actionmeasure

Action measure is a term encountered in several disciplines to denote a quantitative representation of the action chosen or applied in a system. In control theory and robotics, action measure often refers to a scalar cost or energy associated with applying a control input u(t) to a dynamical system. A common definition is the running cost defined as the time integral of a function L that depends on the state x(t) and the action u(t), or a simpler form that uses the norm of the control input, possibly with state-dependent weights. This action measure is used in optimal control and model predictive control to favor low energy or smooth control, to respect actuator limits, and to balance performance against wear and risk. Variants include quadratic costs, norms, or more general penalties.

In reinforcement learning and decision making, action measure can describe the policy-induced measure over actions. For a given state s, the policy specifies a probability distribution over the action space A; this distribution is the action measure. In continuous action settings, the policy becomes a density function over actions with respect to a base measure. The action measure governs exploration, stochasticity, and the expected return of a policy.

In mathematics and economics literature, the phrase may also appear as a heuristic for the effect or impact of a chosen course of action, but it is not a standardized technical term across all fields.

See also: cost function, action cost, control theory, reinforcement learning, policy, probability measure.