Inparticular, dynamic regret [Zinkevich,2003;Zhang et al.,2018a]and adaptiveregret [Hazan and Seshadhri, 2009; Daniely et al., 2015] are proposed as two principled metrics to guide the algorithm design. Theunknowncomparators orunknown intervals bring considerable uncertainty to online optimization.

However,neitherthedata nor the tools existed in the past to extensively support these explanations. The era of big data opens a new opportunity to study input-driven approaches. We introduce atool that computes the likelihood ofpatches, given alarge dataset to learn from. Given this tool, we present a model that supports the approach and explains lightness and color visual illusions in a unified manner.

We now introduce notation that will let us represent the above expression in a more compactmanner.