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rom 1933 to today: How has Thompson sampling influenced modern machine learning
Thompson Sampling, named after William R. Thompson, is also known as the solution to the greedy decision dilemma and was first proposed in 1933. As an online learning and decision-making method, it aims to solve the exploration-exploitation dilemma in the multi-arm gambling problem. This approach plays an increasingly important role in today's machine learning, big data, and automated decision making.
Basic concepts of Thompson sampling
The core of Thompson sampling is to select actions based on randomly sampled beliefs so that the selected actions maximize the expected reward. Specifically, in each turn, players are given a context, choose an action, and are subsequently rewarded based on the outcome of that action. The purpose of this process is to maximize the cumulative rewards.
The advantage of Thompson sampling is that it uses the posterior distribution to express the confidence in different actions, thus finding a balance between exploring new actions and exploiting known actions.Historical Background
Since Thompson sampling was first proposed in 1933, it has been rediscovered by several independent research teams. In 1997, the convergence property of the "multi-armed gambling problem" was first proved. Subsequently, the application of Thompson sampling in Markov decision processes was proposed in 2000, and subsequent studies found that it has the characteristics of rapid self-correction. In 2011, he published the asymptotic convergence results for contextual bandits, demonstrating the potential application of Thompson sampling in various online learning problems.
How Thompson Sampling Influences Modern Machine LearningThompson sampling has applications in modern machine learning, ranging from A/B testing in website design to optimizing online advertising to accelerating learning in decentralized decision making. Thompson sampling is particularly well suited for use in changing environments because it effectively balances the needs of exploration and exploitation. For example, in advertising, companies increasingly rely on Thompson sampling to ensure the selection of the best ads.
As data proliferates and requirements change, Thompson sampling's flexibility and efficiency make it indispensable in online learning and decision-making systems.
Relationship with other strategies
Probability Matching
Probability matching is a decision strategy that makes predictions based on class base rates. In this strategy, the model’s predictions for positive and negative examples match their proportions in the training set. Thompson sampling can also be viewed as an extension of probability matching to some extent, as it takes into account the expected rewards of different choices.
Bayesian Control Rule
Bayesian control rules are a further generalization of Thompson sampling that allow action selection in a variety of dynamic environments. This approach emphasizes the acquisition of causal structure during the learning process, helping the agent find the best decision path in the behavior space.
Upper Confidence Bound (UCB) Algorithm
Thompson sampling and upper confidence bound algorithms have similar basic properties, both tend to give more exploration to actions that are potentially optimal. This feature allows the theoretical results of the two to be derived from each other, thus forming a more comprehensive regret analysis.
Future Outlook
The evolution of Thompson sampling continues as AI technology advances. In the future, this strategy may be integrated with other technologies such as deep learning to further improve the decision-making capabilities of intelligent systems. In addition, with the enhancement of computing resources and the diversification of actual application scenarios, the specific practice of Thompson sampling will continue to evolve.
Thompson sampling is undoubtedly an important bridge between exploratory behavior and optimal decision-making. So what challenges and opportunities will we face in the future of machine learning?
