Competitive regret

In decision theory, competitive regret is the relative regret compared to an oracle with limited or unlimited power in the process of distribution estimation.

Consider estimating a discrete probability distribution ${\displaystyle p}$ on a discrete set ${\displaystyle {\mathcal {X}}}$ based on data ${\displaystyle X}$, the regret of an estimator${\displaystyle q}$ is defined as

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