We consider the robust planning of energy-constrained unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), which act as mobile charging stations, to perform long-horizon aerial monitoring missions. More specifically, given a set of points to be visited by the UAVs and desired final positions of the UAV-UGV teams, the objective is to find a robust plan (the vehicle trajectories) that can be realized without a major revision in the face of uncertainty (e.g., unknown obstacles/terrain, wind) to complete this mission in minimum time. We provide a formal description of this problem as a mixed-integer program (MIP), which is NP-hard. Since exact solution methods are computationally intractable for such problems, we propose RSPECT, a scalable and efficient heuristic. We provide theoretical results on the complexity of our algorithm and the feasibility and robustness of resulting plans. We also demonstrate the performance of our method via simulations and experiments.

While there exist well known algorithms for choosing the decision maker's actions which guarantee

Neural Information Processing Systems http://nips.cc/

A.1 On the ES fairness notion In this paper, we defined the ES fairness notion as follows, Pr {E Consider classifier R = r (X,A). A.4 Restating Theorem 5 for the statistical parity (SP) fairness notion Here we restate Theorem 5 for the statistical parity. The proof is similar to the proof of Theorem 5. Note that ( X,Y) and A are conditionally independent given A . Pr{r (X, 0) = ˆy |Y = 1,A = 0 } A.7 Numerical Experiment We compared EO and ES fairness notions in Table 2 after adding the following constraints to (13). Next, we prove the second part of the theorem.

This greedy behavior may hinder an algorithm's

Computing tight Lipschitz bounds for deep neural networks is crucial for analyzing their robustness and stability, but existing approaches either produce relatively conservative estimates or rely on semidefinite programming (SDP) formulations (namely the LipSDP condition) that face scalability issues. Building upon ECLipsE-Fast, the state-of-the-art Lipschitz bound method that avoids SDP formulations, we derive a new family of improved scalable Lipschitz bounds that can be combined to outperform ECLipsE-Fast. Specifically, we leverage more general parameterizations of feasible points of LipSDP to derive various closed-form Lipschitz bounds, avoiding the use of SDP solvers. In addition, we show that our technique encompasses ECLipsE-Fast as a special case and leads to a much larger class of scalable Lipschitz bounds for deep neural networks. Our empirical study shows that our bounds improve ECLipsE-Fast, further advancing the scalability and precision of Lipschitz estimation for large neural networks.