However, the completion accuracy can be drastically different over different entries.

On the positive side, we give anα = 1.01-approximate proper learner that uses O(1/( 2γ2)) samples (which is optimal) and runs in timepoly(d/) 2 O(1/γ

Figure 2: RN "100) when structure (see(A)stationary (B)altered T{3and2T{3as

However,existing algorithms lack universality in the sense that they can only handle one type of convex functions and need apriori knowledge of parameters.

Welet

Recently, researchers from convex optimization proposed the notions of "relative Lipschitz continuity" and "relative strong convexity". Both of the notions are generalizations oftheirclassicalcounterparts.

In this paper, we revisit the problem of smoothed online learning, in which the online learner suffersboth ahitting costandaswitching cost, andtargettwoperformance metrics: competitiveratio anddynamic regretwith switching cost. To bound the competitive ratio, we assume the hitting cost is known to the learner in each round, and investigate the simple idea of balancing the two costs by an optimizationproblem.

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.