Background

Introduction

The multi-armed bandit problem is a classic problem in probability theory and reinforcement learning that exemplifies the exploration-exploitation tradeoff dilemma. In this problem, a fixed limited set of resources must be allocated between competing choices in a way that maximizes their expected gain, when each choice’s properties are only partially known at the time of allocation.

Problem Description

In the multi-armed bandit problem:

  1. There are multiple “arms” (choices) available

  2. Each arm provides a random reward from a probability distribution specific to that arm

  3. The objective is to maximize the sum of rewards earned through a sequence of selections

  4. The crucial tradeoff is between: - “Exploitation” of the arm that has the highest expected payoff - “Exploration” to get more information about the expected payoffs of other arms

This trade-off between exploration and exploitation is fundamental to many real-world problems, including: - Managing research projects in large organizations - Clinical trials in pharmaceutical companies - Online advertising and recommendation systems - Resource allocation in cloud computing - Portfolio optimization in finance

Algorithms

The thompson package implements three main algorithms for solving the multi-armed bandit problem:

  1. Thompson Sampling - A Bayesian approach that maintains probability distributions over the expected rewards - Samples from these distributions to select the next arm to pull - Naturally balances exploration and exploitation - Particularly effective when the reward distributions are unknown

  2. Upper Confidence Bound (UCB) - A deterministic algorithm that uses confidence bounds - Selects arms based on their estimated rewards and uncertainty - Provides theoretical guarantees on performance - Good for problems with known reward distributions

  3. Randomized Sampling - A baseline method that randomly selects arms - Useful for comparison with more sophisticated methods - Demonstrates the importance of intelligent exploration

Applications

The multi-armed bandit algorithms implemented in this package can be applied to various real-world problems:

  1. Online Advertising - Optimizing ad placement and selection - Maximizing click-through rates - A/B testing of different ad designs

  2. Clinical Trials - Optimizing treatment allocation - Minimizing patient exposure to inferior treatments - Accelerating drug discovery

  3. Recommendation Systems - Personalizing content recommendations - Optimizing user engagement - Balancing exploration of new items with exploitation of known preferences

  4. Resource Allocation - Optimizing cloud resource allocation - Load balancing in distributed systems - Network routing optimization

Aim

The thompson package provides a comprehensive implementation of multi-armed bandit algorithms in Python, making it easy to: - Apply these algorithms to real-world problems - Compare different approaches - Visualize and analyze results - Make data-driven decisions in uncertain environments