Human-Machine Collaborative Optimization via Apprenticeship Scheduling

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the ``single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes, causing the codification of this knowledge to become laborious. We propose a new approach for capturing domain-expert heuristics through a pairwise ranking formulation. Our approach is model-free and does not require enumerating or iterating through a large state space. We empirically demonstrate that this approach accurately learns multifaceted heuristics on a synthetic data set incorporating job-shop scheduling and vehicle routing problems, as well as on two real-world data sets consisting of demonstrations of experts solving a weapon-to-target assignment problem and a hospital resource allocation problem. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of a branch-and-bound search for an optimal schedule. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates solutions substantially superior to those produced by human domain experts at a rate up to 9.5 times faster than an optimization approach and can be applied to optimally solve problems twice as complex as those solved by a human demonstrator.Comment: Portions of this paper were published in the Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper consists of 50 pages with 11 figures and 4 table

A Parametric Non-Convex Decomposition Algorithm for Real-Time and Distributed NMPC

A novel decomposition scheme to solve parametric non-convex programs as they arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of a fixed number of alternating proximal gradient steps and a dual update per time step. Hence, the proposed approach is attractive in a real-time distributed context. Assuming that the Nonlinear Program (NLP) is semi-algebraic and that its critical points are strongly regular, contraction of the sequence of primal-dual iterates is proven, implying stability of the sub-optimality error, under some mild assumptions. Moreover, it is shown that the performance of the optimality-tracking scheme can be enhanced via a continuation technique. The efficacy of the proposed decomposition method is demonstrated by solving a centralised NMPC problem to control a DC motor and a distributed NMPC program for collaborative tracking of unicycles, both within a real-time framework. Furthermore, an analysis of the sub-optimality error as a function of the sampling period is proposed given a fixed computational power.Comment: 16 pages, 9 figure