In this paper, we study oracle-efficient algorithms for beyond worst-case analysis of online learning. We focus on two settings. First, the smoothed analysis setting of [RST11,HRS21] where an adversary is constrained to generating samples from distributions whose density is upper bounded by 1/σ times the uniform density. Second, the setting of K-hint transductive learning, where the learner is given access to K hints per time step that are guaranteed to include the true instance. We give the first known oracle-efficient algorithms for both settings that depend only on the VC dimension of the class and parameters σ and K that capture the power of the adversary. In particular, we achieve oracle-efficient regret bounds of O( T (d/σ) 1/2 ) and O( √ T dK) respectively for these setting. For the smoothed analysis setting, our results give the first oracle-efficient algorithm for online learning with smoothed adversaries [HRS21]. This contrasts the computational separation between online learning with worst-case adversaries and offline learning established by [HK16]. Our algorithms also imply improved bounds for worst-case setting with small domains. In particular, we give an oracle-efficient algorithm with regret of O( T (d|X |) 1/2 ), which is a refinement of the earlier O( T |X |) bound by [DS16].
The First-Come First-Served (FCFS) scheduling policy is the most popular scheduling algorithm used in practice. Furthermore, its usage is theoretically validated: for light-tailed job size distributions, FCFS has weakly optimal asymptotic tail of response time. But what if we don't just care about the asymptotic tail? What if we also care about the 99th percentile of response time, or the fraction of jobs that complete in under one second? Is FCFS still best? Outside of the asymptotic regime, only loose bounds on the tail of FCFS are known, and optimality is completely open.
In this paper, we introduce a new policy, Nudge, which is the first policy to provably stochastically improve upon FCFS. We prove that Nudge simultaneously improves upon FCFS at every point along the tail, for light-tailed job size distributions. As a result, Nudge outperforms FCFS for every moment and every percentile of response time. Moreover, Nudge provides a multiplicative improvement over FCFS in the asymptotic tail. This resolves a long-standing open problem by showing that, counter to previous conjecture, FCFS is not strongly asymptotically optimal.
This paper represents an abridged version of [2].
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