Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: Adaptive Staircase Policy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP.

Vehicle routing is a well-known optimization research topic with significant practical importance. Among different approaches to solving vehicle routing, heuristics can produce a satisfactory solution at a reasonable computational cost. Consequently, much effort has been made in the past decades to develop vehicle routing heuristics. In this article, we systematically survey the existing vehicle routing heuristics, particularly on works carried out in recent years. A classification of vehicle routing heuristics is presented, followed by a review of their methodologies, recent developments, and applications. Moreover, we present a general framework of state-of-the-art methods and provide insights into their success. Finally, three emerging research topics with notable works and future directions are discussed.

Offline reinforcement learning (RL) aims at learning an optimal strategy using a pre-collected dataset without further interactions with the environment. While various algorithms have been proposed for offline RL in the previous literature, the minimax optimality has only been (nearly) established for tabular Markov decision processes (MDPs). In this paper, we focus on offline RL with linear function approximation and propose a new pessimism-based algorithm for offline linear MDP. At the core of our algorithm is the uncertainty decomposition via a reference function, which is new in the literature of offline RL under linear function approximation. Theoretical analysis demonstrates that our algorithm can match the performance lower bound up to logarithmic factors. We also extend our techniques to the two-player zero-sum Markov games (MGs), and establish a new performance lower bound for MGs, which tightens the existing result, and verifies the nearly minimax optimality of the proposed algorithm. To the best of our knowledge, these are the first computationally efficient and nearly minimax optimal algorithms for offline single-agent MDPs and MGs with linear function approximation.

Beam search is the default decoding strategy for many sequence generation tasks in NLP. The set of approximate K-best items returned by the algorithm is a useful summary of the distribution for many applications; however, the candidates typically exhibit high overlap and may give a highly biased estimate for expectations under our model. These problems can be addressed by instead using stochastic decoding strategies. In this work, we propose a new method for turning beam search into a stochastic process: Conditional Poisson stochastic beam search. Rather than taking the maximizing set at each iteration, we sample K candidates without replacement according to the conditional Poisson sampling design. We view this as a more natural alternative to Kool et. al. 2019's stochastic beam search (SBS). Furthermore, we show how samples generated under the CPSBS design can be used to build consistent estimators and sample diverse sets from sequence models. In our experiments, we observe CPSBS produces lower variance and more efficient estimators than SBS, even showing improvements in high entropy settings.

Feature preprocessing, which transforms raw input features into numerical representations, is a crucial step in automated machine learning (AutoML) systems. However, the existing systems often have a very small search space for feature preprocessing with the same preprocessing pipeline applied to all the numerical features. This may result in sub-optimal performance since different datasets often have various feature characteristics, and features within a dataset may also have their own preprocessing preferences. To bridge this gap, we explore personalized preprocessing pipeline search, where the search algorithm is allowed to adopt a different preprocessing pipeline for each feature. This is a challenging task because the search space grows exponentially with more features. To tackle this challenge, we propose ClusterP3S, a novel framework for Personalized Preprocessing Pipeline Search via Clustering. The key idea is to learn feature clusters such that the search space can be significantly reduced by using the same preprocessing pipeline for the features within a cluster. To this end, we propose a hierarchical search strategy to jointly learn the clusters and search for the optimal pipelines, where the upper-level search optimizes the feature clustering to enable better pipelines built upon the clusters, and the lower-level search optimizes the pipeline given a specific cluster assignment. We instantiate this idea with a deep clustering network that is trained with reinforcement learning at the upper level, and random search at the lower level. Experiments on benchmark classification datasets demonstrate the effectiveness of enabling feature-wise preprocessing pipeline search.

Based on the weight-sharing mechanism, one-shot NAS methods train a supernet and then inherit the pre-trained weights to evaluate sub-models, largely reducing the search cost. However, several works have pointed out that the shared weights suffer from different gradient descent directions during training. And we further find that large gradient variance occurs during supernet training, which degrades the supernet ranking consistency. To mitigate this issue, we propose to explicitly minimize the gradient variance of the supernet training by jointly optimizing the sampling distributions of PAth and DAta (PA&DA). We theoretically derive the relationship between the gradient variance and the sampling distributions, and reveal that the optimal sampling probability is proportional to the normalized gradient norm of path and training data. Hence, we use the normalized gradient norm as the importance indicator for path and training data, and adopt an importance sampling strategy for the supernet training. Our method only requires negligible computation cost for optimizing the sampling distributions of path and data, but achieves lower gradient variance during supernet training and better generalization performance for the supernet, resulting in a more consistent NAS. We conduct comprehensive comparisons with other improved approaches in various search spaces. Results show that our method surpasses others with more reliable ranking performance and higher accuracy of searched architectures, showing the effectiveness of our method. Code is available at https://github.com/ShunLu91/PA-DA.

ALNS is a popular metaheuristic with renowned efficiency in solving combinatorial optimisation problems. However, despite 16 years of intensive research into ALNS, whether the embedded adaptive layer can efficiently select operators to improve the incumbent remains an open question. In this work, we formulate the choice of operators as a Markov Decision Process, and propose a practical approach based on Deep Reinforcement Learning and Graph Neural Networks. The results show that our proposed method achieves better performance than the classic ALNS adaptive layer due to the choice of operator being conditioned on the current solution. We also discuss important considerations such as the size of the operator portfolio and the impact of the choice of operator scales. Notably, our approach can also save significant time and labour costs for handcrafting problem-specific operator portfolios.

The sheer size of modern neural networks makes model serving a serious computational challenge. A popular class of compression techniques overcomes this challenge by pruning or sparsifying the weights of pretrained networks. While useful, these techniques often face serious tradeoffs between computational requirements and compression quality. In this work, we propose a novel optimization-based pruning framework that considers the combined effect of pruning (and updating) multiple weights subject to a sparsity constraint. Our approach, CHITA, extends the classical Optimal Brain Surgeon framework and results in significant improvements in speed, memory, and performance over existing optimization-based approaches for network pruning. CHITA's main workhorse performs combinatorial optimization updates on a memory-friendly representation of local quadratic approximation(s) of the loss function. On a standard benchmark of pretrained models and datasets, CHITA leads to significantly better sparsity-accuracy tradeoffs than competing methods. For example, for MLPNet with only 2% of the weights retained, our approach improves the accuracy by 63% relative to the state of the art. Furthermore, when used in conjunction with fine-tuning SGD steps, our method achieves significant accuracy gains over the state-of-the-art approaches.

The design of algorithms or protocols that are able to align the goals of the planner with the selfish interests of the agents involved in these protocols is of paramount importance in almost every decentralized setting (such as, computer networks, markets, etc.) as shown by the rich literature in Mechanism Design. Recently, huge interest has been devoted to the design of mechanisms for imperfectly rational agents, i.e., mechanisms for which agents are able to easily grasp that there is no action different from following the protocol that would satisfy their interests better. This work has culminated in the definition of Obviously Strategyproof (OSP) Mechanisms, that have been shown to capture the incentives of agents without contingent reasoning skills. Without an understanding of the algorithmic nature of OSP mechanisms, it is hard to assess how well these mechanisms can satisfy the goals of the planner. For the case of binary allocation problems and agents whose private type is a single number, recent work has shown that a generalization of greedy completely characterizes OSP. In this work, we strengthen the connection between greedy and OSP by providing a characterization of OSP mechanisms for all optimization problems involving these single-parameter agents. Specifically, we prove that OSP mechanisms must essentially work as follows: they either greedily look for agents with ``better'' types and allocate them larger outcomes; or reverse greedily look for agents with ``worse'' types and allocate them smaller outcomes; or, finally, split the domain of agents in ``good'' and ``bad'' types, and subsequently proceed in a reverse greedy fashion for the former and greedily for the latter. We further demonstrate how to use this characterization to give bounds on the approximation guarantee of OSP mechanisms for the well known scheduling related machines problem.

Dispatching vehicle fleets to serve flights is a key task in airport ground handling (AGH). Due to the notable growth of flights, it is challenging to simultaneously schedule multiple types of operations (services) for a large number of flights, where each type of operation is performed by one specific vehicle fleet. To tackle this issue, we first represent the operation scheduling as a complex vehicle routing problem and formulate it as a mixed integer linear programming (MILP) model. Then given the graph representation of the MILP model, we propose a learning assisted large neighborhood search (LNS) method using data generated based on real scenarios, where we integrate imitation learning and graph convolutional network (GCN) to learn a destroy operator to automatically select variables, and employ an off-the-shelf solver as the repair operator to reoptimize the selected variables. Experimental results based on a real airport show that the proposed method allows for handling up to 200 flights with 10 types of operations simultaneously, and outperforms state-of-the-art methods. Moreover, the learned method performs consistently accompanying different solvers, and generalizes well on larger instances, verifying the versatility and scalability of our method.