PyCon financial aid grant optimization with COBYLA

cobyla.ipynb

{
 "metadata": {
  "name": "PyCon grant optimization COBYLA"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def expected_regret(grants, k, scores, requested):\n    \"\"\"-1 * the expectance of the scores.\n\n    \"\"\"\n    probabilities = (grants ** k) / (requested ** k)\n    return -1 * sum(scores * probabilities)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "from functools import partial\n\ndef budget_constraint(grants, budget):\n    \"\"\"The budget minus the sum of all grants; must be >= 0.\n\n    \"\"\"\n    return budget - sum(grants)\n\n\ndef make_grant_constraints(requested_amounts):\n    \"\"\"\n    Makes all the grant constraints\n    \"\"\"\n    le_requested = [partial(_grant_le_requested, index=i, requested_amount=amount)\n                    for i, amount in enumerate(requested_amounts)]\n    gt_zero = [(lambda grants, i=i: grants[i]) for i in xrange(len(requested_amounts))]\n    return le_requested + gt_zero\n\n\ndef _grant_le_requested(grants, index, requested_amount):\n    \"\"\"Constraint function that makes sure the grant amount with given\n    index is less than or equal to the requested amount.\n\n    \"\"\"\n    return requested_amount - grants[index]",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "from numpy import array, zeros\nfrom scipy.optimize import fmin_cobyla\n\ndef main():\n    scores = array([1, 1, 1, 2, 3, 5, 5])\n    requested = array([10, 20, 30, 30, 50, 10, 50])\n    budget = 150\n\n    print \"scores: {}\".format(scores)\n    print \"requested: {} total: {}, budget: {}\".format(requested, sum(requested), budget)\n\n    the_budget_constraint = partial(budget_constraint, budget=budget)\n    the_grant_constraints = make_grant_constraints(requested)\n    constraints = [the_budget_constraint] + the_grant_constraints\n\n    for ik in [(1./2), 1, 2, 3, 5, 10, 100]:\n        res = fmin_cobyla(expected_regret, args=(1./ik, scores, requested),\n                          x0=zeros(len(scores)),\n                          cons=constraints, consargs=(),\n                          disp=0)\n        print \"k = 1/{}: {}, sum: {}\".format(ik, res.round(), res.sum())",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "main()\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "scores: [1 1 1 2 3 5 5]\nrequested: [10 20 30 30 50 10 50] total: 200, budget: 150\nk = 1/0.5: [ 10.  20.  30.  30.  50.  10.   0.], sum: 150.0"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nk = 1/1: [ 10.  -0.   0.  30.  50.  10.  50.], sum: 150.0"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nk = 1/2: [ 10.  10.   7.  27.  36.  10.  50.], sum: 150.0"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nk = 1/3: [ 10.  11.   9.  25.  35.  10.  50.], sum: 150.0"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nk = 1/5: [ 10.  11.  10.  24.  35.  10.  50.], sum: 150.0"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nk = 1/10: [ 10.  11.  11.  23.  35.  10.  50.], sum: 150.0"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nk = 1/100: [ 10.  11.  11.  23.  34.  10.  50.], sum: 150.0"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\n"
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}