Thompson Sampling is a statistical method used for solving the multi-armed bandit problem, which focuses on balancing the exploration of new options and the exploitation of known successful ones. It is commonly used in scenarios like online advertising, recommendation systems, and clinical trials where a decision maker must choose from a set of options with uncertain rewards. The key idea behind Thompson Sampling is to maintain probability distributions for the expected rewards of each option and to use these distributions to make confident decisions over time.
In practice, Thompson Sampling works by assigning a prior distribution to the success rate of each option, often using a Beta distribution for binary rewards (success or failure). During each decision-making round, a sample is drawn from each option's distribution. The option with the highest sampled value is then selected. After the decision is made and the outcome is observed, the distribution for that option is updated to incorporate the new data. This continuous process allows the algorithm to learn the effective strategies over time while still exploring less selected options to find potentially better alternatives.
An example where Thompson Sampling can be useful is in A/B testing for a website's layout. Suppose you have two different page designs and want to determine which one leads to more conversions. Rather than fixing your choice from the start, you could implement Thompson Sampling to continuously evaluate which layout performs better, adjusting your decisions based on the performance data you gather over time. This adaptive approach can lead to higher overall conversion rates compared to testing each layout independently with a fixed allocation of traffic.