Prediction-Specific Design of Learning-Augmented Algorithms

TL;DR

The paper addresses designing online algorithms that leverage ML predictions in a problem-structure-aware, prediction-specific way. It introduces prediction-specific consistency and robustness, and defines strong optimality as Pareto-optimal performance for every prediction value. A bi-level optimization-based meta-algorithm is developed to systematically construct strongly-optimal algorithms, and explicit instances are provided for deterministic and randomized ski rental as well as one-max search. The framework is extended to handle prediction errors via ε-consistency and to support practical cases with empirical validation on dynamic power management and volatility-based trading. Overall, the results show significant performance gains over prior worst-case designs, demonstrating practical impact across online decision-making tasks.

Abstract

Algorithms with predictions} has emerged as a powerful framework to combine the robustness of traditional online algorithms with the data-driven performance benefits of machine-learned (ML) predictions. However, most existing approaches in this paradigm are overly conservative, {as they do not leverage problem structure to optimize performance in a prediction-specific manner}. In this paper, we show that such prediction-specific performance criteria can enable significant performance improvements over the coarser notions of consistency and robustness considered in prior work. Specifically, we propose a notion of \emph{strongly-optimal} algorithms with predictions, which obtain Pareto optimality not just in the worst-case tradeoff between robustness and consistency, but also in the prediction-specific tradeoff between these metrics. We develop a general bi-level optimization framework that enables systematically designing strongly-optimal algorithms in a wide variety of problem settings, and we propose explicit strongly-optimal algorithms for several classic online problems: deterministic and randomized ski rental, and one-max search. Our analysis reveals new structural insights into how predictions can be optimally integrated into online algorithms by leveraging a prediction-specific design. To validate the benefits of our proposed framework, we empirically evaluate our algorithms in case studies on problems including dynamic power management and volatility-based index trading. Our results demonstrate that prediction-specific, strongly-optimal algorithms can significantly improve performance across a variety of online decision-making settings.

Figures (9)

• Figure 1: Prediction-specific consistency $\beta_y$ and robustness $\gamma_y$ under different predictions $y$ for DSR with $b=100$ (Left), RSR with $b=100$ (Middle), and OMS with $L=10, U=20$ (Right).
• Figure 2: Prediction-specific consistency $\beta_y(M)$ versus decision $M$ given $y \geq b$.
• Figure 3: Prediction-specific robustness $\gamma_y(M)$ versus decision $M$ given $y \geq b$.
• Figure 4: Empirical competitive ratios versus accuracy $p$ in deterministic setting.
• Figure 5: Empirical competitive ratios versus accuracy $p$ in randomized setting.

Theorems & Definitions (51)

• Definition 1: Classic Metrics
• Definition 2: Prediction-Specific Metrics
• Definition 3: Weak Optimality
• Definition 4: Strong Optimality
• Theorem 2.1
• Proposition 1
• Theorem 4.1
• Theorem 4.2
• Theorem 5.1
• Theorem 5.2