Overcoming Brittleness in Pareto-Optimal Learning-Augmented Algorithms

TL;DR

This work reveals a brittleness phenomenon in Pareto-optimal learning-augmented online algorithms, showing that even near-perfect predictions can yield worst-case-like performance for one-way trading. It introduces performance profiles $F$ to impose smooth, user-controlled guarantees mapping prediction error to competitive ratios, and provides offline feasibility tests plus online algorithms to respect feasible profiles. It further presents Ada-PO, an adaptive Pareto-optimal algorithm that leverages deviations from worst-case inputs to improve performance while maintaining robustness, and proves dominance over existing Pareto-optimal methods. Empirical results on synthetic and Bitcoin data validate the theoretical benefits of profile-based and adaptive approaches, suggesting broad applicability to other learning-augmented optimization problems.

Abstract

The study of online algorithms with machine-learned predictions has gained considerable prominence in recent years. One of the common objectives in the design and analysis of such algorithms is to attain (Pareto) optimal tradeoffs between the consistency of the algorithm, i.e., its performance assuming perfect predictions, and its robustness, i.e., the performance of the algorithm under adversarial predictions. In this work, we demonstrate that this optimization criterion can be extremely brittle, in that the performance of Pareto-optimal algorithms may degrade dramatically even in the presence of imperceptive prediction error. To remedy this drawback, we propose a new framework in which the smoothness in the performance of the algorithm is enforced by means of a user-specified profile. This allows us to regulate the performance of the algorithm as a function of the prediction error, while simultaneously maintaining the analytical notion of consistency/robustness tradeoffs, adapted to the profile setting. We apply this new approach to a well-studied online problem, namely the one-way trading problem. For this problem, we further address another limitation of the state-of-the-art Pareto-optimal algorithms, namely the fact that they are tailored to worst-case, and extremely pessimistic inputs. We propose a new Pareto-optimal algorithm that leverages any deviation from the worst-case input to its benefit, and introduce a new metric that allows us to compare any two Pareto-optimal algorithms via a dominance relation.

Figures (7)

• Figure 1: Illustration of profile functions.
• Figure 2: Summary of the experimental results.
• Figure 3: An illustration of Profile. Here the profile $F$ is as follows: $F([1,20)=7$,$F([20,35])=5$, $F([35,50])=3$, $F([50,70])=3.5$, and $F([70,100])=4$
• Figure 4: An illustration of the profile $F_\phi$.
• Figure 5: An illustration of Case 1.

Theorems & Definitions (21)

• remark 2.1: el2001optimal
• definition 3.1
• theorem 3.1: Appendix \ref{['app:brittle']}
• definition 3.2
• definition 3.3
• theorem 3.2
• definition 3.4
• definition 3.5
• remark 3.1
• lemma 4.1