On Tradeoffs in Learning-Augmented Algorithms

TL;DR

The paper investigates learning-augmented algorithms that receive predictions and must simultaneously achieve consistency, robustness, and smoothness, while also considering average-case performance under predictive distributions. It shows that Pareto-optimal strategies for problems like line search and one-max search are brittle, and introduces a randomized deviation controlled by a parameter $\rho$ to restore smoothness at a cost to consistency. This randomized approach is extended to ski-rental, revealing a tunable tradeoff between smoothness and average-case performance; all three problems are accompanied by theoretical guarantees and experiments. The results provide practical guidance for designing prediction-aware algorithms, showing how controlled randomness can balance worst-case guarantees with graceful degradation and improved average outcomes.

Abstract

The field of learning-augmented algorithms has gained significant attention in recent years. These algorithms, using potentially inaccurate predictions, must exhibit three key properties: consistency, robustness, and smoothness. In scenarios where distributional information about predictions is available, a strong expected performance is required. Typically, the design of these algorithms involves a natural tradeoff between consistency and robustness, and previous works aimed to achieve Pareto-optimal tradeoffs for specific problems. However, in some settings, this comes at the expense of smoothness. This paper demonstrates that certain problems involve multiple tradeoffs between consistency, robustness, smoothness, and average performance.

Figures (6)

• Figure 1: The mapping $y \mapsto \textsf{A}^{\operatorname{LS}}_b(x,y)/x$ for $x$ arbitrary large and $y \in [\tfrac{x}{b^2}, b^2x]$.
• Figure 2: Upper bound on the competitive ratio of $\textsf{A}^{\operatorname{SR}}_{\lambda, \rho}$ with $\lambda, \rho$ as in Corollary \ref{['cor:sr-avg']}, and with $\lambda, \rho$ as in Lemma 2.2 of benomar2023advice.
• Figure 3: Consistency-smoothness tradeoff of $\textsf{A}^{\operatorname{LS}}_b$ with a prediction randomized as in Theorem \ref{['thm:smooth-LS']}
• Figure 4: Consistency-smoothness tradeoff of Algorithm $\textsf{A}^{\operatorname{OM}}_{\lambda,\rho}$ for $\rho \in \{0,0.5,1\}$.
• Figure 5: Consistency-smoothness tradeoff of $\textsf{A}^{\operatorname{SR}}_{\lambda, \rho}$, with $y \sim x + \mathcal{N}(0,\sigma^2)$

Theorems & Definitions (24)

• Definition 1.1: Brittleness
• Lemma 2.1
• proof
• Proposition 2.2: $\textsf{A}^{\operatorname{LS}}_b$ is brittle
• proof
• Theorem 2.3
• proof
• Lemma 3.1
• proof
• Lemma 3.2