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Payoff distribution

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A payoff distribution is a probability distribution describing the rewards produced by a particular bandit action.

A payoff distribution describes the probabilities of rewards produced by a particular action, such as pulling one slot machine. Its mean and standard deviation summarize typical payoff and variation. section 12.1.6

Three slot machines

A noncontextual multi-armed bandit offers three machines with payoff parameters (mean, standard deviation) of (8, 0.5), (10, 0.7), and (5, 0.45). Each pull samples a reward from the selected machine; learning these distributions supports the exploration–exploitation trade-off. section 12.1.6

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Defines distributions through rewards, means, and standard deviations, then samples them in Python without deriving distribution theory.
Examples
Uses three slot machines with parameter pairs (8, 0.5), (10, 0.7), and (5, 0.45), sampled across 90 trials.
What it assumes
Assumes the learner can interpret rewards and bandit actions while leaving distribution details initially unknown.
What you can do after
Apply it via Python and NumPy by sampling rewards from specified distributions for bandit-strategy experiments.
How it connects
Connects payoff distributions to multi-armed bandits, exploration, exploitation, cumulative reward, regret, mean, and standard deviation.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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