And maybe use cartesian product notation instead of pi product for X. -l106: slightly tune down radically different -l118: +more structured -l201: phi is not defined here when introducing Nesterov's setting -ref [17]: venue missing Q2: Please summarize your review in 1-2 sentences The paper proposes a primal dual optimization scheme for decomposable problems with linear coupling constraints, which can recover augmented Lagrangian, ADMM and fast dual descent methods. The paper is novel and highly non-trivial, but incremental in the sense that it provides convergence rates for the iterates themselves, avoiding the need to average as in existing methods. The presented theory only applies with known accuracy for the subproblem solutions in each iteration, however the experiments (e.g.

Multi-robot systems enhance efficiency and productivity across various applications, from manufacturing to surveillance. While single-robot motion planning has improved by using databases of prior solutions, extending this approach to multi-robot motion planning (MRMP) presents challenges due to the increased complexity and diversity of tasks and configurations. Recent discrete methods have attempted to address this by focusing on relevant lower-dimensional subproblems, but they are inadequate for complex scenarios like those involving manipulator robots. To overcome this, we propose a novel approach that %leverages experience-based planning by constructs and utilizes databases of solutions for smaller sub-problems. By focusing on interactions between fewer robots, our method reduces the need for exhaustive database growth, allowing for efficient handling of more complex MRMP scenarios. We validate our approach with experiments involving both mobile and manipulator robots, demonstrating significant improvements over existing methods in scalability and planning efficiency. Our contributions include a rapidly constructed database for low-dimensional MRMP problems, a framework for applying these solutions to larger problems, and experimental validation with up to 32 mobile and 16 manipulator robots.

There has been much recent interest in application of the pool-adjacent-violators (PAV) algorithm for the purpose of calibrating the probabilistic outputs of automatic pattern recognition and machine learning algorithms. Special cost functions, known as proper scoring rules form natural objective functions to judge the goodness of such calibration. We show that for binary pattern classifiers, the non-parametric optimization of calibration, subject to a monotonicity constraint, can be solved by PAV and that this solution is optimal for all regular binary proper scoring rules. This extends previous results which were limited to convex binary proper scoring rules. We further show that this result holds not only for calibration of probabilities, but also for calibration of log-likelihood-ratios, in which case optimality holds independently of the prior probabilities of the pattern classes.