# -*- coding: utf-8 -*-
""" rhoLearn: implementation of the multi-player policy from [Distributed Algorithms for Learning..., Anandkumar et al., 2010](http://ieeexplore.ieee.org/document/5462144/), using a learning algorithm instead of a random exploration for choosing the rank.
- Each child player is selfish, and plays according to an index policy (any index policy, e.g., UCB, Thompson, KL-UCB, BayesUCB etc),
- But instead of aiming at the best (the 1-st best) arm, player i aims at the rank_i-th best arm,
- At first, every player has a random rank_i from 1 to M, and when a collision occurs, rank_i is given by a second learning algorithm, playing on arms = ranks from [1, .., M], where M is the number of player.
- If rankSelection = Uniform, this is like rhoRand, but if it is a smarter policy, it *might* be better! Warning: no theoretical guarantees exist!
- Reference: [Proof-of-Concept System for Opportunistic Spectrum Access in Multi-user Decentralized Networks, S.J.Darak, C.Moy, J.Palicot, EAI 2016](https://doi.org/10.4108/eai.5-9-2016.151647), algorithm 2. (for BayesUCB only)
.. note:: This is not fully decentralized: as each child player needs to know the (fixed) number of players.
"""
from __future__ import division, print_function # Python 2 compatibility
__author__ = "Lilian Besson"
__version__ = "0.6"
try:
from sys import path
path.insert(0, '..')
try:
from .Policies import Uniform
except ImportError:
from Policies import Uniform
except ImportError:
try:
from SMPyBandits.Policies import Uniform
except ImportError:
print("Warning: ../Policies/Uniform.py was not imported correctly...") # DEBUG
# ... Just reimplement it here manually, if not found in ../Policies/Uniform.py
from random import randint
class Uniform():
"""Quick reimplementation of Policies.Uniform"""
def __init__(self, nbArms, lower=0., amplitude=1.):
self.nbArms = nbArms
def startGame(self):
pass
def getReward(self, arm, reward):
pass
def choice(self):
return randint(0, self.nbArms - 1)
try:
from .rhoRand import oneRhoRand, rhoRand
except ImportError:
from rhoRand import oneRhoRand, rhoRand
#: Should oneRhoLearn players select a (possibly new) rank *at each step* ?
#: The algorithm P2 from https://doi.org/10.4108/eai.5-9-2016.151647 suggests to do so.
#: But I found it works better **without** this trick.
CHANGE_RANK_EACH_STEP = True
CHANGE_RANK_EACH_STEP = False
# --- Class oneRhoLearn, for children
[docs]class oneRhoLearn(oneRhoRand):
""" Class that acts as a child policy, but in fact it pass all its method calls to the mother class, who passes it to its i-th player.
- Except for the handleCollision method: a (possibly new) rank is sampled after observing a collision, from the rankSelection algorithm.
- When no collision is observed on a arm, a small reward is given to the rank used for this play, in order to learn the best ranks with rankSelection.
- And the player does not aim at the best arm, but at the rank-th best arm, based on her index policy.
"""
[docs] def __init__(self, maxRank, rankSelectionAlgo, change_rank_each_step, *args, **kwargs):
super(oneRhoLearn, self).__init__(maxRank, *args, **kwargs)
self.rankSelection = rankSelectionAlgo(maxRank)
self.maxRank = maxRank #: Max rank, usually nbPlayers but can be different
self.rank = 1 #: Current rank, starting to 1
self.change_rank_each_step = change_rank_each_step #: Change rank at each step?
[docs] def __str__(self): # Better to recompute it automatically
return r"#{}<RhoLearn[{}, rank{} ~ {}]>".format(self.playerId + 1, self.mother._players[self.playerId], "" if self.rank is None else (": %i" % self.rank), self.rankSelection)
[docs] def startGame(self):
"""Initialize both rank and arm selection algorithms."""
self.rankSelection.startGame()
super(oneRhoLearn, self).startGame()
self.rank = 1 + self.rankSelection.choice() # XXX Start with a rank given from the algorithm (probably uniformly at random, not important)
[docs] def getReward(self, arm, reward):
"""Give a 1 reward to the rank selection algorithm (no collision), give reward to the arm selection algorithm, and if self.change_rank_each_step, select a (possibly new) rank."""
# Obtaining a reward, even 0, means no collision on that arm for this time
# So, first, we count one more step for this rank
# First give a reward to the rank selection learning algorithm (== collision avoidance)
self.rankSelection.getReward(self.rank - 1, 1)
# Note: this is NOTHING BUT a heuristic! See equation (13) in https://doi.org/10.4108/eai.5-9-2016.151647
# Then, use the rankSelection algorithm to select a (possibly new) rank
if self.change_rank_each_step: # That's new! rhoLearn (can) change its rank at ALL steps!
self.rank = 1 + self.rankSelection.choice()
# print(" - A oneRhoLearn player {} received a reward {:.3g}, and selected a (possibly new) rank from her algorithm {} : {} ...".format(self, reward, self.rankSelection, self.rank)) # DEBUG
# else:
# print(" - A oneRhoLearn player {} received a reward {:.3g}, without selecting a new rank...".format(self, reward)) # DEBUG
# Then use the reward for the arm learning algorithm
return super(oneRhoLearn, self).getReward(arm, reward)
[docs] def handleCollision(self, arm, reward=None):
"""Give a 0 reward to the rank selection algorithm, and select a (possibly new) rank."""
# rhoRand UCB indexes learn on the SENSING, not on the successful transmissions!
if reward is not None:
# print("Info: rhoRand UCB internal indexes DOES get updated by reward, in case of collision, learning is done on SENSING, not successful transmissions!") # DEBUG
super(oneRhoLearn, self).getReward(arm, reward)
# And give a 0 reward to this rank
self.rankSelection.getReward(self.rank - 1, 0)
# Then, use the rankSelection algorithm to select a (possibly new) rank
self.rank = 1 + self.rankSelection.choice()
# print(" - A oneRhoLearn player {} saw a collision, so she had to select a (possibly new) rank from her algorithm {} : {} ...".format(self, self.rankSelection, self.rank)) # DEBUG
# --- Class rhoRand
[docs]class rhoLearn(rhoRand):
""" rhoLearn: implementation of the multi-player policy from [Distributed Algorithms for Learning..., Anandkumar et al., 2010](http://ieeexplore.ieee.org/document/5462144/), using a learning algorithm instead of a random exploration for choosing the rank.
"""
[docs] def __init__(self, nbPlayers, nbArms, playerAlgo, rankSelectionAlgo=Uniform,
lower=0., amplitude=1., maxRank=None, change_rank_each_step=CHANGE_RANK_EACH_STEP,
*args, **kwargs):
"""
- nbPlayers: number of players to create (in self._players).
- playerAlgo: class to use for every players.
- nbArms: number of arms, given as first argument to playerAlgo.
- rankSelectionAlgo: algorithm to use for selecting the ranks.
- maxRank: maximum rank allowed by the rhoRand child (default to nbPlayers, but for instance if there is 2 × rhoRand[UCB] + 2 × rhoRand[klUCB], maxRank should be 4 not 2).
- `*args`, `**kwargs`: arguments, named arguments, given to playerAlgo.
Example:
>>> from Policies import *
>>> import random; random.seed(0); import numpy as np; np.random.seed(0)
>>> nbArms = 17
>>> nbPlayers = 6
>>> stickyTime = 5
>>> s = rhoLearn(nbPlayers, nbArms, UCB, UCB)
>>> [ child.choice() for child in s.children ]
[12, 15, 0, 3, 3, 7]
>>> [ child.choice() for child in s.children ]
[9, 4, 6, 12, 1, 6]
- To get a list of usable players, use ``s.children``.
- Warning: ``s._players`` is for internal use ONLY!
"""
assert nbPlayers > 0, "Error, the parameter 'nbPlayers' for rhoRand class has to be > 0."
if maxRank is None:
maxRank = nbPlayers
self.maxRank = maxRank #: Max rank, usually nbPlayers but can be different
self.nbPlayers = nbPlayers #: Number of players
self._players = [None] * nbPlayers
self.children = [None] * nbPlayers #: List of children, fake algorithms
self.rankSelectionAlgo = rankSelectionAlgo #: Policy to use to chose the ranks
self.nbArms = nbArms #: Number of arms
self.change_rank_each_step = change_rank_each_step #: Change rank at every steps?
for playerId in range(nbPlayers):
self._players[playerId] = playerAlgo(nbArms, *args, **kwargs)
self.children[playerId] = oneRhoLearn(maxRank, rankSelectionAlgo, change_rank_each_step, self, playerId)
# Fake rankSelection algorithm, for pretty print
self._rankSelection = rankSelectionAlgo(maxRank)
[docs] def __str__(self):
return "rhoLearn({} x {}, ranks ~ {})".format(self.nbPlayers, str(self._players[0]), self._rankSelection)