🤖 AI Summary
This work investigates the impact of prediction accuracy on the performance of online algorithms under the distributionally robust competitive ratio (DRCR) framework. By integrating machine-learned predictions, we establish that the optimal DRCR is a monotone concave function of prediction accuracy and extend this property to settings with multiple predictions. Leveraging tools from distributionally robust optimization and competitive analysis, we introduce a method to compute the “critical accuracy”—the minimum prediction precision required to outperform the prediction-free benchmark. Focusing on the ski rental problem, we derive explicit conditions on the accuracy needed to achieve a target DRCR and provide an exact solution for this critical threshold, offering both theoretical guarantees and practical guidance for designing prediction-augmented online algorithms.
📝 Abstract
The field of algorithms with predictions aims to improve algorithm performance by integrating machine learning predictions into algorithm design. A central question in this area is how predictions can improve performance, and a key aspect of this analysis is the role of prediction accuracy. In this context, prediction accuracy is defined as a guaranteed probability that an instance drawn from the distribution belongs to the predicted set. As a performance measure that incorporates prediction accuracy, we focus on the distributionally-robust competitive ratio (DRCR), introduced by Sun et al.~(ICML 2024). The DRCR is defined as the expected ratio between the algorithm's cost and the optimal cost, where the expectation is taken over the worst-case instance distribution that satisfies the given prediction and accuracy requirement. A known structural property is that, for any fixed algorithm, the DRCR decreases linearly as prediction accuracy increases. Building on this result, we establish that the optimal DRCR value (i.e., the infimum over all algorithms) is a monotone and concave function of prediction accuracy. We further generalize the DRCR framework to a multiple-prediction setting and show that monotonicity and concavity are preserved in this setting. Finally, we apply our results to the ski rental problem, a benchmark problem in online optimization, to identify the conditions on prediction accuracies required for the optimal DRCR to attain a target value. Moreover, we provide a method for computing the critical accuracy, defined as the minimum accuracy required for the optimal DRCR to strictly improve upon the performance attainable without any accuracy guarantee.