= Optimism in the face of uncertainty
A decision principle that maximizes possible reward jointly over an action and a parameter in a <confidence set>. On the event that the set contains the true parameter, the reward predicted for this selected pair is at least the true optimal reward. This inequality bounds <pseudoregret> by the width of the <confidence set> in the selected action's direction. For an $L$-<Lipschitz continuous> reward link and a radius-$\beta$ <confidence ellipsoid>, <Cauchy-Schwarz inequality> and the <triangle inequality> bound that width by $2L\beta\sqrt{x^TV^{-1}x}$.
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