+02            ddp_linquad_reg     \n",
      "8                   0:00:05.435394      5.72e-02            1.00e+02            ddp_linquad_reg     \n",
      "9                   0:00:06.107609      5.62e-02            1.00e+02            ddp_linquad_reg     \n",
      "10                  0:00:06.783973      5.52e-02            1.00e+02            ddp_linquad_reg     \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from finite_horizon_control.utils_plot import plot_conv_costs\n",
    "\n",
    "horizon = 40\n",
    "\n",
    "# Try with simple or real models\n",
    "env = Car(model='simple', track='simple', horizon=horizon,\n",
    "          reg_cont=1., reg_lag=10., reg_speed=1., reg_bar=100., vref=3.)\n",
    "algos = ['classic_linquad_reg', 'ddp_linquad_reg']\n",
    "\n",
    "metrics_algos = pd.DataFrame()\n",
    "cmd_opts = list()\n",
    "for algo in algos:\n",
    "    print('Run with {}'.format(algo))\n",
    "    cmd_opt, metrics = run_min_algo(env, max_iter=10, algo=algo)\n",
    "    cmd_opts.append(cmd_opt)\n",
    "    metrics_algos = pd.concat([metrics_algos, pd.DataFrame(metrics)], ignore_index=True)\n",
    "\n",
    "plot_conv_costs(metrics_algos, start_plot_after=5)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from finite_horizon_control.utils_plot import get_nice_writing\n",
    "\n",
    "nice_writing = get_nice_writing()\n",
    "\n",
    "# Observe the trajectories \n",
    "fig, axs = plt.subplots(ncols=2, figsize=(8, 4))\n",
    "\n",
    "for i, cmd in enumerate(cmd_opts):\n",
    "    fig, ax = env.plot_track(fig, axs[i])\n",
    "    traj, _ = env.forward(cmd)\n",
    "    fig = env.plot_traj(traj, fig, ax, add_colorbar=False)\n",
    "    ax.title.set_text(nice_writing[algos[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "FALLBACK (log once): Fallback to SW vertex for line stipple\n",
      "FALLBACK (log once): Fallback to SW vertex processing, m_disable_code: 2000\n",
      "FALLBACK (log once): Fallback to SW vertex processing in drawCore, m_disable_code: 2000\n"
     ]
    }
   ],
   "source": [
    "# Visualize the movements \n",
    "for i, cmd in enumerate(cmd_opts):\n",
    "    env.reset()\n",
    "    env.render(title=nice_writing[algos[i]])\n",
    "    for ctrl in cmd:\n",
    "        time.sleep(env.dt)\n",
    "        env.step(ctrl)\n",
    "        env.render(title=nice_writing[algos[i]])\n",
    "    time.sleep(car.dt)\n",
    "env.viewer.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For short horizons (e.g. 40 time steps), we observe that the algorithms converge fast, yet the horizon is too small for the car to travel the whole track. For longer horizons, the problem gets more difficult as shown in the following code. To observe the trajectories after different maximum number of iterations, we wrap our code in a pipeline that regularly saves the results, see the source code for more details on the pipeline. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "env_cfg:{'env': 'simple_car', 'track': 'simple', 'reg_cont': 0.1, 'reg_lag': 10.0, 'reg_speed': 1.0, 'reg_bar': 100.0, 'vref': 3.0}\n",
      "optim_cfg:{'max_iter': 100, 'algo': 'classic_linquad_reg'}\n",
      "env_cfg:{'env': 'simple_car', 'track': 'simple', 'reg_cont': 0.1, 'reg_lag': 10.0, 'reg_speed': 1.0, 'reg_bar': 100.0, 'vref': 3.0}\n",
      "optim_cfg:{'max_iter': 100, 'algo': 'ddp_linquad_reg'}\n",
      "env_cfg:{'env': 'simple_car', 'track': 'simple', 'reg_cont': 0.1, 'reg_lag': 10.0, 'reg_speed': 1.0, 'reg_bar': 100.0, 'vref': 3.0}\n",
      "optim_cfg:{'max_iter': 30, 'algo': 'ddp_linquad_reg'}\n",
      "17                  0:00:15.510475      4.89e-03            1.56e-07            9.11e+01            ddp_linquad_reg     \n",
      "18                  0:00:15.987693      4.89e-03            9.38e-08            1.25e-04            ddp_linquad_reg     \n",
      "19                  0:00:16.260207      4.89e-03            8.11e-08            6.00e-04            ddp_linquad_reg     \n",
      "20                  0:00:16.730512      4.89e-03            5.15e-08            6.49e-05            ddp_linquad_reg     \n",
      "21                  0:00:16.998972      4.89e-03            4.16e-08            3.29e-04            ddp_linquad_reg     \n",
      "22                  0:00:17.518626      4.89e-03            1.85e-08            1.66e-05            ddp_linquad_reg     \n",
      "23                  0:00:17.783271      4.89e-03            9.33e-09            5.92e-05            ddp_linquad_reg     \n",
      "24                  0:00:18.110888      4.89e-03            9.64e-09            5.97e-05            ddp_linquad_reg     \n",
      "25                  0:00:18.561898      4.89e-03            5.62e-09            7.71e-06            ddp_linquad_reg     \n",
      "26                  0:00:18.819139      4.89e-03            6.10e-09            3.59e-05            ddp_linquad_reg     \n",
      "27                  0:00:19.267979      4.89e-03            3.57e-09            4.88e-06            ddp_linquad_reg     \n",
      "28                  0:00:19.557158      4.89e-03            2.34e-09            1.14e-05            ddp_linquad_reg     \n",
      "29                  0:00:19.972820      4.89e-03            1.53e-09            1.87e-06            ddp_linquad_reg     \n",
      "30                  0:00:20.229875      4.89e-03            1.45e-09            9.78e-06            ddp_linquad_reg     \n",
      "env_cfg:{'env': 'simple_car', 'track': 'simple', 'reg_cont': 0.1, 'reg_lag': 10.0, 'reg_speed': 1.0, 'reg_bar': 100.0, 'vref': 3.0}\n",
      "optim_cfg:{'max_iter': 40, 'algo': 'ddp_linquad_reg'}\n",
      "31                  0:00:20.709396      4.89e-03            6.38e-10            5.79e-07            ddp_linquad_reg     \n",
      "32                  0:00:20.964627      4.89e-03            3.43e-10            2.04e-06            ddp_linquad_reg     \n",
      "33                  0:00:21.424915      4.89e-03            3.54e-10            1.10e-06            ddp_linquad_reg     \n",
      "34                  0:00:21.851244      4.89e-03            2.17e-10            2.83e-07            ddp_linquad_reg     \n",
      "35                  0:00:22.109442      4.89e-03            1.23e-10            1.39e-06            ddp_linquad_reg     \n",
      "36                  0:00:22.462882      4.89e-03            9.77e-11            7.88e-07            ddp_linquad_reg     \n",
      "37                  0:00:22.915693      4.89e-03            5.26e-11            7.82e-08            ddp_linquad_reg     \n",
      "38                  0:00:23.176602      4.89e-03            5.07e-11            3.37e-07            ddp_linquad_reg     \n",
      "39                  0:00:23.650836      4.89e-03            2.94e-11            4.05e-08            ddp_linquad_reg     \n",
      "40                  0:00:23.914165      4.89e-03            1.97e-11            1.88e-07            ddp_linquad_reg     \n",
      "env_cfg:{'env': 'simple_car', 'track': 'simple', 'reg_cont': 0.1, 'reg_lag': 10.0, 'reg_speed': 1.0, 'reg_bar': 100.0, 'vref': 3.0}\n",
      "optim_cfg:{'max_iter': 50, 'algo': 'ddp_linquad_reg'}\n",
      "41                  0:00:24.361410      4.89e-03            1.15e-11            1.58e-08            ddp_linquad_reg     \n",
      "42                  0:00:24.750790      4.89e-03            7.30e-12            4.60e-09            ddp_linquad_reg     \n",
      "line-search failed\n",
      "43                  0:00:27.856632      4.89e-03            7.30e-12            7.55e-35            ddp_linquad_reg     \n",
      "ddp_linquad_reg converged in 43 iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from finite_horizon_control.fhc_pipeline import solve_ctrl_pb_incrementally\n",
    "\n",
    "env_cfg = dict(env='simple_car', track='simple',\n",
    "               reg_cont=0.1, reg_lag=10., reg_speed=1., reg_bar=100., vref=3.\n",
    "               )\n",
    "optim_cfg = dict(max_iter=100)\n",
    "\n",
    "algos = ['classic_linquad_reg','ddp_linquad_reg']\n",
    "\n",
    "metrics_algos = pd.DataFrame()\n",
    "cmd_opts = list()\n",
    "for algo in algos:\n",
    "    optim_cfg.update(algo=algo)\n",
    "    exp_outputs = solve_ctrl_pb_incrementally(env_cfg, optim_cfg)\n",
    "    cmd_opts.append(exp_outputs['cmd_opt'])\n",
    "    metrics = exp_outputs['metrics']\n",
    "    metrics_algos = pd.concat([metrics_algos, pd.DataFrame(metrics)], ignore_index=True)\n",
    "    \n",
    "plot_conv_costs(metrics_algos, start_plot_after=5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from envs.choose_env import make_env\n",
    "\n",
    "env = make_env(env_cfg)\n",
    "# Observe the trajectories \n",
    "fig, axs = plt.subplots(ncols=2, figsize=(8, 4))\n",
    "\n",
    "for i, cmd in enumerate(cmd_opts):\n",
    "    fig, ax = env.plot_track(fig, axs[i])\n",
    "    traj, _ = env.forward(cmd)\n",
    "    fig = env.plot_traj(traj, fig, ax, add_colorbar=False)\n",
    "    ax.title.set_text(nice_writing[algos[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Visualize the movements \n",
    "for i, cmd in enumerate(cmd_opts):\n",
    "    env.reset()\n",
    "    env.render(title=nice_writing[algos[i]])\n",
    "    for ctrl in cmd:\n",
    "        time.sleep(env.dt)\n",
    "        env.step(ctrl)\n",
    "        env.render(title=nice_writing[algos[i]])\n",
    "    time.sleep(car.dt)\n",
    "env.viewer.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For long horizons, the algorithms can be very slow. On the other hand, we need long horizons to ensure that the car makes a whole loop on the track. To trade-off these constraints with consider a Model Predictive Control approach presented in the notebook [Model Predictive Control](mpc.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Additional Details\n",
    "The code presented in this notebook is almost identical to the one provided in the folder src. The main difference is that we implemented the oracles for both the risk neutral case (i.e., the case presented above) and the risk sensitive case where an additional noise parameter is to be optimized. The objective consists then in a min-max problem which minimizes with respect to the control variables and maximizes with respect to the noise variables. Hence noises variables are added in the formulation of the environments and the oracles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='refs'></a>\n",
    "## References\n",
    "\n",
    "**Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates.**  \n",
    "Vincent Roulet, Siddharta Srinivasa, Maryam Fazel, Zaid Harchaoui.  \n",
    "*Technical Report*\n",
    "\n",
    "**Iterative Linearized Control: Stable Algorithms and Complexity Guarantees.**  \n",
    "Vincent Roulet, Siddharta Srinivasa, Dmitry Drusvyatskiy, Zaid Harchaoui.  \n",
    "*Proceedings of the 36th International Conference on Machine Learning (ICML 2019).*  "
   ]
  }
 ],
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