Combinatorial optimization (CO) problems arise in a wide range of fields from medicine to logistics and manufacturing. While exact solutions are often not necessary, many applications require finding high-quality solutions quickly. For this purpose, we propose a data-driven approach to improve existing non-learned approximation algorithms for CO. We parameterize the approximation algorithm and train a graph neural network (GNN) to predict parameter values that lead to the best possible solutions. Our pipeline is trained end-to-end in a self-supervised fashion using gradient estimation, treating the approximation algorithm as a black box. We propose a novel gradient estimation scheme for this purpose, which we call preference-based gradient estimation. Our approach combines the benefits of the neural network and the non-learned approximation algorithm: The GNN leverages the information from the dataset to allow the approximation algorithm to find better solutions, while the approximation algorithm guarantees that the solution is feasible. We validate our approach on two well-known combinatorial optimization problems, the travelling salesman problem and the minimum k-cut problem, and show that our method is competitive with state of the art learned CO solvers.

We consider enhancing large language models (LLMs) for complex planning tasks. While existing methods allow LLMs to explore intermediate steps to make plans, they either depend on unreliable self-verification or external verifiers to evaluate these steps, which demand significant data and computations. Here, we propose automated heuristics discovery (AutoHD), a novel approach that enables LLMs to explicitly generate heuristic functions to guide inference-time search, allowing accurate evaluation of intermediate states. These heuristic functions are further refined through a heuristic evolution process, improving their robustness and effectiveness. Our proposed method requires no additional model training or fine-tuning, and the explicit definition of heuristic functions generated by the LLMs provides interpretability and insights into the reasoning process. Extensive experiments across diverse benchmarks demonstrate significant gains over multiple baselines, including nearly twice the accuracy on some datasets, establishing our approach as a reliable and interpretable solution for complex planning tasks.

Large language models (LLMs) often struggle with complex reasoning tasks due to their limitations in addressing the vast reasoning space and inherent ambiguities of natural language. We propose the Mixture-of-Search-Agents (MoSA) paradigm, a novel approach leveraging the collective expertise of multiple LLMs to enhance search-based reasoning. MoSA integrates diverse reasoning pathways by combining independent exploration with iterative refinement among LLMs, mitigating the limitations of single-model approaches. Using Monte Carlo Tree Search (MCTS) as a backbone, MoSA enables multiple agents to propose and aggregate reasoning steps, resulting in improved accuracy. Our comprehensive evaluation across four reasoning benchmarks demonstrates MoSA's consistent performance improvements over single-agent and other multi-agent baselines, particularly in complex mathematical and commonsense reasoning tasks.

The goal of causal discovery is to learn a directed acyclic graph from data. One of the most well-known methods for this problem is Greedy Equivalence Search (GES). GES searches for the graph by incrementally and greedily adding or removing edges to maximize a model selection criterion. It has strong theoretical guarantees on infinite data but can fail in practice on finite data. In this paper, we first identify some of the causes of GES's failure, finding that it can get blocked in local optima, especially in denser graphs. We then propose eXtremely Greedy Equivalent Search (XGES), which involves a new heuristic to improve the search strategy of GES while retaining its theoretical guarantees. In particular, XGES favors deleting edges early in the search over inserting edges, which reduces the possibility of the search ending in local optima. A further contribution of this work is an efficient algorithmic formulation of XGES (and GES). We benchmark XGES on simulated datasets with known ground truth. We find that XGES consistently outperforms GES in recovering the correct graphs, and it is 10 times faster. XGES implementations in Python and C++ are available at https://github.com/ANazaret/XGES.

Satisfiability Modulo Linear Integer Arithmetic, SMT(LIA) for short, is pivotal across various critical domains. Previous research has primarily focused on SMT solving techniques. However, in practical applications such as software and hardware testing, there is a need to generate a diverse set of solutions for use as test inputs. We have developed the first sampling framework that integrates local search with CDCL(T) techniques, named HighDiv, capable of generating a highly diverse set of solutions for constraints under linear integer theory. Initially, in the local search phase, we introduced a novel operator called boundary-aware movement. This operator performs random moves by considering the current state's constraints on variables, thereby enhancing the diversity of variables during the search process. Furthermore, we have conducted an in-depth study of the preprocessing and variable initialization mechanisms within the framework, which significantly enhances the efficiency of subsequent local searches. Lastly, we use the solutions obtained from local search sampling as additional constraints to further explore the solution space using the stochastic CDCL(T) method. Experimental results demonstrate that \HighDiv generates solutions with greater diversity compared to the state-of-the-art SMT(LIA) sampling tool, MeGASampler.

Recent advances in Large Language Models have led to remarkable achievements across a variety of Natural Language Processing tasks, making prompt engineering increasingly central to guiding model outputs. While manual methods can be effective, they typically rely on intuition and do not automatically refine prompts over time. In contrast, automatic prompt optimization employing heuristic-based search algorithms can systematically explore and improve prompts with minimal human oversight. This survey proposes a comprehensive taxonomy of these methods, categorizing them by where optimization occurs, what is optimized, what criteria drive the optimization, which operators generate new prompts, and which iterative search algorithms are applied. We further highlight specialized datasets and tools that support and accelerate automated prompt refinement. We conclude by discussing key open challenges pointing toward future opportunities for more robust and versatile LLM applications.

This paper is the second in a series of studies on developing efficient artificial intelligence-based approaches to pathfinding on extremely large graphs (e.g. $10^{70}$ nodes) with a focus on Cayley graphs and mathematical applications. The open-source CayleyPy project is a central component of our research. The present paper proposes a novel combination of a reinforcement learning approach with a more direct diffusion distance approach from the first paper. Our analysis includes benchmarking various choices for the key building blocks of the approach: architectures of the neural network, generators for the random walks and beam search pathfinding. We compared these methods against the classical computer algebra system GAP, demonstrating that they "overcome the GAP" for the considered examples. As a particular mathematical application we examine the Cayley graph of the symmetric group with cyclic shift and transposition generators. We provide strong support for the OEIS-A186783 conjecture that the diameter is equal to n(n-1)/2 by machine learning and mathematical methods. We identify the conjectured longest element and generate its decomposition of the desired length. We prove a diameter lower bound of n(n-1)/2-n/2 and an upper bound of n(n-1)/2+ 3n by presenting the algorithm with given complexity. We also present several conjectures motivated by numerical experiments, including observations on the central limit phenomenon (with growth approximated by a Gumbel distribution), the uniform distribution for the spectrum of the graph, and a numerical study of sorting networks. To stimulate crowdsourcing activity, we create challenges on the Kaggle platform and invite contributions to improve and benchmark approaches on Cayley graph pathfinding and other tasks.

Existing LLM-based agents have achieved strong performance on held-in tasks, but their generalizability to unseen tasks remains poor. Hence, some recent work focus on fine-tuning the policy model with more diverse tasks to improve the generalizability. In this work, we find that finetuning a reward model to guide the policy model is more robust than directly finetuning the policy model. Based on this finding, we propose AgentRM, a generalizable reward model, to guide the policy model for effective test-time search. We comprehensively investigate three approaches to construct the reward model, including explicit reward modeling, implicit reward modeling and LLM-as-a-judge. We then use AgentRM to guide the answer generation with Best-of-N sampling and step-level beam search. On four types of nine agent tasks, AgentRM enhances the base policy model by $8.8$ points on average, surpassing the top general agent by $4.0$. Moreover, it demonstrates weak-to-strong generalization, yielding greater improvement of $12.6$ on LLaMA-3-70B policy model. As for the specializability, AgentRM can also boost a finetuned policy model and outperform the top specialized agent by $11.4$ on three held-in tasks. Further analysis verifies its effectiveness in test-time scaling. Codes will be released to facilitate the research in this area.

Multi-preference optimization enriches language-model alignment beyond pairwise preferences by contrasting entire sets of helpful and undesired responses, thereby enabling richer training signals for large language models. During self-play alignment, these models often produce numerous candidate answers per query, rendering it computationally infeasible to include all responses in the training objective. In this work, we propose $\textit{Active Multi-Preference Optimization}$ (AMPO), a novel approach that combines on-policy generation, a multi-preference group-contrastive loss, and active subset selection. Specifically, we score and embed large candidate pools of responses and then select a small, yet informative, subset that covers reward extremes and distinct semantic clusters for preference optimization. Our contrastive training scheme is capable of identifying not only the best and worst answers but also subtle, underexplored modes that are crucial for robust alignment. Theoretically, we provide guarantees for expected reward maximization using our active selection method, and empirically, AMPO achieves state-of-the-art results on $\textit{AlpacaEval}$ using Llama 8B.

The label ranking problem is a supervised learning scenario in which the learner predicts a total order of the class labels for a given input instance. Recently, research has increasingly focused on the partial label ranking problem, a generalization of the label ranking problem that allows ties in the predicted orders. So far, most existing learning approaches for the partial label ranking problem rely on approximation algorithms for rank aggregation in the final prediction step. This paper explores several alternative aggregation methods for this critical step, including scoring-based and probabilistic-based rank aggregation approaches. To enhance their suitability for the more general partial label ranking problem, the investigated methods are extended to increase the likelihood of producing ties. Experimental evaluations on standard benchmarks demonstrate that scoring-based variants consistently outperform the current state-of-the-art method in handling incomplete information. In contrast, probabilistic-based variants fail to achieve competitive performance.