用离线数据构建查表策略，让MPC提速100-1000倍且保证性能
Data-driven Acceleration of MPC with Guarantees
- 用离线MPC解构建非参数查表策略，替代在线优化
- 实验显示提速100~1000倍，性能损失小
- 支持持续加入新数据，无需重新训练
模型预测控制（MPC）虽具强大优化能力，但在线求解速度慢，难以满足低延迟需求。本文提出一种数据驱动框架，通过离线收集的MPC解构建非参数策略，替代在线优化。该策略基于构造的最优代价上界进行贪心选择，可实现非参数查表形式，比在线求解快数个数量级。理论分析表明，在离线数据覆盖充分条件下，策略具有递归可行性，并拥有可证明的有界最优性差距。该条件明确揭示了数据量与边界紧致性之间的权衡关系。新解可直接融入，无需重训，支持持续改进。实验结果表明，该策略在100至1000倍提速的同时仅带来适度性能下降，具备实时控制应用潜力。
原文摘要 · Abstract (English)
Model Predictive Control (MPC) is a powerful framework for optimal control but can be too slow for low-latency applications. We present a data-driven framework to accelerate MPC by replacing online optimization with a nonparametric policy constructed from offline MPC solutions. Our policy is greedy with respect to a constructed upper bound on the optimal cost-to-go, and can be implemented as a nonparametric lookup rule that is orders of magnitude faster than solving MPC online. Our analysis shows that under sufficient coverage conditions of the offline data, the policy is recursively feasible and admits provable, bounded optimality gap. These conditions establish an explicit trade-off between the amount of data collected and the tightness of the bounds. New solutions can be incorporated straightforwardly without the need for retraining, enabling continual improvement. Our experiments show that this policy is between 100 and 1000 times faster than standard MPC with only a modest hit to optimality, showing potential for real-time control tasks.
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