We present online learning of Hierarchical Task Network (HTN) methods in the context of integrated HTN planning and LLM-based chatbots. Methods indicate when and how to decompose tasks into subtasks. Our method learner is built on top of the ChatHTN planner. ChatHTN queries ChatGPT to generate a decomposition of a task into primitive tasks when no applicable method for the task is available. In this work, we extend ChatHTN. Namely, when ChatGPT generates a task decomposition, ChatHTN learns from it, akin to memoization. However, unlike memoization, it learns a generalized method that applies not only to the specific instance encountered, but to other instances of the same task.. We conduct experiments on two domains and demonstrate that our online learning procedure reduces the number of calls to ChatGPT while solving at least as many problems, and in some cases, even more.

Bayesian Optimization (BO) is a powerful method for tackling expensive black-box optimization problems.

A novel distributed algorithm is proposed for finite-time converging to a feasible consensus solution satisfying global optimality to a certain accuracy of the distributed robust convex optimization problem (DRCO) subject to bounded uncertainty under a uniformly strongly connected network. Firstly, a distributed lower bounding procedure is developed, which is based on an outer iterative approximation of the DRCO through the discretization of the compact uncertainty set into a finite number of points. Secondly, a distributed upper bounding procedure is proposed, which is based on iteratively approximating the DRCO by restricting the constraints right-hand side with a proper positive parameter and enforcing the compact uncertainty set at finitely many points. The lower and upper bounds of the global optimal objective for the DRCO are obtained from these two procedures. Thirdly, two distributed termination methods are proposed to make all agents stop updating simultaneously by exploring whether the gap between the upper and the lower bounds reaches a certain accuracy. Fourthly, it is proved that all the agents finite-time converge to a feasible consensus solution that satisfies global optimality within a certain accuracy. Finally, a numerical case study is included to illustrate the effectiveness of the distributed algorithm.