Decision-makers often have access to machine-learned predictions about future demand that can help guide online resource allocation decisions. However, such predictions may be inaccurate. We develop a framework for online resource allocation with potentially unreliable machine-learned advice, where the advice is represented as a convex uncertainty set for the demand vector rather than a single point estimate. We introduce a parameterized class of Pareto-optimal online algorithms that balance consistency and robustness. The consistent ratio measures performance when the advice is accurate, while the robust ratio measures performance under adversarial demand when the advice is inaccurate. For a target consistency level C, our algorithms maximize robustness subject to achieving at least consistency level C. Our approach extends classical protection-level algorithms by introducing adaptive protection levels that dynamically respond to uncertainty in the advice. We also provide a method for computing the maximum achievable consistency level. Numerical experiments demonstrate that our algorithms outperform benchmark methods, including approaches based solely on point forecasts, by effectively balancing worst-case and average-case performance.

翻译：决策者常能获取关于未来需求的机器学习预测，以指导在线资源分配决策。然而，此类预测可能存在偏差。我们提出一个面向潜在不可靠机器学习建议的在线资源分配框架，其中建议以需求向量的凸不确定性集合而非单一估计值表示。我们引入一类可权衡一致性与鲁棒性的参数化帕累托最优在线算法。一致性比率衡量建议准确时的性能，而鲁棒性比率衡量建议不准确时在对抗性需求下的性能。针对目标一致性水平C，我们的算法在达到至少一致性水平C的前提下最大化鲁棒性。该方法通过引入能动态响应建议不确定性的自适应防护水平，扩展了经典防护水平算法。我们还提出一种计算最大可实现一致性水平的方法。数值实验表明，我们的算法通过有效平衡最坏情况与平均性能，优于基准方法（包括仅基于点预测的方法）。