The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better scalability of neural combinatorial optimization. Specifically, we develop an efficient self-improved mechanism that enables direct model training on large-scale problem instances without any labeled data. Powered by an innovative local reconstruction approach, this method can iteratively generate better solutions by itself as pseudo-labels to guide efficient model training. In addition, we design a linear complexity attention mechanism for the model to efficiently handle large-scale combinatorial problem instances with low computation overhead. Comprehensive experiments on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes in both uniform and real-world distributions demonstrate the superior scalability of our method.

We propose a novel algorithm that extends the methods of ball smoothing and Gaussian smoothing for noisy derivative-free optimization by accounting for the heterogeneous curvature of the objective function. The algorithm dynamically adapts the shape of the smoothing kernel to approximate the Hessian of the objective function around a local optimum. This approach significantly reduces the error in estimating the gradient from noisy evaluations through sampling. We demonstrate the efficacy of our method through numerical experiments on artificial problems. Additionally, we show improved performance when tuning NP-hard combinatorial optimization solvers compared to existing state-of-the-art heuristic derivative-free and Bayesian optimization methods.

One key decision for heuristic search algorithms is how to balance exploration and exploitation. In classical planning, novelty search has come out as the most successful approach in this respect. The idea is to favor states that contain previously unseen facts when searching for a plan. This is done by maintaining a record of the tuples of facts observed in previous states. Then the novelty of a state is the size of the smallest previously unseen tuple. The most successful version of novelty search is best-first width search (BFWS), which combines novelty measures with heuristic estimates. An orthogonal approach to balance exploration-exploitation is to use several open-lists. These open-lists are ordered using different heuristic estimates, which diversify the information used in the search. The search algorithm then alternates between these open-lists, trying to exploit these different estimates. This is the approach used by LAMA, a classical planner that, a decade after its release, is still considered state-of-the-art in agile planning. In this paper, we study how to combine LAMA and BFWS. We show that simply adding the strongest open-list used in BFWS to LAMA harms performance. However, we show that combining only parts of each planner leads to a new state-of-the-art agile planner.

Feature selection aims to identify the optimal feature subset for enhancing downstream models. Effective feature selection can remove redundant features, save computational resources, accelerate the model learning process, and improve the model overall performance. However, existing works are often time-intensive to identify the effective feature subset within high-dimensional feature spaces. Meanwhile, these methods mainly utilize a single downstream task performance as the selection criterion, leading to the selected subsets that are not only redundant but also lack generalizability. To bridge these gaps, we reformulate feature selection through a neuro-symbolic lens and introduce a novel generative framework aimed at identifying short and effective feature subsets. More specifically, we found that feature ID tokens of the selected subset can be formulated as symbols to reflect the intricate correlations among features. Thus, in this framework, we first create a data collector to automatically collect numerous feature selection samples consisting of feature ID tokens, model performance, and the measurement of feature subset redundancy. Building on the collected data, an encoder-decoder-evaluator learning paradigm is developed to preserve the intelligence of feature selection into a continuous embedding space for efficient search. Within the learned embedding space, we leverage a multi-gradient search algorithm to find more robust and generalized embeddings with the objective of improving model performance and reducing feature subset redundancy. These embeddings are then utilized to reconstruct the feature ID tokens for executing the final feature selection. Ultimately, comprehensive experiments and case studies are conducted to validate the effectiveness of the proposed framework.

Building on the progress in Boolean satisfiability (SAT) solving over the last decades, maximum satisfiability (MaxSAT) has become a viable approach for solving NP-hard optimization problems, but ensuring correctness of MaxSAT solvers has remained an important concern. For SAT, this is largely a solved problem thanks to the use of proof logging, meaning that solvers emit machine-verifiable proofs of (un)satisfiability to certify correctness. However, for MaxSAT, proof logging solvers have started being developed only very recently. Moreover, these nascent efforts have only targeted the core solving process, ignoring the preprocessing phase where input problem instances can be substantially reformulated before being passed on to the solver proper. In this work, we demonstrate how pseudo-Boolean proof logging can be used to certify the correctness of a wide range of modern MaxSAT preprocessing techniques. By combining and extending the VeriPB and CakePB tools, we provide formally verified, end-to-end proof checking that the input and preprocessed output MaxSAT problem instances have the same optimal value. An extensive evaluation on applied MaxSAT benchmarks shows that our approach is feasible in practice.

While Transformers have enabled tremendous progress in various application settings, such architectures still trail behind traditional symbolic planners for solving complex decision making tasks. In this work, we demonstrate how to train Transformers to solve complex planning tasks. This is accomplished by training an encoder-decoder Transformer model to predict the search dynamics of the $A^*$ search algorithm. We fine tune this model to obtain a Searchformer, a Transformer model that optimally solves previously unseen Sokoban puzzles 93.7% of the time, while using up to 26.8% fewer search steps than the $A^*$ implementation that was used for training initially. In our training method, $A^*$'s search dynamics are expressed as a token sequence outlining when task states are added and removed into the search tree during symbolic planning. Searchformer significantly outperforms baselines that predict the optimal plan directly with a 5-10$\times$ smaller model size and a 10$\times$ smaller training dataset. Lastly, we demonstrate how Searchformer scales to larger and more complex decision making tasks with improved percentage of solved tasks and shortened search dynamics.

The goal of the game is to decrease While Poker, as a family of games, has been studied extensively in the opponent's health to zero. There are many popular collectible the last decades, collectible card games have seen relatively little card games, such as Magic: The Gathering [24], Hearthstone [3], attention. Only recently have we seen an agent that can compete The Elder Scrolls: Legends [20] and many others. A trait that makes with professional human players in Hearthstone, one of the most collectible card games appealing to human players and challenging popular collectible card games. Although artificial agents must be for AI agents is the broad range of ways to mix and match available able to work with imperfect information in both of these genres, cards into decks. Even small collectible card games with tens of collectible card games pose another set of distinct challenges. Unlike available cards can offer more potential decks than the total number in many poker variants, agents must deal with state space so vast of atoms in the universe [17].

Neural architecture search (NAS) is a challenging problem. Hierarchical search spaces allow for cheap evaluations of neural network sub modules to serve as surrogate for architecture evaluations. Yet, sometimes the hierarchy is too restrictive or the surrogate fails to generalize. We present FaDE which uses differentiable architecture search to obtain relative performance predictions on finite regions of a hierarchical NAS space. The relative nature of these ranks calls for a memory-less, batch-wise outer search algorithm for which we use an evolutionary algorithm with pseudo-gradient descent. FaDE is especially suited on deep hierarchical, respectively multi-cell search spaces, which it can explore by linear instead of exponential cost and therefore eliminates the need for a proxy search space. Our experiments show that firstly, FaDE-ranks on finite regions of the search space correlate with corresponding architecture performances and secondly, the ranks can empower a pseudo-gradient evolutionary search on the complete neural architecture search space.

In this paper, we propose a quantum computing oriented benchmark for combinatorial optimization. This benchmark, coined as QOPTLib, is composed of 40 instances equally distributed over four well-known problems: Traveling Salesman Problem, Vehicle Routing Problem, one-dimensional Bin Packing Problem and the Maximum Cut Problem. The sizes of the instances in QOPTLib not only correspond to computationally addressable sizes, but also to the maximum length approachable with non-zero likelihood of getting a good result. In this regard, it is important to highlight that hybrid approaches are also taken into consideration. Thus, this benchmark constitutes the first effort to provide users a general-purpose dataset. Also in this paper, we introduce a first full solving of QOPTLib using two solvers based on quantum annealing. Our main intention with this is to establish a preliminary baseline, hoping to inspire other researchers to beat these outcomes with newly proposed quantum-based algorithms.

The shift from Cloud Computing to a Cloud-Edge continuum presents new opportunities and challenges for data-intensive and interactive applications. Edge computing has garnered a lot of attention from both industry and academia in recent years, emerging as a key enabler for meeting the increasingly strict demands of Next Generation applications. In Edge computing the computations are placed closer to the end-users, to facilitate low-latency and high-bandwidth applications and services. However, the distributed, dynamic, and heterogeneous nature of Edge computing, presents a significant challenge for service placement. A critical aspect of Edge computing involves managing the placement of applications within the network system to minimize each application's runtime, considering the resources available on system devices and the capabilities of the system's network. The placement of application images must be proactively planned to minimize image tranfer time, and meet the strict demands of the applications. In this regard, this paper proposes an approach for proactive image placement that combines Graph Neural Networks and actor-critic Reinforcement Learning, which is evaluated empirically and compared against various solutions. The findings indicate that although the proposed approach may result in longer execution times in certain scenarios, it consistently achieves superior outcomes in terms of application placement.