Thompson sampling

In artificial intelligence, Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that addresses the exploration-exploitation dilemma in the multi-armed bandit problem. It consists in choosing the action that maximizes the expected reward with respect to a randomly drawn belief.

Consider a set of contexts ${\displaystyle {\mathcal {X}}}$, a set of actions ${\displaystyle {\mathcal {A}}}$, and rewards in ${\displaystyle \mathbb {R} }$. In each round, the player obtains a context ${\displaystyle x\in {\mathcal {X}}}$, plays an action ${\displaystyle a\in {\mathcal {A}}}$ and receives a reward ${\displaystyle r\in \mathbb {R} }$ following a distribution that depends on the context and the issued action. The aim of the player is to play actions such as to maximize the cumulative rewards.

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