PoliciesMultiPlayers.rhoLearnEst module

rhoLearnEst: 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, and without knowing the number of users.

• It generalizes PoliciesMultiPlayers.rhoLearn.rhoLearn simply by letting the ranks be \(\{1,\dots,K\}\) and not in \(\{1,\dots,M\}\), by hoping the learning algorithm will be “smart enough” and learn by itself that ranks should be \(\leq M\).

• 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 fully decentralized: each child player does not need to know the (fixed) number of players, it will learn to select ranks only in \(\{1,\dots,M\}\) instead of \(\{1,\dots,K\}\).

Warning

This policy does not work very well!

class PoliciesMultiPlayers.rhoLearnEst.oneRhoLearnEst(maxRank, rankSelectionAlgo, change_rank_each_step, *args, **kwargs)

Bases: PoliciesMultiPlayers.rhoLearn.oneRhoLearn

__str__()

Return str(self).

__module__ = 'PoliciesMultiPlayers.rhoLearnEst'

class PoliciesMultiPlayers.rhoLearnEst.rhoLearnEst(nbPlayers, nbArms, playerAlgo, rankSelectionAlgo=<class 'Policies.Uniform.Uniform'>, lower=0.0, amplitude=1.0, change_rank_each_step=False, *args, **kwargs)

Bases: PoliciesMultiPlayers.rhoLearn.rhoLearn

rhoLearnEst: 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, and without knowing the number of users.

__init__(nbPlayers, nbArms, playerAlgo, rankSelectionAlgo=<class 'Policies.Uniform.Uniform'>, lower=0.0, amplitude=1.0, change_rank_each_step=False, *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.

• *args, **kwargs: arguments, named arguments, given to playerAlgo.

Difference with PoliciesMultiPlayers.rhoLearn.rhoLearn:

• maxRank: maximum rank allowed by the rhoRand child, is not an argument, but it is always nbArms (= K).

Example:

>>> from Policies import *
>>> import random; random.seed(0); import numpy as np; np.random.seed(0)
>>> nbArms = 17
>>> nbPlayers = 6
>>> s = rhoLearnEst(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!

nbPlayers = None

Number of players

children = None

List of children, fake algorithms

rankSelectionAlgo = None

Policy to use to chose the ranks

nbArms = None

Number of arms

change_rank_each_step = None

Change rank at every steps?

__str__()

Return str(self).

__module__ = 'PoliciesMultiPlayers.rhoLearnEst'