Uncoordinated Intelligence

Implements Uncoordinated PGT Intelligence for SemiNFG objects

Created on Wed Jan 2 16:33:36 2013

Copyright (C) 2013 James Bono

GNU Affero General Public License

pynfg.pgtsolutions.intelligence.uncoordinated.uncoordinated_MC(G, S, noise, X, M, innoise, delta=1, integrand=None, mix=False, satisfice=None)

Run Importance Sampling on strategies for PGT Intelligence Calculations

For examples, see below or PyNFG/bin/stackelberg.py for SemiNFG or PyNFG/bin/hideandseek.py for iterSemiNFG

Parameters:

• G (SemiNFG or iterSemiNFG) – the game to be evaluated
• S (int) – number of policy profiles to sample
• noise (float) – the degree of independence of the proposal distribution on the current value. 1 is independent, 0 returns no perturbation.
• X (int) – number of samples of each policy profile
• M (int) – number of random alt policies to compare
• innoise (float) – the perturbation noise for the loop within iq_calc to draw alt CPTs to compare utilities to current CPT.
• delta (float) – the discount factor (ignored if SemiNFG)
• integrand (func) – a user-supplied function of G that is evaluated for each s in S
• mix (bool) – False if restricting sampling to pure strategies. True if mixed strategies are included in sampling. Default is False.
• satisfice (SemiNFG or iterSemiNFG) – game G such that the CPTs of G together with innoise determine the intelligence satisficing distribution.

Returns:

• intel - a sample-keyed dictionary of decision node-keyed iq dicts
• funcout - a sample-keyed dictionary of the output of the user-supplied integrand.
• weight - a sample-keyed dictionay of decision nod-keyed importance weight dictionaries.

Note

This is the uncoordinated approach because intelligence is assigned to decision nodes instead of being assigned to players. As a result, it takes much longer to run than pynfg.pgtsolutions.intelligence.coordinated.coordinated_MC

Example:

def welfare(G):
    #calculate the welfare of a single sample of the SemiNFG G
    G.sample()
    w = G.utility('1')+G.utility('2') #'1' & '2' are player names in G
    return w

import copy
GG = copy.deepcopy(G) #G is a SemiNFG
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.uncoordinated import uncoordinated_MC

intelMC, funcoutMC, weightMC = uncoordinated_MC(GG, S, noise, X, M,
                                                innoise=.2,
                                                delta=1,
                                                integrand=welfare,
                                                mix=False,
                                                satisfice=GG)

pynfg.pgtsolutions.intelligence.uncoordinated.uncoordinated_MH(G, S, density, noise, X, M, innoise=1, delta=1, integrand=None, mix=False, satisfice=None)

Run Metropolis-Hastings on strategies for PGT Intelligence Calculations

For examples, see below or PyNFG/bin/stackelberg.py for SemiNFG or PyNFG/bin/hideandseek.py for iterSemiNFG

Parameters:

• G (SemiNFG or iterSemiNFG) – the game to be evaluated
• S (int) – number of MH iterations
• density (func) – the function that assigns weights to iq
• noise (float) – the degree of independence of the proposal distribution on the current value. 1 is independent, 0 returns no perturbation.
• X (int) – number of samples of each policy profile
• M (int) – number of random alt policies to compare
• innoise (float) – the perturbation noise for the loop within iq_calc to draw alt CPTs to compare utilities to current CPT.
• delta (float) – the discount factor (ignored if SemiNFG)
• integrand (func) – a user-supplied function of G that is evaluated for each s in S
• mix (bool) – if true, proposal distribution is over mixed CPTs. Default is False.
• satisfice (SemiNFG or iterSemiNFG) – game G such that the CPTs of G together with innoise determine the intelligence satisficing distribution.

Returns:

• intel - a sample-keyed dictionary of decision node-keyed iq dicts
• 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.

Note

This is the uncoordinated approach because intelligence is assigned to decision nodes instead of being assigned to players. As a result, it takes much longer to run than pynfg.pgtsolutions.intelligence.coordinated.coordinated_MH

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 SemiNFG G
    G.sample()
    w = G.utility('1')+G.utility('2') #'1' & '2' are player names in G
    return w

import copy
GG = copy.deepcopy(G) #G is a SemiNFG
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.uncoordinated import uncoordinated_MH

intelMH, funcoutMH, densMH = uncoordinated_MH(GG, S, density, noise,
                                              X, M,
                                              innoise=.2,
                                              delta=1,
                                              integrand=welfare,
                                              mix=False,
                                              satisfice=GG)

pynfg.pgtsolutions.intelligence.uncoordinated.uncoordinated_calciq(dn, G, X, M, mix, delta, innoise, satisfice=None)

Estimate IQ of policy at the current decision node

Parameters:

• p (str) – the name of the player whose intelligence is being evaluated.
• G (SemiNFG or iterSemiNFG) – the iterated semi-NFG to be evaluated
• X (int) – number of samples of each policy profile
• M (int) – number of random alt policies with which to compare
• mix (bool) – if true, proposal distribution is over mixed CPTs. Default is False.
• delta (float) – the discount factor (ignored if SemiNFG)
• innoise (float) – the perturbation noise for the inner loop to draw alt CPTs
• satisfice (SemiNFG or iterSemiNFG) – game G such that the CPTs of G together with innoise determine the intelligence satisficing distribution.

Returns:

an estimate of the fraction of alternative strategies that yield lower expected utility than the current policy.