If you’re familiar with the world of machine learning and decision-making, you’ve likely heard of Thompson Sampling. This popular algorithm is widely used for solving the exploration-exploitation tradeoff problem in multi-armed bandit problems. In this article, we’ll take a closer look at the intuition behind Thompson Sampling and show you how to implement it using Python code.
Introduction to Multi-Armed Bandit Problems
Before we dive into Thompson Sampling, let’s first understand the concept of multi-armed bandit problems. In these types of problems, we have a set of actions that we can take, each with an unknown reward probability. The goal is to maximize the total reward gained over time by repeatedly selecting an action and observing the outcome. This can be a difficult problem since we don’t know the reward probabilities and need to balance exploring new actions versus exploiting the actions that we believe are the best.
The Exploration-Exploitation Tradeoff
In multi-armed bandit problems, we face the exploration-exploitation tradeoff. We can either choose to exploit the action that we believe is the best based on our current knowledge, or we can choose to explore new actions to gain more information about their reward probabilities. If we only exploit, we may miss out on better actions that we don’t know about yet. On the other hand, if we only explore, we may waste time on actions that have low rewards.
What is Thompson Sampling?
Thompson Sampling is an algorithm that solves the exploration-exploitation tradeoff problem in multi-armed bandit problems. The algorithm works by maintaining a belief distribution for each action’s reward probability. This belief distribution is updated after each action is taken, based on the observed outcome. When selecting the next action to take, the algorithm samples a reward probability from each belief distribution and chooses the action with the highest sampled value.
The intuition behind Thompson Sampling is that it balances the exploration-exploitation tradeoff by naturally selecting actions that have a higher expected reward while still exploring other actions with potential for higher reward.
Implementing Thompson Sampling in Python
To implement Thompson Sampling in Python, we’ll use the beta distribution to model the belief distribution for each action’s reward probability. The beta distribution is a conjugate prior for the binomial distribution, which makes it a great choice for this problem.
First, we’ll initialize the belief distribution for each action as a beta distribution with parameters alpha=1 and beta=1. This represents a uniform belief that any reward probability is equally likely. Then, for each round, we’ll sample a reward probability from each belief distribution and select the action with the highest sampled value. After observing the outcome of the selected action, we’ll update the belief distribution for that action using the observed reward.
import numpy as np
class ThompsonSampling:
def __init__(self, n_arms):
self.n_arms = n_arms
self.alpha = np.ones(n_arms)
self.beta = np.ones(n_arms)
def select_arm(self):
theta = np.random.beta(self.alpha, self.beta)
return np.argmax(theta)
def update(self, arm, reward):
self.alpha[arm] += reward
self.beta[arm] += 1 - reward
Conclusion
In conclusion, Thompson Sampling is a powerful algorithm that can solve the exploration-exploitation tradeoff problem in multi-armed bandit problems. By maintaining a belief distribution for each action’s reward probability and sampling from those distributions, the algorithm can balance the tradeoff between exploring new actions and exploiting the actions with the highest expected rewards. With the Python code provided in this article, you can easily implement Thompson With the Python code provided in this article, you can easily implement Thompson Sampling in your own multi-armed bandit problems. By understanding the intuition behind Thompson Sampling and how it works, you can improve the performance of your decision-making algorithms and maximize your rewards over time.