Table of Contents¶
An example of a small Multi-Player simulation, with Centralized Algorithms¶
First, be sure to be in the main folder, or to have SMPyBandits installed, and import EvaluatorMultiPlayers from Environment package:
!pip install SMPyBandits watermark
%load_ext watermark
%watermark -v -m -p SMPyBandits -a "Lilian Besson"
# Local imports
from SMPyBandits.Environment import EvaluatorMultiPlayers, tqdm
We also need arms, for instance Bernoulli-distributed arm:
# Import arms
from SMPyBandits.Arms import Bernoulli
And finally we need some single-player and multi-player Reinforcement Learning algorithms:
# Import algorithms
from SMPyBandits.Policies import *
from SMPyBandits.PoliciesMultiPlayers import *
# Just improving the ?? in Jupyter. Thanks to https://nbviewer.jupyter.org/gist/minrk/7715212
from __future__ import print_function
from IPython.core import page
def myprint(s):
try:
print(s['text/plain'])
except (KeyError, TypeError):
print(s)
page.page = myprint
For instance, this imported the UCB algorithm:
UCBalpha?
As well as the CentralizedMultiplePlay multi-player policy:
CentralizedMultiplePlay?
We also need a collision model. The usual ones are defined in the CollisionModels package, and the only one we need is the classical one, where two or more colliding users don't receive any rewards.
# Collision Models
from SMPyBandits.Environment.CollisionModels import onlyUniqUserGetsReward
onlyUniqUserGetsReward?
Creating the problem¶
Parameters for the simulation¶
- $T = 10000$ is the time horizon,
- $N = 100$ is the number of repetitions (should be larger to have consistent results),
- $M = 2$ is the number of players,
N_JOBS = 4is the number of cores used to parallelize the code.
HORIZON = 10000
REPETITIONS = 100
NB_PLAYERS = 2
N_JOBS = 4
collisionModel = onlyUniqUserGetsReward
Three MAB problems with Bernoulli arms¶
We consider in this example $3$ problems, with Bernoulli arms, of different means.
- The first problem is very easy, with two good arms and three arms, with a fixed gap $\Delta = \max_{\mu_i \neq \mu_j}(\mu_{i} - \mu_{j}) = 0.1$.
- The second problem is as easier, with a larger gap.
- Third problem is harder, with a smaller gap, and a very large difference between the two optimal arms and the suboptimal arms.
Note: right now, the multi-environments evaluator does not work well for MP policies, if there is a number different of arms in the scenarios. So I use the same number of arms in all the problems.
ENVIRONMENTS = [ # 1) Bernoulli arms
{ # Scenario 1 from [Komiyama, Honda, Nakagawa, 2016, arXiv 1506.00779]
"arm_type": Bernoulli,
"params": [0.3, 0.4, 0.5, 0.6, 0.7]
},
{ # Classical scenario
"arm_type": Bernoulli,
"params": [0.1, 0.3, 0.5, 0.7, 0.9]
},
{ # Harder scenario
"arm_type": Bernoulli,
"params": [0.005, 0.01, 0.015, 0.84, 0.85]
}
]
Some RL algorithms¶
We will compare Thompson Sampling against $\mathrm{UCB}_1$, using two different centralized policy:
CentralizedMultiplePlayis the naive use of a Bandit algorithm for Multi-Player decision making: at every step, the internal decision making process is used to determine not $1$ arm but $M$ to sample. For UCB-like algorithm, the decision making is based on a $\arg\max$ on UCB-like indexes, usually of the form $I_j(t) = X_j(t) + B_j(t)$, where $X_j(t) = \hat{\mu_j}(t) = \sum_{\tau \leq t} r_j(\tau) / N_j(t)$ is the empirical mean of arm $j$, and $B_j(t)$ is a bias term, of the form $B_j(t) = \sqrt{\frac{\alpha \log(t)}{2 N_j(t)}}$.CentralizedIMPis very similar, but instead of following the internal decision making for all the decisions, the system uses just the empirical means $X_j(t)$ to determine $M-1$ arms to sample, and the bias-corrected term (i.e., the internal decision making, can be sampling from a Bayesian posterior for instance) is used just for one decision. It is an heuristic, proposed in [Komiyama, Honda, Nakagawa, 2016].
nbArms = len(ENVIRONMENTS[0]['params'])
assert all(len(env['params']) == nbArms for env in ENVIRONMENTS), "Error: not yet support if different environments have different nb of arms"
nbArms
SUCCESSIVE_PLAYERS = [
CentralizedMultiplePlay(NB_PLAYERS, nbArms, UCBalpha, alpha=1).children,
CentralizedIMP(NB_PLAYERS, nbArms, UCBalpha, alpha=1).children,
CentralizedMultiplePlay(NB_PLAYERS, nbArms, Thompson).children,
CentralizedIMP(NB_PLAYERS, nbArms, Thompson).children
]
SUCCESSIVE_PLAYERS
The mother class in this case does all the job here, as we use centralized learning.
OnePlayer = SUCCESSIVE_PLAYERS[0][0]
OnePlayer.nbArms
OneMother = OnePlayer.mother
OneMother
OneMother.nbArms
Complete configuration for the problem:
configuration = {
# --- Duration of the experiment
"horizon": HORIZON,
# --- Number of repetition of the experiment (to have an average)
"repetitions": REPETITIONS,
# --- Parameters for the use of joblib.Parallel
"n_jobs": N_JOBS, # = nb of CPU cores
"verbosity": 6, # Max joblib verbosity
# --- Collision model
"collisionModel": onlyUniqUserGetsReward,
# --- Arms
"environment": ENVIRONMENTS,
# --- Algorithms
"successive_players": SUCCESSIVE_PLAYERS,
}
Creating the EvaluatorMultiPlayers objects¶
We will need to create several objects, as the simulation first runs one policy against each environment, and then aggregate them to compare them.
%%time
N_players = len(configuration["successive_players"])
# List to keep all the EvaluatorMultiPlayers objects
evs = [None] * N_players
evaluators = [[None] * N_players] * len(configuration["environment"])
for playersId, players in tqdm(enumerate(configuration["successive_players"]), desc="Creating"):
print("\n\nConsidering the list of players :\n", players)
conf = configuration.copy()
conf['players'] = players
evs[playersId] = EvaluatorMultiPlayers(conf)
Solving the problem¶
Now we can simulate the $2$ environments, for the successive policies. That part can take some time.
%%time
for playersId, evaluation in tqdm(enumerate(evs), desc="Policies"):
for envId, env in tqdm(enumerate(evaluation.envs), desc="Problems"):
# Evaluate just that env
evaluation.startOneEnv(envId, env)
# Storing it after simulation is done
evaluators[envId][playersId] = evaluation
Plotting the results¶
And finally, visualize them, with the plotting method of a EvaluatorMultiPlayers object:
def plotAll(evaluation, envId):
evaluation.printFinalRanking(envId)
# Rewards
evaluation.plotRewards(envId)
# Fairness
#evaluation.plotFairness(envId, fairness="STD")
# Centralized regret
evaluation.plotRegretCentralized(envId, subTerms=True)
#evaluation.plotRegretCentralized(envId, semilogx=True, subTerms=True)
# Number of switches
#evaluation.plotNbSwitchs(envId, cumulated=False)
evaluation.plotNbSwitchs(envId, cumulated=True)
# Frequency of selection of the best arms
evaluation.plotBestArmPulls(envId)
# Number of collisions - not for Centralized* policies
#evaluation.plotNbCollisions(envId, cumulated=False)
#evaluation.plotNbCollisions(envId, cumulated=True)
# Frequency of collision in each arm
#evaluation.plotFrequencyCollisions(envId, piechart=True)
import matplotlib as mpl
mpl.rcParams['figure.figsize'] = (12.4, 7)
First problem¶
$\mu = [0.3, 0.4, 0.5, 0.6, 0.7]$ was an easy Bernoulli problem.
for playersId in tqdm(range(len(evs)), desc="Policies"):
evaluation = evaluators[0][playersId]
plotAll(evaluation, 0)
Second problem¶
$\mu = [0.1, 0.3, 0.5, 0.7, 0.9]$ was an easier Bernoulli problem, with larger gap $\Delta = 0.2$.
for playersId in tqdm(range(len(evs)), desc="Policies"):
evaluation = evaluators[1][playersId]
plotAll(evaluation, 1)
Third problem¶
$\mu = [0.005, 0.01, 0.015, 0.84, 0.85]$ is an harder Bernoulli problem, as there is a huge gap between suboptimal and optimal arms.
for playersId in tqdm(range(len(evs)), desc="Policies"):
evaluation = evaluators[2][playersId]
plotAll(evaluation, 2)
Comparing their performances¶
def plotCombined(e0, eothers, envId):
# Centralized regret
e0.plotRegretCentralized(envId, evaluators=eothers)
# Fairness
e0.plotFairness(envId, fairness="STD", evaluators=eothers)
# Number of switches
e0.plotNbSwitchsCentralized(envId, cumulated=True, evaluators=eothers)
# Number of collisions - not for Centralized* policies
#e0.plotNbCollisions(envId, cumulated=True, evaluators=eothers)
N = len(configuration["environment"])
for envId, env in enumerate(configuration["environment"]):
e0, eothers = evaluators[envId][0], evaluators[envId][1:]
plotCombined(e0, eothers, envId)
That's it for this demo!