Referring to Decision theory:

The mathematical study of strategies for optimal decision-making between options involving different risks or expectations of gain or loss depending on the outcome.

https://www.wikiwand.com/en/Decision_theory

See minimax_and_bayes_estimator.pdf for a description of the formalism decision theory under uncertainty (using the framework Parametric statistical inference as the setting). This also defines the useful concepts of a

• Minimax decision rule
• Bayes optimal decision rule
• Admissible decision rule (related to Pareto optimality)

See also Machine learning, and Reinforcement learning

Decision tree

Maximum expected utility theory

Utility functions in Graphical models

Value of perfect information. The value of making observations/gaining information before making decisions.

Reinforcement learning

very much connected with decision theory

Two types of problems in sequential decision-making:

• Model-free reinforcement learning
• Planning