# -*- coding: utf-8 -*-
""" rhoRandRotating: implementation of a variant of the multi-player policy rhoRand 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 [1, .., M] where M is the number of player.
- The *only* difference with rhoRand is that at every time step, the rank is updated by 1, and cycles in [1, .., M] iteratively.
.. 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"
import numpy.random as rn
try:
from .rhoRand import oneRhoRand, rhoRand
except ImportError:
from rhoRand import oneRhoRand, rhoRand
# --- Class oneRhoRandRotating, for children
[docs]class oneRhoRandRotating(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 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.
"""
[docs] def __init__(self, maxRank, *args, **kwargs):
super(oneRhoRandRotating, self).__init__(maxRank, *args, **kwargs)
self.maxRank = maxRank #: Max rank, usually nbPlayers but can be different
self.rank = 1 #: Current rank, starting to 1 by default
[docs] def __str__(self): # Better to recompute it automatically
return r"#{}<{}[{}{}]>".format(self.playerId + 1, r"$\rho^{\mathrm{RandRotating}}$", self.mother._players[self.playerId], ", rank:{}".format(self.rank) if self.rank is not None else "")
[docs] def startGame(self):
"""Start game."""
super(oneRhoRandRotating, self).startGame()
self.rank = 1 + rn.randint(self.maxRank) # XXX Start with a random rank, safer to avoid first collisions.
[docs] def handleCollision(self, arm, reward=None):
""" Get a new fully random rank, and give reward to the algorithm if not None."""
# rhoRandRotating UCB indexes learn on the SENSING, not on the successful transmissions!
if reward is not None:
# print("Info: rhoRandRotating UCB internal indexes DOES get updated by reward, in case of collision, learning is done on SENSING, not successful transmissions!") # DEBUG
super(oneRhoRandRotating, self).getReward(arm, reward)
self.rank = 1 + rn.randint(self.maxRank) # New random rank
# print(" - A oneRhoRandRotating player {} saw a collision, so she had to select a new random rank : {} ...".format(self, self.rank)) # DEBUG
[docs] def choice(self):
r"""Chose with the new rank, then update the rank:
.. math:: \mathrm{rank}_j(t+1) := \mathrm{rank}_j(t) + 1 \;\mathrm{mod}\; M.
"""
# Note: here we could do another randomization step, but it would just weaken the algorithm, cf. rhoRandRand
result = super(oneRhoRandRotating, self).choiceWithRank(self.rank)
# print(" - A oneRhoRand player {} had to choose an arm among the best from rank {}, her choice was : {} ...".format(self, self.rank, result)) # DEBUG
self.rank = (self.rank % self.maxRank) + 1
# print(" - A oneRhoRand player {} has a new rank {} ...".format(self, self.rank)) # DEBUG
return result
# --- Class rhoRandRotating
[docs]class rhoRandRotating(rhoRand):
""" rhoRandRotating: implementation of a variant of the multi-player policy rhoRand from [Distributed Algorithms for Learning..., Anandkumar et al., 2010](http://ieeexplore.ieee.org/document/5462144/).
"""
[docs] def __init__(self, nbPlayers, nbArms, playerAlgo,
maxRank=None, 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.
- maxRank: maximum rank allowed by the rhoRandRotating child (default to nbPlayers, but for instance if there is 2 × rhoRandRotating[UCB] + 2 × rhoRandRotating[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
>>> s = rhoRandRotating(nbPlayers, nbArms, 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 rhoRandRotating 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.nbArms = nbArms #: Number of arms
for playerId in range(nbPlayers):
self._players[playerId] = playerAlgo(nbArms, *args, **kwargs)
self.children[playerId] = oneRhoRandRotating(maxRank, self, playerId)
[docs] def __str__(self):
return "rhoRandRotating({} x {}{})".format(self.nbPlayers, str(self._players[0]))