Pseudoregret ($R_n={\sum }_{t=1}^n[m(x_{\star })-m(X_t)]$)

The cumulative difference between the mean reward of an optimal fixed action and the mean rewards of the selected actions. For adaptive random actions, this sum is itself a random variable; taking its expected value gives expected pseudoregret. Observation noise is absent from the sum, although earlier noise can influence later actions.