Contract Scheduling with Distributional and Multiple Advice

TL;DR

This work extends contract scheduling to learning-augmented settings by introducing distributional and multiple advice models. It constructs $4$-robust schedules with best possible consistency in both settings: in distributional advice, consistency approaches $4\ln 2$ as the granularity of the advice grows, with the degradation under Earth Mover's Distance bounded by $O(\sqrt{\eta/D})$; in the multiple-advice model, the optimal worst-case consistency is $2^{2-\frac{1}{k}}$, computable in $O(k\log k)$ time. Theoretical results are supported by experiments showing practical performance gains and robustness to prediction errors.

Abstract

Contract scheduling is a widely studied framework for designing real-time systems with interruptible capabilities. Previous work has showed that a prediction on the interruption time can help improve the performance of contract-based systems, however it has relied on a single prediction that is provided by a deterministic oracle. In this work, we introduce and study more general and realistic learning-augmented settings in which the prediction is in the form of a probability distribution, or it is given as a set of multiple possible interruption times. For both prediction settings, we design and analyze schedules which perform optimally if the prediction is accurate, while simultaneously guaranteeing the best worst-case performance if the prediction is adversarial. We also provide evidence that the resulting system is robust to prediction errors in the distributional setting. Last, we present an experimental evaluation that confirms the theoretical findings, and illustrates the performance improvements that can be attained in practice.

Figures (14)

• Figure 1: Illustration of the computation of $\ell(X_j,z)$ for $n=3$ and $j=1$. Note that the time scale is logarithmic. Fix an interruption point $z \in [2^2, 2^3)$. Then $z$ is contained in $I_2^k$ for some value of $k \in \{0,\dots,n-1\}$. If $k \geq n - j = 2$, then the largest completed contract is $c_2$ (of length $2^{2-1/3}$), and otherwise, the largest completed contract is $c_1$ (of length $2^{1-1/3}$).
• Figure 2: Illustration of the definitions of $\delta_j$ and $D_j$.
• Figure 3: Plot of the consistency of Sel$_n$ with advice a truncated normal distribution as function of the mean m.
• Figure 4: Plot of the consistency of Sel$_n$ with advice a uniform distribution in $[0.95t,1.05t]$, as function of $t$.
• Figure 5: Experimental evaluation of MULT$_k$.

Theorems & Definitions (21)

• Proposition 1: Appendix
• Definition 2
• Theorem 3
• proof
• Corollary 4
• Theorem 5
• proof
• Theorem 6: Appendix
• Proposition 7: Appendix
• Theorem 8