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strategies.py
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import numpy as np
import copy
import os
if os.name == 'nt':
from kullback_leibler import klucbBern, klucbGauss
else:
import pyximport
_ = pyximport.install()
from kullback_leibler_cython import klucbBern, klucbGauss
class PlayerStrategy():
def __init__(self, narms, T):
self.T = T # horizon
self.t = 0 # current round
self.K = narms # number of arms
self.means = np.zeros(narms) # empirical means
self.B = np.inf * np.ones(narms) # confidence bound
self.npulls = np.zeros(narms) # number of pulls for each arm
def set_graph_mode(self, relative_id, interface):
raise Exception('Not implemented!')
class SingleAgentKLUCB(PlayerStrategy):
def __init__(self, narms, T):
PlayerStrategy.__init__(self, narms, T)
self.state_round = 0
self.arms_reward = [0 for i in range(self.K)]
self.arms_nselected = [0 for i in range(self.K)]
self.arms_kl_index = [np.inf for i in range(self.K)]
self.arms_kl_index[0] = 0
self.arms_emp_avg_reward = [0 for i in range(self.K)]
self.arms_to_explore = [i + 1 for i in range(self.K)]
self.arms_to_explore.pop(0)
self.is_leader = True
def play(self):
return np.argmax(self.arms_kl_index)
def _kl_index_update(self):
# KL Indexes update
if self.state_round > 2:
f_t = np.log(
self.state_round) + 4 * np.log(np.log(self.state_round))
for k in range(self.K):
if self.arms_nselected[k] > 0:
f_t_k = f_t / self.arms_nselected[k]
self.arms_kl_index[k] = klucbBern(
self.arms_emp_avg_reward[k], f_t_k)
else:
self.arms_kl_index[k] = np.inf
def update(self, play, obs):
self.state_round += 1
arm = play + 1
rew, col = obs
self.arms_nselected[arm - 1] += 1
self.arms_reward[arm - 1] += rew
self.arms_emp_avg_reward[
arm - 1] = self.arms_reward[arm - 1] / self.arms_nselected[arm - 1]
self._kl_index_update()
class GraphDPE(PlayerStrategy):
def __init__(self, narms, T):
PlayerStrategy.__init__(self, narms, T)
self.relative_position = None
self.is_leader = None
self.communication_interface = None
self.best_arm = 1
self.state_round = 0
self.arms_reward = [0 for i in range(self.K)]
self.arms_nselected = [0 for i in range(self.K)]
self.arms_kl_index = [np.inf for i in range(self.K)]
self.arms_kl_index[0] = 0
self.arms_emp_avg_reward = [0 for i in range(self.K)]
self.arms_to_explore = [i + 1 for i in range(self.K)]
self.arms_to_explore.pop(0)
self.s = True
self.last_timestamp = -1
self.n_times_change_of_arm = []
def sanity_check(self):
if self.relative_position is None or \
self.is_leader is None or self.communication_interface is None:
return False
return True
def set_graph_mode(self, relative_id, interface):
self.relative_position = relative_id
self.communication_interface = interface
self.is_leader = True if self.relative_position == 0 else False
def _B_update(self):
# Update set of arms to explore
self.arms_to_explore = []
for arm in range(self.K):
if self.arms_kl_index[arm] > self.arms_emp_avg_reward[self.best_arm
- 1]:
self.arms_to_explore.append(arm + 1)
self.s = len(self.arms_to_explore) > 0
def _kl_index_update(self):
# KL Indexes update,
if self.state_round > 2:
f_t = np.log(
self.state_round) + 4 * np.log(np.log(self.state_round))
for k in range(self.K):
if self.arms_nselected[k] > 0:
f_t_k = f_t / self.arms_nselected[k]
self.arms_kl_index[k] = klucbBern(
self.arms_emp_avg_reward[k], f_t_k)
else:
self.arms_kl_index[k] = np.inf
def _update_arm_stats(self, arm, rew, col):
self.arms_nselected[arm - 1] += 1
self.arms_reward[arm - 1] += rew
self.arms_emp_avg_reward[
arm - 1] = self.arms_reward[arm - 1] / self.arms_nselected[arm - 1]
def play(self):
if not self.sanity_check():
raise Exception('Sanity check not passed!')
if not self.is_leader:
a = self.best_arm
else:
if len(self.arms_to_explore) == 0:
a = self.best_arm
else:
if self.s:
a = self.best_arm
self.s = False
else:
kl_idxs = [
self.arms_kl_index[i - 1] for i in self.arms_to_explore
]
b = np.argmax(kl_idxs)
a = self.arms_to_explore[b]
self.arms_to_explore.pop(b)
return a - 1
def update(self, play, obs):
if not self.sanity_check():
raise Exception('Sanity check not passed!')
self.state_round += 1
arm = play + 1
rew, col = obs
self._update_arm_stats(arm, rew, col)
if self.is_leader:
if len(self.arms_to_explore) == 0:
self._kl_index_update()
self._B_update()
temp_best_arm = np.argmax(self.arms_emp_avg_reward) + 1
if temp_best_arm != self.best_arm:
self.best_arm = temp_best_arm
self.last_timestamp += 1
self.n_times_change_of_arm.append(self.state_round)
self.communication_interface.send(self.last_timestamp,
self.best_arm)
else:
if not self.communication_interface.is_empty():
msgs = self.communication_interface.receive()
new_arm = None
for t, m in msgs:
if m != self.best_arm and t > self.last_timestamp:
new_arm = m
self.last_timestamp = t
if new_arm:
self.best_arm = new_arm
self.communication_interface.send(self.last_timestamp,
self.best_arm)
class DPE(PlayerStrategy):
"""
Decentralized Parsimonious Exploration
"""
INIT = 0
INIT_ORTHOG_SAMPLE = 1
INIT_ORTHOG_VERIFICATION = 2
INIT_RANK_ASSIGN = 3
EXPLOIT = 10
COMMUNICATION = 11
START_OF_COMMUNICATION = 99 # used just for logging
phase_names = {
INIT: 'INIT',
INIT_ORTHOG_SAMPLE: 'INIT_ORTHOG_SAMPLE',
INIT_ORTHOG_VERIFICATION: 'INIT_ORTHOG_VERIFICATION',
INIT_RANK_ASSIGN: 'INIT_RANK_ASSIGN',
EXPLOIT: 'EXPLOIT',
COMMUNICATION: 'COMMUNICATION',
START_OF_COMMUNICATION: 'START_OF_COMMUNICATION'
}
def __init__(self,
narms,
centralized=None,
T=10,
verbose=0,
disable_comp=False,
dpe2=False,
dpe2_param=None):
PlayerStrategy.__init__(self, narms, T)
self.phase = self.INIT_ORTHOG_SAMPLE
self.id = 0
self.num_players = 0
self.backlog_check = False
self.relative_position = 0
self.is_leader = False
self.state_round = 1
self.collisions = 0 # Used to count collisions
self.log = [] # Logging feature
self.log_counter = 0 # Log id
self.i = 0 # Used during rank assignment
self.best_arms_set = []
self.best_arms_min_emp_reward = (1, 0) # (id, avg emp reward)
self.arms_to_explore = [] # Used by the leader
self.cdpe = centralized
self.disable_comp = disable_comp # used to disable computations
self.verbose = verbose
self.total_time = 0
self.dpe2 = dpe2 # Block version of DPE
if self.verbose == 1:
self.log_func = lambda x: print(x)
else:
self.log_func = lambda x: self.log.append(x)
self.changes_in_best_arms_set = []
self.arms_reward = [0 for i in range(self.K)]
self.arms_nselected = [0 for i in range(self.K)]
self.arms_kl_index = [0 for i in range(self.K)]
self.arms_emp_avg_reward = [0 for i in range(self.K)]
self.arms_to_remove = []
self.arms_to_add = []
if self.cdpe:
self.players = None
self.leader = None
self.backlog = [[0 for i in range(self.K)],
[0 for i in range(self.K)]]
# Variables used during communication
self.t0 = 0
self.t1 = 0
self.t2 = 0
self.t3 = 0
self.total_collisions = 0
# These stats are updated every time we play an arm,
# therefore they have to be divided by the number of players
self.stats = {
self.INIT_ORTHOG_SAMPLE: 0,
self.INIT_ORTHOG_VERIFICATION: 0,
self.INIT_RANK_ASSIGN: 0,
self.EXPLOIT: 0,
self.COMMUNICATION: 0,
self.START_OF_COMMUNICATION: 0
}
if self.dpe2:
self._add_log('DPE2 Enabled!')
if not dpe2_param:
self.J = int(np.ceil(self.K**0.5))
else:
self.J = int(dpe2_param)
print('J:{}'.format(self.J))
def _log_phase(self):
self._add_log('Phase is {}'.format(self.phase_names[self.phase]))
def _log_id(self):
self._add_log('Player id: {}'.format(self.id))
def _add_log(self, text):
if self.verbose > 0:
self.log_func('[{}] - {}'.format(self.state_round, text))
self.log_counter += 1
def play(self):
"""
"""
self._log_phase()
self._log_id()
self.stats[self.phase] += 1
# In the init phase we do sampling and verification
# to assign uniquely the arms
if self.phase >= self.INIT and self.phase < self.EXPLOIT:
# Used to identify the round
self._add_log('State round: {}'.format(self.state_round))
# In sampling we choose an arm uniformly if the ID is 0, otherwise
# we choose id.
if self.phase == self.INIT_ORTHOG_SAMPLE:
# We don't sample the k-th arm, reserved for verification
a = self.id if self.id > 0 else np.random.choice(
[i + 1 for i in range(self.K - 1)])
# In verification, depending on the round and our ID, we choose our
# ID or arm K.
elif self.phase == self.INIT_ORTHOG_VERIFICATION:
if self.state_round != self.id and self.id > 0:
a = self.id
else:
a = self.K
# The goal of this phase is to understand how many Players
# there are, our relative position, and if we are the leader.
elif self.phase == self.INIT_RANK_ASSIGN:
a = self.id + max(0, self.i) if (
self.id + self.i <= self.K) else self.id
self.i += 1 if (self.state_round >= 2 * self.id - 1) else 0
elif self.phase == self.EXPLOIT:
if not self.is_leader:
a = self.best_arms_set[(
(self.state_round + self.relative_position) %
self.num_players)]
else:
m = ((self.state_round + self.relative_position) %
self.num_players)
exploration_set = self.arms_to_explore
if self.dpe2:
j = int(
np.floor(((self.state_round - m) / self.num_players %
self.J)))
exploration_set = self.arms_to_explore[j]
if len(exploration_set) == 0 or self.best_arms_set[
m] != self.best_arms_min_emp_reward[0]:
a = self.best_arms_set[m]
else:
if np.random.choice([0, 1]) == 0:
# Play arm with lowest empirical mean
a = self.best_arms_min_emp_reward[0]
else:
# Choose arm uniformly from B
a = np.random.choice(exploration_set)
elif self.phase == self.COMMUNICATION:
if self.state_round > self.t0 and self.state_round <= self.t1 and self.is_leader:
a = self.best_arms_set[((self.t0 + 1) % self.num_players)]
elif self.state_round > self.t1 and self.state_round <= self.t2 and self.is_leader:
a = self.arms_to_remove[0]
self._add_log(
'Leader broadcasting arm to remove: {}'.format(a))
elif self.state_round > self.t2 and self.state_round <= self.t3 and self.is_leader:
a = self.arms_to_add[0]
self._add_log('Leader broadcasting arm to add: {}'.format(a))
elif not self.is_leader:
if self.state_round > self.t2:
a = ((self.state_round + self.relative_position) %
self.K) + 1
else:
a = self.best_arms_set[(
(self.state_round + self.relative_position) %
self.num_players)]
else:
raise Exception('Someone ended up in a wrong state!')
else:
self._add_log('Unknown phase: {}'.format(self.phase))
raise Exception('Unknown phase: {}'.format(self.phase))
self._add_log('Chose arm: {}'.format(a))
return a - 1
def _update_arm_stats(self, arm, rew, col):
self._add_log('Played arm {} - Reward: {} - Collision: {}'.format(
arm, rew, col))
if col == 0:
# We care about reward only before starting exploiting/exploring or if we
# are the leader
self.arms_nselected[arm - 1] += 1
self.arms_reward[arm - 1] += rew
self.arms_emp_avg_reward[
arm -
1] = self.arms_reward[arm - 1] / self.arms_nselected[arm - 1]
if self.cdpe and not self.is_leader:
if not self.leader or not self.players:
self.players, self.leader = self.cdpe.centralized()
# If the leader is not present, just update all the other players also
if not self.leader:
self.backlog[0][arm - 1] += 1
self.backlog[1][arm - 1] += rew
else:
if not self.backlog_check:
self.backlog_check = True
for i in range(self.K):
self.leader.arms_nselected[i] += self.backlog[0][i]
self.leader.arms_reward[i] += self.backlog[1][i]
if self.leader.arms_nselected[i] > 0:
self.leader.arms_emp_avg_reward[
i] = self.leader.arms_reward[
i] / self.leader.arms_nselected[i]
self.leader.arms_nselected[arm - 1] += 1
self.leader.arms_reward[arm - 1] += rew
self.leader.arms_emp_avg_reward[
arm - 1] = self.leader.arms_reward[
arm - 1] / self.leader.arms_nselected[arm - 1]
def _kl_index_update(self):
# KL Indexes update
if not self.disable_comp:
f_t = np.log(
self.state_round) + 4 * np.log(np.log(self.state_round))
self._add_log(
'Starting update of KL-UCB idxs, f(t): {}'.format(f_t))
for k in range(self.K):
if self.arms_nselected[k] > 0:
f_t_k = f_t / self.arms_nselected[k]
self.arms_kl_index[k] = klucbBern(
self.arms_emp_avg_reward[k], f_t_k)
else:
self.arms_kl_index[k] = np.inf
self._add_log('Updating KL-UCB index for arm {}. b: {}'.format(
k, self.arms_kl_index[k]))
def _B_update(self, arms):
# Update set of arms to explore
if not self.disable_comp:
if not self.dpe2:
self.arms_to_explore = []
for ra in arms:
if self.arms_kl_index[
ra - 1] >= self.best_arms_min_emp_reward[1]:
self.arms_to_explore.append(ra)
else:
self.arms_to_explore = [[] for i in range(self.J)]
for s in range(self.J):
for ra in arms:
if (s - 1) * self.J <= ra and ra < self.J * s:
if self.arms_kl_index[
ra -
1] >= self.best_arms_min_emp_reward[1]:
self.arms_to_explore[s].append(ra)
def _update_best_arms_min_emp_rew(self):
# Used to obtain mu_Mhat
if not self.disable_comp:
self.best_arms_min_emp_reward = [1, np.inf]
for arm in self.best_arms_set:
if self.arms_emp_avg_reward[
arm - 1] < self.best_arms_min_emp_reward[1]:
self.best_arms_min_emp_reward[0] = arm
self.best_arms_min_emp_reward[
1] = self.arms_emp_avg_reward[arm - 1]
def _best_arms_update(self):
if not self.disable_comp:
M_minus = set(self.best_arms_set)
# Get a list of the sorted arms according to the empirical avg reward
sorted_arms = np.argsort(self.arms_emp_avg_reward)
# The new set of best arms has the first M elements of the list of sorted arms
new_best_arms = [i + 1 for i in sorted_arms[-self.num_players:]]
M_plus = set(new_best_arms)
# Compute arms to be removed/added
self.arms_to_remove = list(M_minus - M_plus)
self.arms_to_add = list(M_plus - M_minus)
L = len(self.arms_to_remove)
if L != len(self.arms_to_add):
self._add_log(
'Arms to remove and arms to add have different size!'
'To remove: {} - To add: {}'.format(
self.arms_to_remove, self.arms_to_add))
raise Exception(
'Arms to remove and arms to add have different size!'
'To remove: {} - To add: {}'.format(
self.arms_to_remove, self.arms_to_add))
if L > 0:
self.changes_in_best_arms_set.append((self.total_time, L))
self._add_log(
'Leader: arms to remove {} - arms to add {}'.format(
self.arms_to_remove, self.arms_to_add))
if self.cdpe:
self._add_log(
'Leader is communicating immediately the change o
10000
f arm (CENTRALIZED CASE).'
)
self._centralized_update()
# Update set B
self._B_update([i + 1 for i in sorted_arms[:-self.num_players]])
return True if (L > 0 and not self.cdpe) else False
def _centralized_update(self):
if not self.disable_comp:
if not self.cdpe:
raise Exception(
'Tried to do a centralized update, but CDPE is not enabled!.'
)
if self.is_leader:
while len(self.arms_to_remove) > 0:
ar = self.best_arms_set.index(self.arms_to_remove.pop(0))
self.best_arms_set[ar] = self.arms_to_add.pop(0)
self.best_arms_set = np.sort(self.best_arms_set).tolist()
if not self.players:
self.players, _ = self.cdpe.centralized()
for p in self.players:
p.best_arms_set = self.best_arms_set
self._add_log('Centralized update finished')
else:
self._add_log('A follower tried to do a centralized update!')
raise Exception('A follower tried to do a centralized update!')
def update(self, play, obs):
self.total_time += 1
arm = play + 1
rew, col = obs
self.total_collisions += col
if col > 0 and self.phase >= self.EXPLOIT:
self._add_log('Had a collision! Playing {}'.format(arm))
self._update_arm_stats(arm, rew, col)
# If we are in Sampling phase, we move to verification and
# assign state 'arm' if no collision happened
if self.phase == self.INIT_ORTHOG_SAMPLE:
self.phase = self.INIT_ORTHOG_VERIFICATION
self.collisions = 0
self.state_round = 1
if self.id == 0:
self.id = arm if col == 0 else 0
self._add_log('ID is: {}'.format(self.id))
# In verification phase we count the number of collisions we make
# If at the end we have no collisions we move to the next phase,
# otherwise we restart the process from the sampling phase
elif self.phase == self.INIT_ORTHOG_VERIFICATION:
self.collisions += col
if self.state_round == self.K:
if self.collisions == 0:
self.phase = self.INIT_RANK_ASSIGN
self.state_round = 1
self.collisions = 0
else:
self.phase = self.INIT_ORTHOG_SAMPLE
self.state_round = 1
self.collisions = 0
else:
self.state_round += 1
elif self.phase == self.INIT_RANK_ASSIGN:
# Increase number of collisions, this will be equal to M at the end of
# the round.
self.collisions += col
if self.state_round == 2 * self.id - 1:
self.relative_position = self.collisions + 1
self._add_log('Identified relative position: {}'.format(
self.relative_position))
if self.collisions == 0:
self.is_leader = True
self._add_log('We are leader')
self.state_round += 1
# Finished all the rounds, move to next phase
if self.state_round == 2 * self.K - 2:
# At the end of our block we check how many collisions we
# had. That number is the number of players
self.num_players = self.collisions + 1
self.collisions = 0
self._add_log('Identified number of players: {}'.format(
self.num_players))
self.best_arms_set = [i + 1 for i in range(self.num_players)]
# If we are the leader, we need to update the kl-indexes in order to understand
# which arms to explore
if self.is_leader:
self._kl_index_update()
self._B_update([
self.num_players + 1 + i
for i in range(self.K - self.num_players)
])
self.phase = self.EXPLOIT
elif self.phase == self.EXPLOIT:
self.state_round += 1
if self.is_leader:
# Check if we have to do update of the best arms
m = self.state_round % self.num_players
if self.dpe2:
j = ((self.state_round - m) / self.num_players % self.J)
m = m == j
else:
m = m == 0
if m:
self._kl_index_update()
if self._best_arms_update():
self.phase = self.COMMUNICATION
self.stats[self.START_OF_COMMUNICATION] += 1
self.t0 = self.state_round - 1
self.t1 = self.t0 + self.num_players - 1
self.t2 = self.t1 + self.num_players
self.t3 = self.t2 + self.K
self._add_log(
'Leader started communication: t0 {} t1 {} t2 {}'.
format(self.t0, self.t1, self.t2))
elif not self.is_leader and col > 0:
# Leader is starting communication
self.t0 = self.state_round - (
2 + self.num_players - self.relative_position)
self.t1 = self.t0 + self.num_players - 1
self.t2 = self.t1 + self.num_players
self.t3 = self.t2 + self.K
self._add_log(
'Leader started communication: t0 {} t1 {} t2 {}'.format(
self.t0, self.t1, self.t2))
self.phase = self.COMMUNICATION
elif not self.is_leader and self.cdpe and col > 0:
self._add_log(
'There has been a collision, even though this is a follower and we are in the centralized case!'
)
raise Exception(
'There has been a collision, even though this is a follower and we are in the centralized case!'
)
elif self.phase == self.COMMUNICATION:
if self.cdpe:
self._add_log(
'We switched to communication phase though this is the centralized case! Mrel: {}'
.format(self.relative_position))
raise Exception(
'We switched to communication phase though this is the centralized case! Mrel: {}'
.format(self.relative_position))
self.state_round += 1
if not self.is_leader and col > 0:
if self.state_round - 1 >= self.t1 and self.state_round - 1 <= self.t2:
self._add_log('Arm to remove: {}'.format(
self.is_leader, arm))
self.arms_to_remove = [arm]
if arm not in self.best_arms_set:
raise Exception('Arm to be removed not present!')
elif self.state_round - 1 > self.t2 and self.state_round - 1 <= self.t3:
self._add_log('Arm to add:{}'.format(self.is_leader, arm))
self.arms_to_add = [arm]
if self.state_round == self.t3 + 1:
if len(self.arms_to_remove) > 0:
ar = self.best_arms_set.index(self.arms_to_remove.pop(0))
self.best_arms_set[ar] = self.arms_to_add.pop(0)
self.best_arms_set = np.sort(self.best_arms_set).tolist()
self._add_log('Ended communication, new set of arms {}'.format(
self.best_arms_set))
if not self.is_leader:
self.phase = self.EXPLOIT
elif self.is_leader:
# Compute the min empirical average reward from the best arms
self._update_best_arms_min_emp_rew()
if len(self.arms_to_add) == 0:
self.phase = self.EXPLOIT
else:
# Leader is starting communication again
self.t0 = self.state_round - 1
self.t1 = self.t0 + self.num_players - 1
self.t2 = self.t1 + self.num_players
self.t3 = self.t2 + self.K
self._add_log(
'Leader started communication (again): t0 {} t1 {} t2 {}'
.format(self.t0, self.t1, self.t2))
self.phase = self.COMMUNICATION
self.stats[self.START_OF_COMMUNICATION] += 1
class CDPE(object):
# Used for centralized coordination
def __init__(self):
self.players = None
self.leader = None
self.env = None
def centralized(self):
if not self.players or not self.leader:
self._get_players()
return self.players, self.leader
def _get_players(self):
if not self.env:
raise Exception('Environment not provided to CDPE!')
for p in self.env.players:
if p.is_leader:
self.leader = p
else:
if not self.players:
self.players = []
self.players.append(p)
if len(self.players) == 0:
self.players = None
def update_env(self, env):
self.env = env
self.players = None
self.leaders = None
self._get_players()
class SynchComm(PlayerStrategy):
"""
SIC MMAB
"""
def __init__(self, narms, T=10, verbose=False):
PlayerStrategy.__init__(self, narms, T)
self.K0 = narms # true number of arms (K used as number of active arms)
self.name = 'SynchComm'
self.ext_rank = -1 # -1 until known
self.int_rank = 0 # starts index with 0 here
self.M = 1 # number of active players
self.T0 = np.ceil(
self.K * np.e *
np.log(T)) # length of Musical Chairs in initialization
self.last_action = np.random.randint(
self.K) # last play for sequential hopping
self.phase = 'fixation'
self.t_phase = 0 # step in the current phase
self.round_number = 0 # phase number of exploration phase
self.active_arms = np.arange(0, self.K)
self.sums = np.zeros(self.K) # means*npulls
self.last_phase_stats = np.zeros(self.K)
self.verbose = verbose
def play(self):
"""
return arm to pull based on past information (given in update)
"""
# Musical Chairs procedure in initialization
if self.phase == 'fixation':
if self.ext_rank == -1: # still trying to fix to an arm
return np.random.randint(self.K)
else: # fix
return self.ext_rank
# estimation of internal rank and number of players
if self.phase == 'estimation':
if self.t <= self.T0 + 2 * self.ext_rank: # waiting its turn to sequential hop
return self.ext_rank
else: # sequential hopping
return (self.last_action + 1) % self.K
# exploration phase
if self.phase == 'exploration':
last_index = np.where(self.active_arms == self.last_action)[0][0]
return self.active_arms[(last_index + 1) %
self.K] # sequentially hop
# communication phase
if self.phase == 'communication':
if (self.t_phase < (self.int_rank + 1) * (self.M - 1) * self.K *
(self.round_number + 2)
and (self.t_phase >= (self.int_rank) *
(self.M - 1) * self.K * (self.round_number + 2))):
# your turn to communicate
# determine the number of the bit to send, the channel and the player
t0 = self.t_phase % (
(self.M - 1) * self.K * (self.round_number + 2)
) # the actual time step in the communication phase (while giving info)
b = (int)(
t0 %
(self.round_number + 2)) # the number of the bit to send
k0 = (int)(((t0 - b) / (self.round_number + 2)) %
self.K) # the arm to send
k = self.active_arms[k0]
if (((int)(self.last_phase_stats[k]) >> b) %
2): # has to send bit 1
j = (t0 - b - (self.round_number + 2) * k0) / (
(self.round_number + 2) * self.K) # the player to send
j = (int)(j + (j >= self.int_rank))
#print('Communicate bit {} about arm {} at player on arm {} by player {} at timestep {}'.format(b, k, self.active_arms[j], self.ext_rank, self.t_phase))
return self.active_arms[j] # send 1
else:
return self.active_arms[self.int_rank] # send 0
else:
return self.active_arms[
self.int_rank] # receive protocol or wait
# exploitation phase
if self.phase == 'exploitation':
return self.last_action
def update(self, play, obs):
"""
Update the information, phase, etc. given the last round information
X = obs[0]
C = obs[1]
"""
self.last_action = play
if self.phase == 'fixation':
if self.ext_rank == -1:
if not (obs[1]): # succesfully fixed during Musical Chairs
self.ext_rank = play
# end of Musical Chairs
if self.t == self.T0:
self.phase = 'estimation' # estimation of M
self.last_action = self.ext_rank
elif self.phase == 'estimation':
if obs[1]: # collision with a player
if self.t <= self.T0 + 2 * self.ext_rank: # increases the internal rank
self.int_rank += 1
self.M += 1 # increases number of active players
# end of initialization
if self.t == self.T0 + 2 * self.K:
self.phase = 'exploration'
self.t_phase = 0
self.round_number = (int)(
np.ceil(np.log2(self.M))
) # we actually not start at the phase p=1 to speed up the exploration, without changing the asymptotic regret
elif self.phase == 'exploration':
self.last_phase_stats[play] += obs[0] # update stats
self.sums[play] += obs[0]
self.t_phase += 1
# end of exploration phase
if self.t_phase == (2 << self.round_number) * self.K:
self.phase = 'communication'
self.t_phase = 0
elif self.phase == 'communication':
# reception case
if (self.t_phase >= (self.int_rank + 1) * (self.M - 1) * self.K *
(self.round_number + 2)
or (self.t_phase < (self.int_rank) *
(self.M - 1) * self.K * (self.round_number + 2))):
if obs[1]:
t0 = self.t_phase % (
(self.M - 1) * self.K * (self.round_number + 2)
) # the actual time step in the communication phase (while giving info)
b = (int)(t0 % (self.round_number + 2)
) # the number of the bit to send
k0 = (int)(((t0 - b) / (self.round_number + 2)) %
self.K) # the channel to send
k = self.active_arms[k0]
self.sums[k] += ((2 << b) >> 1)
self.t_phase += 1
# end of the communication phase
# update many things
if (self.t_phase == (self.M) * (self.M - 1) * self.K *
(self.round_number + 2) or self.M == 1):
# update centralized number of pulls
for k in self.active_arms:
self.npulls[k] += (2 << self.round_number) * self.M
# update confidence intervals
b_up = self.sums[self.active_arms] / self.npulls[
self.active_arms] + np.sqrt(
2 * np.log(self.T) / (self.npulls[self.active_arms]))
b_low = self.sums[self.active_arms] / self.npulls[
self.active_arms] - np.sqrt(
2 * np.log(self.T) / (self.npulls[self.active_arms]))
reject = []
accept = []
# compute the arms to accept/reject
for i, k in enumerate(self.active_arms):
better = np.sum(b_low > (b_up[i]))
worse = np.sum(b_up < b_low[i])
if better >= self.M:
reject.append(k)
if self.verbose:
print(
'player {} rejected arm {} at round {}'.format(
self.ext_rank, k, self.round_number))
if worse >= (self.K - self.M):
accept.append(k)
if self.verbose:
print(
'player {} accepted arm {} at round {}'.format(
self.ext_rank, k, self.round_number))
# update set of active arms
for k in reject:
self.active_arms = np.setdiff1d(self.active_arms, k)
for k in accept:
self.active_arms = np.setdiff1d(self.active_arms, k)
# update number of active players and arms
self.M -= len(accept)
self.K -= (len(accept) + len(reject))
if len(accept) > self.int_rank: # start exploitation
self.phase = 'exploitation'
if self.verbose:
print('player {} starts exploiting arm {}'.format(
self.ext_rank, accept[self.int_rank]))
self.last_action = accept[self.int_rank]
else: # new exploration phase and update internal rank (old version of the algorithm where the internal rank was changed, but it does not change the results)
self.phase = 'exploration'
self.int_rank -= len(accept)
self.last_action = self.active_arms[
self.
int_rank] # start new phase in an orthogonal setting
self.round_number += 1
self.last_phase_stats = np.zeros(self.K0)
self.t_phase = 0
self.t += 1
class MCTopM(PlayerStrategy):
"""
MCTopM strategy introduced by Besson and Kaufmann
"""
def __init__(self, narms, M, T=10):
PlayerStrategy.__init__(self, narms, T)
self.name = 'MCTopM'
self.last_action = np.random.randint(narms)
self.C = False
self.s = False
self.bestM = np.arange(0, narms)
self.M = M
self.b = np.copy(self.B)
self.previous_b = np.copy(self.B)
def play(self):
"""
return arm to pull
"""
if self.last_action not in self.bestM: # transition 3 or 5
action = np.random.choice(
np.intersect1d(
self.bestM,
np.nonzero(
self.previous_b <= self.previous_b[self.last_action])))
self.s = False
elif (self.C and not (self.s)): # collision and not fixed
action = np.random.choice(self.bestM)
self.s = False
else: # tranistion 1 or 4
action = self.last_action
self.s = True
return action
def update(self, play, obs):
self.last_action = play
self.C = obs[1]
self.t += 1
self.means[play] = (self.npulls[play] * self.means[play] + obs[0]) / (
self.npulls[play] + 1)
self.npulls[play] += 1
self.B[play] = np.sqrt(np.log(self.T) / (2 * self.npulls[play]))
self.previous_b = np.copy(self.b)
self.b = self.means + self.B
self.bestM = np.argpartition(-self.b, self.M)[:self.M]
class MusicalChairs(PlayerStrategy):
"""
Musical chairs strategy introduced by Rosenski et al.
"""
def __init__(self, narms, T=10, delta=0.1):
PlayerStrategy.__init__(self, narms, T)
self.name = 'SynchComm'
self.M = 1
self.T0 = np.ceil(
np.max([
narms * np.log(2 * narms * narms * T) / 2,
16 * narms * np.log(4 * narms * narms * T) / (delta * delta),
narms * narms * np.log(2 * T) / 0.02
]))
self.phase = 'exploration'
self.fixed = -1
self.bestM = None
self.colls = 0
def play(self):
if self.phase == 'exploration':
return np.random.randint(self.K)
elif self.phase == 'fixation':
return np.random.choice(self.bestM)
else:
return self.fixed
def update(self, play, obs):
self.t += 1