A new look at shifting regret

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A Closer Look at Adaptive Regret (2012, background): “A slightly weaker upper bound was obtained in [2].”
Tracking Slowly Moving Clairvoyant: Optimal Dynamic Regret of Online Learning with True and Noisy Gradient (2016, background): “In fact, a similar dynamic regret bound to √ V pT T has been established for online convex optimization over the simplex (Cesa-Bianchi et al., 2012), where the path variation is measured inℓ1 norm.”
Online Optimization in Dynamic Environments (2013, methodology): “We use Corollary 3 of [26] to bound T1.”
Dynamical Models and tracking regret in online convex programming (2013, background): “…or dynamic comparator sequence has been studied previously in the literature in the context of tracking regret, shifting regret (Herbster & Warmuth, 2001; Cesa-Bianchi et al., 2012), and the closely-related concept of adaptive regret (Littlestone & Warmuth, 1994; Hazan & Seshadhri, 2009).”
Online Convex Optimization in Dynamic Environments (2015, methodology): “Note that when corresponds to an identity operator, the bound in Theorem 2 corresponds to existing tracking or shifting regret bounds [14], [21].”