Learn to Tour: Operator Design For Solution Feasibility Mapping in Pickup-and-delivery Traveling Salesman Problem

This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes. One-to-one here means that the transported people or goods are associated with designated pairs of pickup and delivery nodes, in contrast to that indistinguishable goods can be delivered to any nodes. In PDTSP, precedence constraints need to be satisfied that each pickup node must be visited before its corresponding delivery node. Classic operations research (OR) algorithms for PDTSP are difficult to scale to large-sized problems. Recently, reinforcement learning (RL) has been applied to TSPs. The basic idea is to explore and evaluate visiting sequences in a solution space. However, this approach could be less computationally efficient, as it has to potentially evaluate many infeasible solutions of which precedence constraints are violated. To restrict solution search within a feasible space, we utilize operators that always map one feasible solution to another, without spending time exploring the infeasible solution space. Such operators are evaluated and selected as policies to solve PDTSPs in an RL framework. We make a comparison of our method and baselines, including classic OR algorithms and existing learning methods. Results show that our approach can find tours shorter than baselines.

Confucius: Iterative Tool Learning from Introspection Feedback by Easy-to-Difficult Curriculum

Augmenting large language models (LLMs) with external tools has emerged as a promising approach to extending the capability of LLMs. Although some works employ open-source LLMs for the tool learning task, most of them are trained in a controlled environment in which LLMs only learn to execute the human-provided tools. However, selecting proper tools from the large toolset is also a crucial ability for the tool learning model to be applied in real-world applications. Existing methods usually directly employ self-instruction methods to train the model, which ignores differences in tool complexity. In this paper, we propose the Confucius, a novel tool learning framework to train LLM to use complicated tools in real-world scenarios, which contains two main phases: (1) We first propose a multi-stage learning method to teach the LLM to use various tools from an easy-to-difficult curriculum; (2) thenceforth, we propose the Iterative Self-instruct from Introspective Feedback (ISIF) to dynamically construct the dataset to improve the ability to use the complicated tool. Extensive experiments conducted on both controlled and real-world settings demonstrate the superiority of our tool learning framework in the real-world application scenarios compared to both tuning-free (e.g. ChatGPT, Claude) and tuning-based baselines (e.g. GPT4Tools).

A Neural RDE-based model for solving path-dependent PDEs

The concept of the path-dependent partial differential equation (PPDE) was first introduced in the context of path-dependent derivatives in financial markets. Its semilinear form was later identified as a non-Markovian backward stochastic differential equation (BSDE). Compared to the classical PDE, the solution of a PPDE involves an infinite-dimensional spatial variable, making it challenging to approximate, if not impossible. In this paper, we propose a neural rough differential equation (NRDE)-based model to learn PPDEs, which effectively encodes the path information through the log-signature feature while capturing the fundamental dynamics. The proposed continuous-time model for the PPDE solution offers the benefits of efficient memory usage and the ability to scale with dimensionality. Several numerical experiments, provided to validate the performance of the proposed model in comparison to the strong baseline in the literature, are used to demonstrate its effectiveness.