Agentmodels, WebPPL: Monty Hall Example

monty.wppl

// Remove each element in array ys from array xs
var remove = function(xs, ys) {
  return _.without.apply(null, [xs].concat(ys));
};

var doors = [1, 2, 3];

// Monty chooses a door that is neither Alice's door
// nor the prize door
var monty = function(aliceDoor, prizeDoor) {
  return Infer({ 
    model() {
      var door = uniformDraw(doors);
      condition(door != aliceDoor);
      condition(door != prizeDoor);
      return door;
    }});
};


var actions = ['switch', 'stay'];

// If Alice switches, she randomly chooses a door that is
// neither the one Monty showed nor her previous door
var transition = function(state, action) {
  if (action === 'switch') {
    return {
      prizeDoor: state.prizeDoor,
      montyDoor: state.montyDoor,
      aliceDoor: uniformDraw(remove(doors,[state.aliceDoor,state.montyDoor]))
    };
  } else {
    return state;
  }
};

// Utility is high (say 10) if Alice's door matches the
// prize door, 0 otherwise.
var utility = function(state) {
  if (state.aliceDoor === state.prizeDoor)
    return 10;
  else
    return 0;
};

var sampleState = function() {
  var aliceDoor = uniformDraw(doors);
  var prizeDoor = uniformDraw(doors);
  return {
    aliceDoor,
    prizeDoor,
    montyDoor: sample(monty(aliceDoor, prizeDoor))
  }
}

var agent = function() {  
  var action = uniformDraw(actions);
  var expectedUtility = function(action){    
    return expectation(Infer({ 
      model() {
        var state = sampleState();
        return utility(transition(state, action));
      }}));
  };
  factor(expectedUtility(action));
  return { action };
};

viz(Infer({ model: agent }));