def compare_all(runs=2000, time=1000):
"""Compare all algorithms.
"""
labels = ['epsilon-greedy', 'gradient bandit',
'UCB', 'optimistic initialization']
generators = [lambda epsilon: Bandit(epsilon=epsilon, sample_averages=True),
lambda alpha: Bandit(gradient=True, step_size=alpha, gradient_baseline=True),
lambda coef: Bandit(epsilon=0, UCB_param=coef, sample_averages=True),
lambda initial: Bandit(epsilon=0, optimistic_init=initial, step_size=0.1)]
parameters = [np.arange(-7, -1, dtype=np.float),
np.arange(-5, 2, dtype=np.float),
np.arange(-4, 3, dtype=np.float),
np.arange(-2, 3, dtype=np.float)]
bandits = []
for generator, parameter in zip(generators, parameters):
for param in parameter:
bandits.append(generator(pow(2, param)))
_, average_rewards = simulate(bandits, runs, time)
rewards = np.mean(average_rewards, axis=1)
i = 0
for label, parameter in zip(labels, parameters):
l = len(parameter)
plt.plot(parameter, rewards[i:i+l], label=label)
i += l
plt.xlabel('Parameter(2^x)')
plt.ylabel('Average reward')
plt.legend()
plt.savefig(os.path.join(SAVING_PATH, "figure_2_6_compare_all.png"))
plt.close()
def run_experiment(m1, m2, m3, eps, N, experiment_name):
bandits = [Bandit(m1), Bandit(m2), Bandit(m3)]
data = np.empty(N)
for i in range(N):
# epsilon greedy
p = np.random.random()
if p < eps:
j = np.random.choice(3)
else:
j = np.argmax([b.mean for b in bandits])
x = bandits[j].pull()
bandits[j].update(x)
# for the plot
data[i] = x
cumulative_average = np.cumsum(data) / (np.arange(N) + 1)
# # plot moving average ctr
# plt.plot(cumulative_average)
# plt.plot(np.ones(N) * m1)
# plt.plot(np.ones(N) * m2)
# plt.plot(np.ones(N) * m3)
# plt.xscale('log')
# plt.show()
for i, b in enumerate(bandits):
print(f'{experiment_name}, bandit {i + 1} mean: {b.mean} win: {np.sum(data)}')
return cumulative_average
def gradient(runs=2000, time=1000):
"""Test the k-armed bandit with gradient.
Args:
runs (int): test each bandit with the # of runs.
time (int): the # of the time-steps in each run.
"""
bandits = []
bandits.append(Bandit(gradient=True, step_size=0.1,
gradient_baseline=True, true_reward=4))
bandits.append(Bandit(gradient=True, step_size=0.1,
gradient_baseline=False, true_reward=4))
bandits.append(Bandit(gradient=True, step_size=0.4,
gradient_baseline=True, true_reward=4))
bandits.append(Bandit(gradient=True, step_size=0.4,
gradient_baseline=False, true_reward=4))
print("===== %s =====" % ("Gradient"))
best_action_counts, _ = simulate(bandits, runs, time)
labels = ['alpha = 0.1, with baseline',
'alpha = 0.1, without baseline',
'alpha = 0.4, with baseline',
'alpha = 0.4, without baseline', ]
for i in range(0, len(bandits)):
plt.plot(best_action_counts[i], label=labels[i])
plt.xlabel('Steps')
plt.ylabel('% Optimal action')
plt.legend()
plt.savefig(os.path.join(SAVING_PATH, "figure_2_5_gradient.png"))
plt.close()
def experiment2():
params = [{
"time_horizon" : 500,
"number_of_arms" : 5
},
{
"time_horizon" : 5000,
"number_of_arms" : 5
},
{
"time_horizon" : 500,
"number_of_arms" : 10
},
{
"time_horizon" : 5000,
"number_of_arms" : 10
},
{
"time_horizon" : 500,
"number_of_arms" : 20
},
{
"time_horizon" : 5000,
"number_of_arms" : 20
},
]
for i in range(len(params)):
results = []
time_horizon = params[i]["time_horizon"]
number_of_arms = params[i]["number_of_arms"]
agent1 = agentFactory("random",time_horizon,number_of_arms)
epsilons = []
for j in range(time_horizon):
epsilons.append(math.pow((j+1)*number_of_arms*math.log(j+1),1/3))
agent2 = agentFactory("epsilon-greedy",time_horizon,number_of_arms,epsilons)
agent3 = agentFactory("explore-then-exploit",time_horizon,number_of_arms,time_horizon/100)
agent4 = agentFactory("ucb1",time_horizon,number_of_arms)
agent5 = agentFactory("successive-elimination",time_horizon,number_of_arms)
bandit = Bandit(time_horizon,number_of_arms,agent1)
results.append(mc_simulate(n_sim,bandit))
bandit = Bandit(time_horizon,number_of_arms,agent2)
results.append(mc_simulate(n_sim,bandit))
bandit = Bandit(time_horizon,number_of_arms,agent3)
results.append(mc_simulate(n_sim,bandit,"N=T/100"))
bandit = Bandit(time_horizon,number_of_arms,agent4)
results.append(mc_simulate(n_sim,bandit))
bandit = Bandit(time_horizon,number_of_arms,agent5)
results.append(mc_simulate(n_sim,bandit))
plot(results,time_horizon,params[i])
def plot_figures(k,
n_bandits,
n_steps,
eps_list,
weight_fn=sample_average,
random_walk=False,
y_bounds=[0, 1.5],
Q_1=0,
show=True,
method='epsilon-greedy',
extra_label='',
title=None,
percentage=False):
avg_rew_per_eps = [np.zeros(n_steps) for _ in range(len(eps_list))]
avg_rew_in_perc = [np.zeros(n_steps) for _ in range(len(eps_list))]
for i in range(n_bandits):
print(i)
bandit_pb = Bandit(k)
for i, eps in enumerate(eps_list):
_, per, avg_rew, _ = a_simple_bandit_algorithm(
bandit_pb,
n_iterations=n_steps,
eps=eps,
weight_fn=weight_fn,
random_walk=random_walk,
Q_1=Q_1,
method=method)
avg_rew_per_eps[i] += avg_rew
avg_rew_in_perc[i] += per
to_plot = avg_rew_in_perc if percentage else avg_rew_per_eps
bounds = [0, 100] if percentage else y_bounds
plot_average(to_plot, eps_list, n_bandits, bounds, show, extra_label,
title, percentage)
def epsilon_greedy(runs=2000, time=1000):
"""Test the k-armed bandit with the policy of epsilon greedy.
Args:
runs (int): test each bandit with the # of runs.
time (int): the # of the time-steps in each run.
"""
epsilons = [0, 0.01, 0.1, 0.2]
bandits = [Bandit(epsilon=eps, sample_averages=True) for eps in epsilons]
print("===== {} =====".format("Epsilon greedy"))
best_action_counts, rewards = simulate(bandits, runs, time)
plt.figure(figsize=(10, 20))
plt.subplot(2, 1, 1)
for eps, rewards in zip(epsilons, rewards):
plt.plot(rewards, label="epsilon = %.02f" % (eps))
plt.xlabel('steps')
plt.ylabel('average reward')
plt.legend()
plt.subplot(2, 1, 2)
for eps, counts in zip(epsilons, best_action_counts):
plt.plot(counts, label="epsilon = %.02f" % (eps))
plt.xlabel('steps')
plt.ylabel('% optimal action')
plt.legend()
plt.savefig(os.path.join(SAVING_PATH, "figure_2_2_epsilon_greedy.png"))
plt.close()
def fig_2_5(n_bandits=2000, n_steps=1000, k=10, alpha_list=[0.1, 0.4]):
d = {}
for baseline in [False, True]:
for alpha in alpha_list:
d[(baseline, alpha)] = np.zeros(n_steps)
for n in range(n_bandits):
print(n)
bandit = Bandit(k, mean=4)
for baseline in [False, True]:
for alpha in alpha_list:
result_arr, _ = gradient_bandit(bandit, n_steps=n_steps,
alpha=alpha, baseline=baseline)
d[(baseline, alpha)] += result_arr
def label(baseline, alpha):
return ("with" if baseline else "without") + f" baseline, alpha={alpha}"
for key, avg_rew in d.items():
plt.plot((avg_rew / n_bandits) * 100, label=label(key[0], key[1]))
axes = plt.gca()
axes.set_ylim([0, 100])
plt.xlabel("Steps")
plt.ylabel("Optimal Action %")
plt.title("Figure 2.5")
plt.legend()
plt.show()
def create_bandit(means, variances):
def reward_fn(mu, variance):
stddev = np.sqrt(variance)
return lambda: np.random.normal(mu, stddev)
arms = list(map(lambda a: reward_fn(*a), zip(means, variances)))
return Bandit(arms)
def run(self, name, agent_name, **agent_parameters):
"""
:param name: Name of experiments
:param agent_name: Name of Agent
:param agent_parameters: Parameters of Agent
"""
rewards = np.zeros(self.pulls)
optimal_actions = np.zeros(self.pulls)
for _ in tqdm(range(self.experiments)):
bandit = Bandit(self.pulls, self.actions, agent_name,
**agent_parameters)
reward, optimal_action = bandit.experiment()
rewards += reward
optimal_actions += optimal_action
pass
rewards /= np.float(self.experiments)
optimal_actions /= np.float(self.experiments)
self.values[name] = {}
self.values[name]['rewards'] = rewards
self.values[name]['optimal_actions'] = optimal_actions
pass
def run_greedy(number_bandits, epsilon, iterations):
bandits = [Bandit(i + 1, 0) for i in range(number_bandits)]
current_best = bandits[0]
data = np.empty(iterations)
print(f'Starting with bandit {current_best.true_mean}.')
for i in range(iterations):
explore_exploit = np.random.rand()
bandit = current_best
# explore
if explore_exploit < epsilon:
selection = np.random.randint(0, number_bandits)
#print(f'Machine {selection} selected.')
bandit = bandits[selection]
# exploit
value = bandit.pull()
bandit.update(value)
data[i] = value
#update
if current_best.current_mean < bandit.current_mean:
print(f'Updated to bandit {bandit.true_mean}')
current_best = bandit
print(f'Chose bandit {current_best.true_mean}')
cumulative_average = np.cumsum(data) / (np.arange(iterations) + 1)
plt.plot(cumulative_average)
for i in range(number_bandits):
plt.plot(np.ones(iterations) * (i + 1))
plt.xscale('log')
plt.show()
return cumulative_average
def captions_bandit():
data = captions_data
def reward_fn(percentage):
return lambda: np.random.choice((0, 0.5, 1), 1, p=percentage)[0]
arms = list(map(reward_fn, data))
return Bandit(arms)
def bandit():
bandit = Bandit()
game.init_bandit(bandit)
player = game.get_player()
return render_template('bandit.html',
credits_demanded=bandit.get_credits_demanded(),
fskills=player.get_fighter_skills(),
pskills=player.get_pilotskills())
def experiment1():
params = [{
"time_horizon" : 1000,
"number_of_arms" : 5
},
{
"time_horizon" : 10000,
"number_of_arms" : 5
},
{
"time_horizon" : 1000,
"number_of_arms" : 10
},
{
"time_horizon" : 10000,
"number_of_arms" : 10
},
{
"time_horizon" : 1000,
"number_of_arms" : 20
},
{
"time_horizon" : 10000,
"number_of_arms" : 20
},
]
for i in range(len(params)):
results = []
time_horizon = params[i]["time_horizon"]
number_of_arms = params[i]["number_of_arms"]
agent1 = agentFactory("explore-then-exploit",time_horizon,number_of_arms,5)
agent2 = agentFactory("explore-then-exploit",time_horizon,number_of_arms,time_horizon/10)
agent3 = agentFactory("explore-then-exploit",time_horizon,number_of_arms,time_horizon/100)
bandit = Bandit(time_horizon,number_of_arms,agent1)
results.append(mc_simulate(n_sim,bandit,"N=5"))
bandit = Bandit(time_horizon,number_of_arms,agent2)
results.append(mc_simulate(n_sim,bandit,"N=T/10"))
bandit = Bandit(time_horizon,number_of_arms,agent3)
results.append(mc_simulate(n_sim,bandit,"N=T/100"))
plot(results,time_horizon,params[i])
def main():
"""
Constants
"""
k: int = 20
epsilon: float = 0.01
init_val: int = 10
c: float = 1.0
max_time: int = 1000
rounds: int = 1000
policy: Policy = EpsilonGreedyPolicy(epsilon)
agent = Agent(k, policy)
bandits = [Bandit() for _ in range(k)]
def play_round():
"""
Simulates one round of the game.
"""
# get the next action
action = agent.choose_action()
# get a reward from the bandit
reward = bandits[action].get_reward()
# play the action
agent.play_action(action, reward)
return reward
def reset():
agent.reset()
for bandit in bandits:
bandit.reset()
optimal_bandit = np.argmax([bandit.get_reward() for bandit in bandits])
def print_bandits():
for i, bandit in enumerate(bandits):
print('Bandit {} reward={}'.format(i, bandit.get_reward()))
def experiment():
scores = np.zeros(max_time, dtype=float)
for _ in range(rounds):
for t in range(max_time):
scores[t] += play_round()
reset()
return scores / rounds
def plot(label):
print_bandits()
scores = experiment()
time = range(max_time)
plt.title(label + " for k = " + str(k))
plt.ylim([0.0, 2.0])
plt.xlabel('Steps')
plt.ylabel('Avg. Reward')
plt.scatter(x=time, y=scores, s=0.5)
plt.show()
plot(policy.__str__())
def captions_bandit(n):
categories = np.array([0, 0.5, 1])
data = captions_data()[:n]
def reward_fn(percentage):
return lambda: np.random.choice(categories, 1, p=percentage)[0]
arms = list(map(reward_fn, data))
return Bandit(arms)
def poisson_exp_bandit():
n = n_arms()
means_ = poisson_exp_means()
def reward_fn(lambda_):
return lambda: np.random.poisson(lambda_)
arms = list(map(reward_fn, means_))
return Bandit(arms)
def sparse_bandit(n_arms, variance):
means = sparse_means(n_arms)
stddev = np.sqrt(variance)
def reward_fn(mu):
return lambda: np.random.normal(mu, stddev)
arms = list(map(reward_fn, means))
return Bandit(arms)
def polynomial_bandit(n, variance):
means = polynomial_means(n)
stddev = np.sqrt(variance)
def reward_fn(mu):
return lambda: np.random.normal(mu, stddev)
arms = list(map(reward_fn, means))
return Bandit(arms)
def upper_confidence_bound(runs=2000, time=1000):
"""Test the k-armed bandit with UCB.
Args:
runs (int): test each bandit with the # of runs.
time (int): the # of the time-steps in each run.
"""
bandits = []
bandits.append(Bandit(epsilon=0, UCB_param=2, sample_averages=True))
bandits.append(Bandit(epsilon=0.1, sample_averages=True))
_, average_rewards = simulate(bandits, runs, time)
plt.plot(average_rewards[0], label='UCB c = 2')
plt.plot(average_rewards[1], label='epsilon greedy epsilon = 0.1')
plt.xlabel('Steps')
plt.ylabel('Average reward')
plt.legend()
plt.savefig(os.path.join(SAVING_PATH, "figure_2_4_UCB.png"))
plt.close()
def get_market_data():
global username
if request.method == "GET":
band1 = Bandit()
trader1 = Trader()
police1 = Police()
cost1 = Cost()
market_inventory = regions.child(currRegion).child('inventory').get()
ship_inventory = users.child(username).child('ship').child(
'inventory').get()
difficulty = users.child(username).child('difficulty').get()
ship_cargo = users.child(username).child('ship').child('cargo').get()
credit_val = users.child(username).child('credit').get()
ship_health = users.child(username).child('ship').child('health').get()
pilot_skill = users.child(username).child('skills').child(
'pilot').get()
engineer = users.child(username).child('skills').child(
'engineer').get()
fighter_skill = users.child(username).child('skills').child(
'fighter').get()
merchant_skill = users.child(username).child('skills').child(
'merchant').get()
fuel = users.child(username).child('ship').child('fuel').get()
fuelcost = cost1.calculate_fuel(difficulty, credit_val)
demand = band1.calculate_demand(difficulty, credit_val)
repair = cost1.calculate_repair(difficulty, engineer, credit_val)
price = trader1.item_to_sell(difficulty, credit_val)
qty = trader1.qty
item = trader1.item
stolen = police1.stolen_item(ship_inventory)
to_return = {
'username': username,
'currRegion': currRegion,
'market_inventory': market_inventory,
'ship_inventory': ship_inventory,
'cargo': ship_cargo,
'credit': credit_val,
'health': ship_health,
'demand': demand,
'qty': qty,
'item': item,
'price': price,
'eng': engineer,
'stolen': stolen,
'difficulty': difficulty,
'pilot': pilot_skill,
'fighter': fighter_skill,
'fuel': fuel,
'fuelcost': fuelcost,
'merch': merchant_skill,
'repair': repair
}
return to_return
return None
def run_experiment(m1, m2, m3, N, experiment_name):
bandits = [Bandit(m1), Bandit(m2), Bandit(m3)]
data = np.empty(N)
for i in range(N):
j = np.argmax([ucb(b.mean, i + 1, b.N) for b in bandits])
x = bandits[j].pull()
bandits[j].update(x)
# for the plot
data[i] = x
cumulative_average = np.cumsum(data) / (np.arange(N) + 1)
for i, b in enumerate(bandits):
print(
f'{experiment_name}, bandit {i + 1} mean: {b.mean} win: {np.sum(data)}'
)
return cumulative_average
def __init__(self, predict_market, num_bids, trials,
label='Multi-Armed Prediction Market Bandit'):
self.predict_market = predict_market
self.n_arms = predict_market.arms
self.agents = predict_market.agents
self.data = predict_market.dataframe
self.num_bids = num_bids
self.label = label
self.bandit = Bandit(self.n_arms, self.data)
self.trials = trials
self.scores = None
self.optimal = None
def init_bandits(self, holdout=True):
"""Specify some way to split up the indices?"""
df_len = len(self.data_sim.df.index)
num_divide = self.n_bandits + 1 if holdout else self.n_bandits
increment = int(df_len / num_divide)
for i in range(self.n_bandits):
indices = [i * increment, (i + 1) * increment]
self.bandits.append(Bandit(self.n_arms, self.data_sim.df,
data_indices=indices))
if holdout:
self.df_holdout = self.data_sim.df[df_len - increment + 1:]
self.trials = increment if self.trials is None else self.trials
def createBanditInstancesAndSimulate(params,n_mc_sim):
n_sim = n_mc_sim
for i in range(len(params)):
results = []
time_horizon = params[i]['time_horizon']
number_of_arms = params[i]['number_of_arms']
number_of_exploration_per_arm = params[i]['number_of_exploration_per_arm']
exp_agent = ExploreThenExploit(time_horizon,number_of_arms,number_of_exploration_per_arm)
epsilon_greedy_constant_half_epsilonAgent = EpsilonGreedy(time_horizon,number_of_arms,[1/2]*time_horizon)
epsilon_greedy_constant_epsilonAgent = EpsilonGreedy(time_horizon,number_of_arms,[number_of_exploration_per_arm*number_of_arms/time_horizon]*time_horizon)
ubc_agent = UBC1Agent(time_horizon,number_of_arms)
se_agent = SuccessiveEliminationAgent(time_horizon,number_of_arms)
random_agent = Agent()
bandit = Bandit(time_horizon,number_of_arms,random_agent)
results.append(mc_simulate(n_sim,bandit))
bandit = Bandit(time_horizon,number_of_arms,exp_agent)
results.append(mc_simulate(n_sim,bandit))
bandit = Bandit(time_horizon,number_of_arms,epsilon_greedy_constant_epsilonAgent)
results.append(mc_simulate(n_sim,bandit,"constant-epsilon=rate-of-explore-exploit"))
bandit = Bandit(time_horizon,number_of_arms,epsilon_greedy_constant_half_epsilonAgent)
results.append(mc_simulate(n_sim,bandit,"constant-epsilon=0.5"))
bandit = Bandit(time_horizon,number_of_arms,ubc_agent)
results.append(mc_simulate(n_sim,bandit))
bandit = Bandit(time_horizon,number_of_arms,se_agent)
results.append(mc_simulate(n_sim,bandit))
plot(results,time_horizon,params[i])
def __init__(self, models, n, a, task=None):
self.models = models
self.n = n
self.a = a
self.num_arms = models.shape[1]
self.num_models = models.shape[0]
self.counts = np.zeros([self.num_arms])
self.means = np.zeros([self.num_arms])
if task is None:
self.task = np.random.choice(self.num_models)
else:
self.task = task
self.bandit = Bandit(self.models[self.task])
def run(algorithm, non_stationary=False):
"""Runs an algorithm with the specified paramters.
algorithm: Instance of an algorithm from `algorithms.py`.
non_stationary: Whether to run the stationary or non_stationary test bench.
"""
with open('config.yml') as cfile:
config = y.load(cfile)['run']
runs, steps = config['runs'], config['steps']
avg_rewards, optim_action_percent = np.zeros(steps), np.zeros(steps)
for run in range(runs):
bandit = Bandit(non_stationary)
print(f'Run number {run + 1}.')
# One-run rewards
or_rewards = []
# One-run actions
or_actions = []
optim_action = np.argmax([bandit.q_star(a) for a in range(10)])
# One-run optimal actions
or_optim_actions = [] if non_stationary else optim_action
for step in range(1, steps + 1):
action = algorithm.act(step)
reward = bandit(action)
if non_stationary:
optim_action = np.argmax([bandit.q_star(a) for a in range(10)])
algorithm.update(action, reward, step)
or_rewards.append(reward)
or_actions.append(action)
if non_stationary:
or_optim_actions.append(optim_action)
avg_rewards += or_rewards
if non_stationary:
a, o = np.array(or_actions), np.array(or_optim_actions)
else:
a, o = np.array(or_actions), or_optim_actions
optim_action_percent += (a == o)
algorithm.reset()
avg_rewards /= runs
optim_action_percent = (optim_action_percent / runs) * 100.0
return avg_rewards, optim_action_percent
def __init__(self, agent, k=10, stationary=True):
print(f'Initialising {k} Bandits')
self.k = k
self.timestep = 0
self.player = agent
self.stationary = stationary
if agent.character == 'optimistic':
self.values = [np.random.randint(50, 100)] * self.k
else:
self.values = np.zeros(self.k)
mu = [np.random.randint(10) for _ in range(self.k)]
sig = [np.random.rand() for _ in range(self.k)]
print(f"Initial actual average rewards are {mu}")
self.bandits = [
Bandit(mean, sd, stationary) for (mean, sd) in zip(mu, sig)
]
def run_optimistic(number_bandits, iterations):
bandits = [Bandit(i + 1, 10) for i in range(number_bandits)]
data = np.empty(iterations)
for i in range(iterations):
bandit = bandits[np.argmax([bandit.current_mean
for bandit in bandits])]
# exploit
value = bandit.pull()
bandit.update(value)
data[i] = value
cumulative_average = np.cumsum(data) / (np.arange(iterations) + 1)
plt.plot(cumulative_average)
for i in range(number_bandits):
plt.plot(np.ones(iterations) * (i + 1))
plt.xscale('log')
plt.show()
return cumulative_average
def compare_epsilons(
epsilons: List[float],
bandits_true_means: List[float],
iterations: int,
) -> Tuple[List[EpsilonGreedyAgent], List[float]]:
"""
Compare different epsilons for epsilon-greedy algorithm.
"""
agents = []
bandits = [Bandit(m) for m in bandits_true_means]
for epsilon in epsilons:
logger.info("Running epsilon-greedy for epsilon = %f", epsilon)
agent = EpsilonGreedyAgent(bandits=bandits, epsilon=epsilon)
agent.take_actions(iterations)
agents.append(agent)
return agents, epsilons
def test_greedy(epsilon, num_iterations):
# Problem setup
num_bandits = 5 # set number of bandits
m_vals = [np.random.randint(30,41) for _ in range(num_bandits)] # create True Mean values
bandits = [Bandit(m=i) for i in m_vals] # create bandits
data = np.empty(num_iterations) # create an empty array for output data
# Epsilon-Greedy algorithm
for i in range(num_iterations):
probability = np.random.rand()
if probability < epsilon:
bandit = bandits[np.random.choice(num_bandits)]
else:
bandit = bandits[np.argmax([bandit.mean for bandit in bandits])]
output = bandit.pull()
bandit.update(output)
data[i] = output
# Get cumulative average of all spins
cumulative_average = np.cumsum(data) / (np.arange(num_iterations) + 1)
return cumulative_average