# Source code for PoliciesMultiPlayers.rhoEst

```
# -*- coding: utf-8 -*-
r""" rhoEst: implementation of the 2nd multi-player policy from [Distributed Algorithms for Learning..., Anandkumar et al., 2010](http://ieeexplore.ieee.org/document/5462144/).
- 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 sampled from a uniform distribution on :math:`[1, \dots, \hat{M}_i(t)]` where :math:`\hat{M}_i(t)` is the current estimated number of player by player i,
- The procedure to estimate :math:`\hat{M}_i(t)` is not so simple, but basically everyone starts with :math:`\hat{M}_i(0) = 1`, and when colliding :math:`\hat{M}_i(t+1) = \hat{M}_i(t) + 1`, for some time (with a complicated threshold).
- My choice for the threshold function, see :func:`threshold_on_t`, does not need the horizon either, and uses :math:`t` instead.
.. note:: This is **fully decentralized**: each child player does NOT need to know the number of players and does NOT require the horizon :math:`T`.
.. note:: For a more generic approach, see the wrapper defined in :class:`EstimateM.EstimateM`.
"""
from __future__ import division, print_function # Python 2 compatibility
__author__ = "Lilian Besson"
__version__ = "0.8"
import numpy as np
import numpy.random as rn
try:
from .rhoRand import oneRhoRand, rhoRand
from .EstimateM import threshold_on_t_with_horizon, threshold_on_t_doubling_trick, threshold_on_t
except ImportError:
from rhoRand import oneRhoRand, rhoRand
from EstimateM import threshold_on_t_with_horizon, threshold_on_t_doubling_trick, threshold_on_t
# --- Class oneRhoEst, for children
[docs]class oneRhoEst(oneRhoRand):
r""" 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 new random rank is sampled after observing a collision,
- And the player does not aim at the best arm, but at the rank-th best arm, based on her index policy,
- The rhoEst policy is used to keep an estimate on the total number of players, :math:`\hat{M}_i(t)`.
- The procedure to estimate :math:`\hat{M}_i(t)` is not so simple, but basically everyone starts with :math:`\hat{M}_i(0) = 1`, and when colliding :math:`\hat{M}_i(t+1) = \hat{M}_i(t) + 1`, for some time (with a complicated threshold).
"""
[docs] def __init__(self, threshold, *args, **kwargs):
if 'horizon' in kwargs:
self.horizon = kwargs['horizon']
del kwargs['horizon']
else:
self.horizon = None
super(oneRhoEst, self).__init__(*args, **kwargs)
# Parameters
if hasattr(self, 'maxRank'):
self.maxRank = 1 # <-- make SURE that maxRank is NOT used by the policy!
self.threshold = threshold #: Threshold function
# Internal variables
self.nbPlayersEstimate = 1 #: Number of players. Optimistic: start by assuming it is alone!
self.rank = 1 #: Current rank, starting to 1
self.collisionCount = np.zeros(self.nbArms, dtype=int) #: Count collisions on each arm, since last increase of nbPlayersEstimate
self.timeSinceLastCollision = 0 #: Time since last collision. Don't remember why I thought using this could be useful... But it's not!
self.t = 0 #: Internal time
[docs] def __str__(self): # Better to recompute it automatically
# return r"#{}<RhoEst{}-{}{}{}>".format(self.playerId + 1, "Plus" if self.horizon else "", self.mother._players[self.playerId], "(rank:{})".format(self.rank) if self.rank is not None else "", "($T={}$)".format(self.horizon) if self.horizon else "")
return r"#{}<RhoEst{}-{}{}>".format(self.playerId + 1, "Plus" if self.horizon else "", self.mother._players[self.playerId], "($T={}$)".format(self.horizon) if self.horizon else "")
[docs] def startGame(self):
"""Start game."""
super(oneRhoEst, self).startGame()
self.rank = 1 # Start with a rank = 1: assume she is alone.
# Est part
self.nbPlayersEstimate = 1 # Optimistic: start by assuming it is alone!
self.collisionCount.fill(0)
self.timeSinceLastCollision = 0
self.t = 0
[docs] def handleCollision(self, arm, reward=None):
"""Select a new rank, and maybe update nbPlayersEstimate."""
# 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(oneRhoEst, self).getReward(arm, reward)
# First, pick a new random rank
self.rank = 1 + rn.randint(self.nbPlayersEstimate) # New random rank
# print("\n - A oneRhoEst player {} saw a collision on {}, new random rank : {} ...".format(self, arm, self.rank)) # DEBUG
# we can be smart, and stop all this as soon as M = K !
if self.nbPlayersEstimate < self.nbArms:
self.collisionCount[arm] += 1
# print("\n - A oneRhoEst player {} saw a collision on {}, since last update of nbPlayersEstimate = {} it is the {} th collision on that arm {}...".format(self, arm, self.nbPlayersEstimate, self.collisionCount[arm], arm)) # DEBUG
# Then, estimate the current ranking of the arms and the set of the M best arms
currentBest = self.estimatedBestArms(self.nbPlayersEstimate)
# print("Current estimation of the {} best arms is {} ...".format(self.nbPlayersEstimate, currentBest)) # DEBUG
collisionCount_on_currentBest = np.sum(self.collisionCount[currentBest])
# print("Current count of collision on the {} best arms is {} ...".format(self.nbPlayersEstimate, collisionCount_on_currentBest)) # DEBUG
# And finally, compare the collision count with the current threshold
threshold = self.threshold(self.t, self.nbPlayersEstimate, self.horizon)
# print("Using timeSinceLastCollision = {}, and t = {}, threshold = {:.3g} ...".format(self.timeSinceLastCollision, self.t, threshold))
if collisionCount_on_currentBest > threshold:
self.nbPlayersEstimate = min(1 + self.nbPlayersEstimate, self.nbArms)
# print("The collision count {} was larger than the threshold {:.3g} se we restart the collision count, and increase the nbPlayersEstimate to {}.".format(collisionCount_on_currentBest, threshold, self.nbPlayersEstimate)) # DEBUG
self.collisionCount.fill(0)
# Finally, restart timeSinceLastCollision
self.timeSinceLastCollision = 0
[docs] def getReward(self, arm, reward):
"""One transmission without collision."""
self.t += 1
# Obtaining a reward, even 0, means no collision on that arm for this time
# So, first, we count one more step without collision
self.timeSinceLastCollision += 1
# Then use the reward for the arm learning algorithm
return super(oneRhoEst, self).getReward(arm, reward)
# --- Class rhoEst
[docs]class rhoEst(rhoRand):
""" rhoEst: implementation of the 2nd multi-player policy from [Distributed Algorithms for Learning..., Anandkumar et al., 2010](http://ieeexplore.ieee.org/document/5462144/).
"""
[docs] def __init__(self, nbPlayers, nbArms, playerAlgo,
threshold=threshold_on_t_doubling_trick, lower=0., amplitude=1.,
*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.
- threshold: the threshold function to use, see :func:`EstimateM.threshold_on_t_with_horizon`, :func:`EstimateM.threshold_on_t_doubling_trick` or :func:`EstimateM.threshold_on_t` above.
- `*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
>>> s = rhoEst(nbPlayers, nbArms, UCB, threshold=threshold_on_t)
>>> [ 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."
self.nbPlayers = nbPlayers #: Number of players
self._players = [None] * nbPlayers
self.children = [None] * nbPlayers #: List of children, fake algorithms
self.nbArms = nbArms #: Number of arms
fake_maxRank = None
for playerId in range(nbPlayers):
self._players[playerId] = playerAlgo(nbArms, *args, **kwargs)
self.children[playerId] = oneRhoEst(threshold, fake_maxRank, self, playerId)
# --- Class rhoEstPlus
[docs]class rhoEstPlus(rhoRand):
""" rhoEstPlus: implementation of the 2nd multi-player policy from [Distributed Algorithms for Learning..., Anandkumar et al., 2010](http://ieeexplore.ieee.org/document/5462144/).
"""
[docs] def __init__(self, nbPlayers, nbArms, playerAlgo, horizon,
lower=0., amplitude=1.,
*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.
- horizon: need to know the horizon :math:`T`.
- `*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
>>> horizon = 1000
>>> s = rhoEstPlus(nbPlayers, nbArms, UCB, horizon=horizon)
>>> [ 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."
self.nbPlayers = nbPlayers #: Number of players
self._players = [None] * nbPlayers
self.children = [None] * nbPlayers #: List of children, fake algorithms
self.nbArms = nbArms #: Number of arms
fake_maxRank = None
for playerId in range(nbPlayers):
self._players[playerId] = playerAlgo(nbArms, *args, **kwargs)
self.children[playerId] = oneRhoEst(threshold_on_t_with_horizon, fake_maxRank, self, playerId, horizon=horizon)
[docs] def __str__(self):
return "rhoEstPlus({} x {})".format(self.nbPlayers, str(self._players[0]))
```