```
# -*- coding: utf-8 -*-
"""
Implements Coordinated PGT intelligence for Policies for iterSemiNFG objects
Created on Fri Mar 22 15:32:33 2013
Copyright (C) 2013 James Bono (jwbono@gmail.com)
GNU Affero General Public License
"""
from __future__ import division
import copy
import numpy as np
from pynfg import DecisionNode, iterSemiNFG
from pynfg.utilities.utilities import mh_decision
import sys
[docs]def policy_MC(G, S, noise, X, M, innoise=1, delta=1, integrand=None, \
mix=False, satisfice=None):
"""Run Importance Sampling on policies for PGT Intelligence Calculations
For examples, see below or PyNFG/bin/hideandseek.py
:arg G: the game to be evaluated
:type G: iterSemiNFG
:arg S: number of policy profiles to sample
:type S: int
:arg noise: the degree of independence of the proposal distribution on the
current value. 1 is independent, 0 returns no perturbation.
:type noise: float
:arg X: number of samples of each policy profile
:type X: int
:arg M: number of random alt policies to compare
:type M: int
:arg innoise: the perturbation noise for the loop within iq_calc to draw
alt CPTs to compare utilities to current CPT.
:type innoise: float
:arg delta: the discount factor (ignored if SemiNFG)
:type delta: float
:arg integrand: a user-supplied function of G that is evaluated for each s
in S
:type integrand: func
:arg mix: False if restricting sampling to pure strategies. True if mixed
strategies are included in sampling. Default is False.
:type mix: bool
:arg satisfice: game G such that the CPTs of G together with innoise
determine the intelligence satisficing distribution.
:type satisfice: iterSemiNFG
:returns:
* intel - a sample-keyed dictionary of player-keyed iq dictionaries
* funcout - a sample-keyed dictionary of the output of the
user-supplied integrand.
* weight - a sample-keyed dictionay of player-keyed importance weight
dictionaries.
.. warning::
This will throw an error if there is a decision node in G.starttime that
is not repeated throughout the net.
.. note::
This is the policy-approach because intelligence is assigned to a
player instead of being assigned to a DecisionNode, and all DNs with
the same basename have the same CPT.
Example::
def welfare(G):
#calculate the welfare of a single sample of the iterSemiNFG G
G.sample()
w = 0
for p in G.players:
w += G.npv_reward(p, G.starttime, 1.0)
return w
import copy
GG = copy.deepcopy(G) #G is an iterSemiNFG
S = 50 #number of MC samples
X = 10 #number of samples of utility of G in calculating iq
M = 20 #number of alternative strategies sampled in calculating iq
noise = .2 #noise in the perturbations of G for MC sampling
from pynfg.pgtsolutions.intelligence.policy import policy_MC
intelMC, funcoutMC, weightMC = policy_MC(GG, S, noise, X, M,
innoise=.2,
delta=1,
integrand=welfare,
mix=False,
satisfice=GG)
"""
intel = {} #keys are sample indices, vals are iq dictionaries
iq = {} #keys are player names, vals are iqs
weight = {} #keys are
w = {}
funcout = {} #keys are s in S, vals are eval of integrand of G(s)
bndict = {}
T0 = G.starttime
for p in G.players: #getting player-keyed dict of basenames
bndict[p] = [x.basename for x in G.partition[p] if x.time==T0]
for s in xrange(1, S+1): #sampling S policy profiles
sys.stdout.write('\r')
sys.stdout.write('MC Sample ' + str(s))
sys.stdout.flush()
GG = copy.deepcopy(G)
for p in G.players:
w[p] = 1
for bn in bndict[p]: #getting importance weights for each player
w[p] *= GG.bn_part[bn][0].perturbCPT(noise, mixed=mix, \
returnweight=True)
for dn in GG.bn_part[bn][1::]:
dn.CPT = GG.bn_part[bn][0].CPT
for p in G.players: #find the iq of each player's policy in turn
iq[p] = policy_calciq(p, GG, X, M, mix, delta, innoise, satisfice)
if integrand is not None:
funcout[s] = integrand(GG) #eval integrand G(s), assign to funcout
intel[s] = copy.deepcopy(iq)
weight[s] = copy.deepcopy(w)
return intel, funcout, weight
[docs]def policy_MH(G, S, density, noise, X, M, innoise=1, delta=1, \
integrand=None, mix=False, satisfice=None):
"""Run Metropolis-Hastings on policies for PGT Intelligence Calculations
For examples, see below or PyNFG/bin/hideandseek.py
:arg G: the game to be evaluated
:type G: iterSemiNFG
:arg S: number of MH iterations
:type S: int
:arg density: the function that assigns weights to iq
:type density: func
:arg noise: the degree of independence of the proposal distribution on the
current value. 1 is independent, 0 returns no perturbation.
:type noise: float
:arg X: number of samples of each policy profile
:type X: int
:arg M: number of random alt policies to compare
:type M: int
:arg innoise: the perturbation noise for the loop within iq_calc to draw
alt CPTs to compare utilities to current CPT.
:type innoise: float
:arg delta: the discount factor (ignored if SemiNFG)
:type delta: float
:arg integrand: a user-supplied function of G that is evaluated for each s
in S
:type integrand: func
:arg mix: if true, proposal distribution is over mixed CPTs. Default is
False.
:type mix: bool
:arg satisfice: game G such that the CPTs of G together with innoise
determine the intelligence satisficing distribution.
:type satisfice: iterSemiNFG
:returns:
* intel - a sample-keyed dictionary of player-keyed iq dictionaries
* funcout - a sample-keyed dictionary of the output of the
user-supplied integrand.
* dens - a list of the density values, one for each MH draw.
.. warning::
This will throw an error if there is a decision node in G.starttime that
is not repeated throughout the net.
.. note::
This is the policy-approach because intelligence is assigned to a
player instead of being assigned to a DecisionNode, and all DNs with
the same basename have the same CPT.
Example::
def density(iqdict):
#calculate the PGT density for a given iqdict
x = iqdict.values()
y = np.power(x,2)
z = np.product(y)
return z
def welfare(G):
#calculate the welfare of a single sample of the iterSemiNFG G
G.sample()
w = 0
for p in G.players:
w += G.npv_reward(p, G.starttime, 1.0)
return w
import copy
GG = copy.deepcopy(G) #G is an iterSemiNFG
S = 50 #number of MH samples
X = 10 #number of samples of utility of G in calculating iq
M = 20 #number of alternative strategies sampled in calculating iq
noise = .2 #noise in the perturbations of G for MH sampling
from pynfg.pgtsolutions.intelligence.policy import policy_MH
intelMH, funcoutMH, densMH = policy_MH(GG, S, density, noise, X, M,
innoise=.2,
delta=1,
integrand=welfare,
mix=False,
satisfice=GG)
"""
intel = {} #keys are s in S, vals are iq dict (dict of dicts)
iq = {} #keys are base names, iq timestep series
funcout = {} #keys are s in S, vals are eval of integrand of G(s)
dens = np.zeros(S+1) #storing densities for return
bndict = {} #mapping from player name to DN basenames
T0 = G.starttime
for p in G.players: #getting player-keyed dict of basenames
bndict[p] = [x.basename for x in G.partition[p] if x.time==T0]
for s in xrange(1, S+1): #sampling S sequences of policy profiles
sys.stdout.write('\r')
sys.stdout.write('MH Sample ' + str(s))
sys.stdout.flush()
GG = copy.deepcopy(G)
for p in G.players: #taking the new MH draw
for bn in bndict[p]:
GG.bn_part[bn][0].perturbCPT(noise, mixed=mix)
for dn in GG.bn_part[bn][1::]:
dn.CPT = GG.bn_part[bn][0].CPT
for p in GG.players: #getting iq for each player with new MH draw
iq[p] = policy_calciq(p, GG, X, M, mix, delta, innoise, satisfice)
# The MH decision
current_dens = density(iq) #evaluating density of current draw's iq
verdict = mh_decision(current_dens, dens[s-1]) #True if accept new draw
if verdict: #accepting new CPT
intel[s] = copy.deepcopy(iq)
G = copy.deepcopy(GG)
dens[s] = current_dens
else:
intel[s] = intel[s-1]
dens[s] = dens[s-1]
if integrand is not None:
funcout[s] = integrand(G) #eval integrand G(s), assign to funcout
return intel, funcout, dens[1::]
[docs]def policy_calciq(p, G, X, M, mix, delta, innoise, satisfice=None):
"""Estimate IQ of player's policy
:arg p: the name of the player whose intelligence is being evaluated.
:type p: str
:arg G: the iterated semi-NFG to be evaluated
:type G: iterSemiNFG
:arg X: number of samples of each policy profile
:type X: int
:arg M: number of random alt policies with which to compare
:type M: int
:arg mix: if true, proposal distribution is over mixed CPTs. Default is
False.
:type mix: bool
:arg delta: the discount factor (ignored if SemiNFG)
:type delta: float
:arg innoise: the perturbation noise for the inner loop to draw alt CPTs
:type innoise: float
:arg satisfice: game G such that the CPTs of G together with innoise
determine the intelligence satisficing distribution.
:type satisfice: iterSemiNFG
:returns: an estimate of the fraction of alternative policies that have a
lower npv reward than the current policy.
"""
util = 0
altutil = [0]*M
weight = np.ones(M)
tick = 0
T0 = G.starttime
bnlist = [x.basename for x in G.partition[p] if x.time==T0]
for x in xrange(1,X+1):
G.sample()
util += G.npv_reward(p,G.starttime,delta)/X
if satisfice: #using the satisficing distribution for drawing alternatives
G = copy.deepcopy(satisfice)
cptdict = G.get_decisionCPTs(mode='basename')
smalldict = {key: cptdict[key] for key in bnlist}
for m in range(M): #Sample M alt policies for the player
G.set_CPTs(smalldict)
denw = 1
for bn in bnlist: #rand CPT for the DN
#density for the importance sampling distribution
if innoise==1:
G.bn_part[bn][0].randomCPT()
elif satisfice:
G.bn_part[bn][0].perturbCPT(innoise, mixed=mix)
else:
denw *= G.bn_part[bn][0].perturbCPT(innoise, mixed=mix, \
returnweight=True)
if not tick:
numw = denw #scale const. num. to ~mag. of den (save mem.)
weight[m] *= (numw/denw)
tick += 1
# import pdb; pdb.set_trace()
for dn in G.bn_part[bn][1::]:
dn.CPT = G.bn_part[bn][0].CPT
G.sample() #sample altpolicy prof. to end of net
altutil[m] = G.npv_reward(p, G.starttime, delta)
#weight of alts worse than G
worse = [weight[m] for m in range(M) if altutil[m]<util]
return np.sum(worse)/np.sum(weight) #fraction of alts worse than G is IQ
```