Data-driven Acceleration of MPC with Guarantees

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 condition 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. 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.

Using Drone Swarm to Stop Wildfire: A Predict-then-optimize Approach

Drone swarms coupled with data intelligence can be the future of wildfire fighting. However, drone swarm firefighting faces enormous challenges, such as the highly complex environmental conditions in wildfire scenes, the highly dynamic nature of wildfire spread, and the significant computational complexity of drone swarm operations. We develop a predict-then-optimize approach to address these challenges to enable effective drone swarm firefighting. First, we construct wildfire spread prediction convex neural network (Convex-NN) models based on real wildfire data. Then, we propose a mixed-integer programming (MIP) model coupled with dynamic programming (DP) to enable efficient drone swarm task planning. We further use chance-constrained robust optimization (CCRO) to ensure robust firefighting performances under varying situations. The formulated model is solved efficiently using Benders Decomposition and Branch-and-Cut algorithms. After 75 simulated wildfire environments training, the MIP+CCRO approach shows the best performance among several testing sets, reducing movements by 37.3\% compared to the plain MIP. It also significantly outperformed the GA baseline, which often failed to fully extinguish the fire. Eventually, we will conduct real-world fire spread and quenching experiments in the next stage for further validation.

Online Long-run Constrained Optimization

In this paper, a novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in online manner, where the objective and constraints are not necessarily convex. In each period, random linear perturbation and strongly concave perturbation are incorporated in primal and dual directions, respectively, to the offline oracle, and a global minimax point is searched as solution. Based on two particular definitions of expected static cumulative regret, we derive the first sublinear $O(T^{8/9})$ regret complexity for this class of problems. The proposed algorithm is applied to tackle a long-term (risk) constrained river pollutant source identification problem, demonstrating the validity of the theoretical results and exhibiting superior performance compared to existing method.