Collaborative Bandit Algorithms: Exact Regret Bounds and Beyond

In this research paper, we explore the concept of collaborative learning in bandit problems, where multiple agents work together to learn the best arm (or action) in a sequence. We aim to develop an algorithm that minimizes the regret, which is the difference between the expected reward of the best arm and the actual reward of the chosen arm. Our main contribution is providing optimal regret bounds for this problem, which means we give the tightest possible upper bound on the regret that our algorithm can achieve.
To understand this concept, imagine you are a chef in a restaurant, and you want to find the perfect dish to serve to your customers. You have a set of ingredients, and each ingredient has a certain quality (reward) associated with it. You want to choose the best ingredients to make the dish that will give you the highest quality (reward) for your customers. However, you don’t know which ingredients are the best until you try them out and observe their quality. This is similar to the problem of collaborative learning in bandits, where each agent tries different actions and observes their rewards to learn the best action.
Our algorithm, called CExp2, uses a novel technique called confidence intervals to balance exploration and exploitation. Exploration means trying new actions to learn about their quality, while exploitation means choosing actions with high-quality observations. We prove that our algorithm achieves optimal regret bounds, which means it is the best possible performance among all algorithms that explore and exploit in a similar way.
In summary, this paper provides a significant contribution to the field of collaborative learning in bandits by developing an algorithm that minimizes the regret and achieves optimal regret bounds. This work has important implications for applications where multiple agents need to learn and make decisions together, such as recommendation systems or ad auctions.