Multi-Armed Bandits (MAB)
Imagine you have three products (A, B, and C) to suggest to users, but you don’t know which one they prefer. You need to balance:
- Exploration: showing different products to learn user preferences
- and Exploitation: recommending the product that seems to perform best so far.
For example, if Product A gets the most clicks from users after some trials, you’ll show it more often, but occasionally test B and C to ensure you’re not missing out on a better option.
In a multi-armed bandit problem, you don’t have any extra information (or context) about the arms—just the reward signals.
Contextual Bandits
Now imagine you’re still recommending products, but you receive some context or information. For example:
A user visits your website, and you know their age, location, and past behavior. Before showing them a product, you know the time of day and the device they’re using.
In a contextual bandit problem, you use the experience to improve future decisions in similar contexts (for example, if younger users tend to click on Product A and older users on Product B, the system learns to recommend products based on the user’s profile).
What’s the difference between Full Reinforcement Learning (RL) and Contextual Bandits?
Contextual Bandits: Only the immediate reward matters. There’s no consideration of long-term consequences. Full RL: Actions affect future states and rewards, and there’s a long-term strategy involved.
Action!
Let’s see a comparison between regular and contextual TS in action!
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import beta
# Simulation Parameters
N_PRODUCTS = 5
N_USERS = 10000
AGE_GROUPS = [20, 30, 40, 50] # User age groups
# Below we are defining the ground truth, that we will later compare against in simulation outcomes
# True conversion rates for products in each age group
true_conversion_rates = {
20: [0.1, 0.3, 0.2, 0.05, 0.1],
30: [0.2, 0.1, 0.4, 0.15, 0.05],
40: [0.05, 0.2, 0.1, 0.4, 0.25],
50: [0.1, 0.15, 0.3, 0.25, 0.2],
}
# Generate users with random ages
np.random.seed(42)
user_ages = np.random.choice(AGE_GROUPS, size=N_USERS)
# Function to simulate user interaction and generate rewards
def get_reward(age, product):
return np.random.rand() < true_conversion_rates[age][product]
def thompson_sampling_non_contextual(n_users):
rewards = []
alpha = np.ones(N_PRODUCTS)
beta_params = np.ones(N_PRODUCTS)
for _ in range(n_users):
sampled_theta = np.random.beta(alpha, beta_params)
selected_product = np.argmax(sampled_theta)
reward = get_reward(np.random.choice(AGE_GROUPS), selected_product)
rewards.append(reward)
if reward:
alpha[selected_product] += 1
else:
beta_params[selected_product] += 1
return np.cumsum(rewards)
Introducing contextual sampling basically means introducing extra parameters that would help evaluate the right alpha and beta, while the rest of the logic remains the same.
def thompson_sampling_contextual(n_users, user_ages):
rewards = []
alpha = {age: np.ones(N_PRODUCTS) for age in AGE_GROUPS}
beta_params = {age: np.ones(N_PRODUCTS) for age in AGE_GROUPS}
for user_idx in range(n_users):
user_age = user_ages[user_idx]
sampled_theta = np.random.beta(alpha[user_age], beta_params[user_age])
selected_product = np.argmax(sampled_theta)
reward = get_reward(user_age, selected_product)
rewards.append(reward)
if reward:
alpha[user_age][selected_product] += 1
else:
beta_params[user_age][selected_product] += 1
return np.cumsum(rewards)
Simulate and Compare
non_contextual_rewards = thompson_sampling_non_contextual(N_USERS)
contextual_rewards = thompson_sampling_contextual(N_USERS, user_ages)
And this illustrates how much you can gain in rewards:
