ddp_solve_lp_py

ddp_solve_lp_py01.ipynb

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   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "import openopt\n",
    "import quantecon as qe\n",
    "from quantecon.markov.ddp import DPSolveResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
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   "source": [
    "def solve(ddp, solver='pclp', iprint=-1):\n",
    "    n = ddp.num_states\n",
    "    L = ddp.num_sa_pairs\n",
    "    \n",
    "    # min  f v\n",
    "    # s.t. A v <= b\n",
    "    A = ddp.Q * ddp.beta\n",
    "    b = -ddp.R\n",
    "    if ddp._sa_pair:\n",
    "        A[np.arange(L), ddp.s_indices] -= 1\n",
    "    else:\n",
    "        A[np.arange(n), :, np.arange(n)] -= 1\n",
    "        A.shape = (L, n)\n",
    "        b.shape = (L,)\n",
    "    f = np.ones(n)\n",
    "    \n",
    "    p = openopt.LP(f=f, A=A, b=b)\n",
    "    r = p.minimize(solver, iprint=iprint)\n",
    "    v = r.xf\n",
    "    \n",
    "    sigma = ddp.compute_greedy(v)\n",
    "    mc = ddp.controlled_mc(sigma)\n",
    "    \n",
    "    res = DPSolveResult(v=v,\n",
    "                        sigma=sigma,\n",
    "                        mc=mc,\n",
    "                        method='linear programming')\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "seed = 1234"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ddp = qe.markov.random_discrete_dp(3, 2, 0.95, random_state=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "       mc: Markov chain with transition matrix \n",
       "P = \n",
       "[[ 0.27646426  0.52540792  0.19812782]\n",
       " [ 0.35781727  0.14317786  0.49900487]\n",
       " [ 0.01376845  0.48931472  0.49691683]]\n",
       " num_iter: 1\n",
       " max_iter: 250\n",
       "    sigma: array([0, 0, 1])\n",
       "   method: 'policy iteration'\n",
       "        v: array([ 19.63935279,  20.45805973,  20.18065736])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ddp.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     mc: Markov chain with transition matrix \n",
       "P = \n",
       "[[ 0.27646426  0.52540792  0.19812782]\n",
       " [ 0.35781727  0.14317786  0.49900487]\n",
       " [ 0.01376845  0.48931472  0.49691683]]\n",
       "  sigma: array([0, 0, 1])\n",
       " method: 'linear programming'\n",
       "      v: array([ 19.63935279,  20.45805973,  20.18065736])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(ddp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     mc: Markov chain with transition matrix \n",
       "P = \n",
       "[[ 0.27646426  0.52540792  0.19812782]\n",
       " [ 0.35781727  0.14317786  0.49900487]\n",
       " [ 0.01376845  0.48931472  0.49691683]]\n",
       "  sigma: array([0, 0, 1])\n",
       " method: 'linear programming'\n",
       "      v: array([ 19.63935279,  20.45805973,  20.18065736])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ddp_sa = qe.markov.random_discrete_dp(3, 2, 0.95, sa_pair=True, random_state=seed)\n",
    "solve(ddp_sa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     mc: Markov chain with transition matrix \n",
       "P = \n",
       "  (0, 2)\t0.198127822465\n",
       "  (0, 1)\t0.525407922392\n",
       "  (0, 0)\t0.276464255143\n",
       "  (1, 2)\t0.499004874477\n",
       "  (1, 1)\t0.143177855566\n",
       "  (1, 0)\t0.357817269958\n",
       "  (2, 2)\t0.496916834692\n",
       "  (2, 1)\t0.489314715717\n",
       "  (2, 0)\t0.0137684495907\n",
       "  sigma: array([0, 0, 1])\n",
       " method: 'linear programming'\n",
       "      v: array([ 19.63935279,  20.45805973,  20.18065736])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ddp_sp = qe.markov.random_discrete_dp(3, 2, 0.95, sparse=True, random_state=seed)\n",
    "solve(ddp_sp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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