We examine the problem of online optimization, where a decision maker must sequentially choose points in a general metric space to minimize the sum of per-round, non-convex hitting costs and the costs of switching decisions between rounds. The decision maker has access to a black-box oracle, such as a machine learning model, that provides untrusted and potentially inaccurate predictions of the optimal decision in each round. The goal of the decision maker is to exploit the predictions if they are accurate, while guaranteeing performance that is not much worse than the hindsight optimal sequence of decisions, even when predictions are inaccurate. We impose the standard assumption that hitting costs are globally $\alpha$-polyhedral. We propose a novel algorithm, Adaptive Online Switching (AOS), and prove that, for any desired $\delta > 0$, it is $(1+2\delta)$-competitive if predictions are perfect, while also maintaining a uniformly bounded competitive ratio of $2^{\tilde{\mathcal{O}}(1/(\alpha \delta))}$ even when predictions are adversarial. Further, we prove that this trade-off is necessary and nearly optimal in the sense that any deterministic algorithm which is $(1+\delta)$-competitive if predictions are perfect must be at least $2^{\tilde{\Omega}(1/(\alpha \delta))}$-competitive when predictions are inaccurate.
翻译:我们检查了在线优化问题, 决策者必须在一般衡量空间中按顺序选择点数, 以最大限度地减少每轮、 非convex的冲击成本和在两轮之间转换决定的成本。 决策者可以使用黑盒子或魔器, 如机器学习模型, 提供对每轮最佳决定的不可信和可能不准确的预测。 决策者的目标是利用预测, 如果预测准确的话, 利用这些预测, 同时保证业绩不会比后视最佳决策顺序差得多, 即便预测不准确。 我们规定标准假设点击成本是全球的$\ alpha$- pollyhedral。 我们提出新的算法, 适应性在线切换( AOS), 并且证明, 对于任何想要的 $delta > 0美元, 如果预测是完美的话, $(1+2\delta) $ - 具有竞争力, 同时保持一个统一、 受约束的竞争力比率为2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\