Solving multi-armed bandit problems with continuous action space - artificial-intelligence

Question

My problem has a single state and an infinite amount of actions on a certain interval (0,1). After quite some time of googling I found a few paper about an algorithm called zooming algorithm which can solve problems with a continous action space. However my implementation is bad at exploiting. Therefore I'm thinking about adding an epsilon-greedy kind of behavior.
Is it reasonable to combine different methods?
Do you know other approaches to my problem?
Code samples:
import portion as P
def choose_action(self, i_ph):
# Activation rule
not_covered = P.closed(lower=0, upper=1)
for arm in self.active_arms:
confidence_radius = calc_confidence_radius(i_ph, arm)
confidence_interval = P.closed(arm.norm_value - confidence_radius, arm.norm_value + confidence_radius)
not_covered = not_covered - confidence_interval
if not_covered != P.empty():
rans = []
height = 0
heights = []
for i in not_covered:
rans.append(np.random.uniform(i.lower, i.upper))
height += i.upper - i.lower
heights.append(i.upper - i.lower)
ran_n = np.random.uniform(0, height)
j = 0
ran = 0
for i in range(len(heights)):
if j < ran_n < j + heights[i]:
ran = rans[i]
j += heights[i]
self.active_arms.append(Arm(len(self.active_arms), ran * (self.sigma_square - lower) + lower, ran))
# Selection rule
max_index = float('-inf')
max_index_arm = None
for arm in self.active_arms:
confidence_radius = calc_confidence_radius(i_ph, arm)
# indexfunction from zooming algorithm
index = arm.avg_learning_reward + 2 * confidence_radius
if index > max_index:
max_index = index
max_index_arm = arm
action = max_index_arm.value
self.current_arm = max_index_arm
return action
def learn(self, action, reward):
arm = self.current_arm
arm.avg_reward = (arm.pulled * arm.avg_reward + reward) / (arm.pulled + 1)
if reward > self.max_profit:
self.max_profit = reward
elif reward < self.min_profit:
self.min_profit = reward
# normalize reward to [0, 1]
high = 100
low = -75
if reward >= high:
reward = 1
self.high_count += 1
elif reward <= low:
reward = 0
self.low_count += 1
else:
reward = (reward - low)/(high - low)
arm.avg_learning_reward = (arm.pulled * arm.avg_learning_reward + reward) / (arm.pulled + 1)
arm.pulled += 1
# zooming algorithm confidence radius
def calc_confidence_radius(i_ph, arm: Arm):
return math.sqrt((8 * i_ph)/(1 + arm.pulled))

Answer 1

You may find this useful, full algorithm description is here. They grid out the probes uniformly, informing this choice (e.g. normal centering on a reputed high energy arm) is also possible (but this might invalidate a few bounds I am not sure).