A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the problem. However, the accuracy of the estimated performance metrics depends on the number of runs and should be studied using statistical tools. We present a statistical analysis of the common metrics, and develop guidelines for experiment design to measure the optimizer's performance using these metrics to a high level of confidence and accuracy. To this end, we first discuss the confidence interval of the metrics and how they are related to the number of runs of an experiment. We then derive a lower bound on the number of repeats in order to guarantee achieving a given accuracy in the metrics. Using this bound, we propose an algorithm to adaptively adjust the number of repeats needed to ensure the accuracy of the evaluated metric. Our simulation results demonstrate the utility of our analysis and how it allows us to conduct reliable benchmarking as well as hyperparameter tuning and prevent us from drawing premature conclusions regarding the performance of stochastic optimizers.

Vehicle Routing Problems (VRPs) are a class of NP-hard problems ubiquitous in several real-world logistics scenarios that pose significant challenges for optimization. Neural Combinatorial Optimization (NCO) has emerged as a promising alternative to classical approaches, as it can learn fast heuristics to solve VRPs. However, most research works in NCO for VRPs focus on simplified settings, which do not account for asymmetric distances and travel durations that cannot be derived by simple Euclidean distances and unrealistic data distributions, hindering real-world deployment. This work introduces RRNCO (Real Routing NCO) to bridge the gap of NCO between synthetic and real-world VRPs in the critical aspects of both data and modeling. First, we introduce a new, openly available dataset with real-world data containing a diverse dataset of locations, distances, and duration matrices from 100 cities, considering realistic settings with actual routing distances and durations obtained from Open Source Routing Machine (OSRM). Second, we propose a novel approach that efficiently processes both node and edge features through contextual gating, enabling the construction of more informed node embedding, and we finally incorporate an Adaptation Attention Free Module (AAFM) with neural adaptive bias mechanisms that effectively integrates not only distance matrices but also angular relationships between nodes, allowing our model to capture rich structural information. RRNCO achieves state-of-the-art results in real-world VRPs among NCO methods. We make our dataset and code publicly available at https://github.com/ai4co/real-routing-nco.

Various studies on perception-aware planning have been proposed to enhance the state estimation accuracy of quadrotors in visually degraded environments. However, many existing methods heavily rely on prior environmental knowledge and face significant limitations in previously unknown environments with sparse localization features, which greatly limits their practical application. In this paper, we present a perception-aware planning method for quadrotor flight in unknown and feature-limited environments that properly allocates perception resources among environmental information during navigation. We introduce a viewpoint transition graph that allows for the adaptive selection of local target viewpoints, which guide the quadrotor to efficiently navigate to the goal while maintaining sufficient localizability and without being trapped in feature-limited regions. During the local planning, a novel yaw trajectory generation method that simultaneously considers exploration capability and localizability is presented. It constructs a localizable corridor via feature co-visibility evaluation to ensure localization robustness in a computationally efficient way. Through validations conducted in both simulation and real-world experiments, we demonstrate the feasibility and real-time performance of the proposed method. The source code will be released to benefit the community.

We present a novel preference learning framework to capture participant preferences efficiently within limited interaction rounds. It involves three main contributions. First, we develop a variational Bayesian approach to infer the participant's preference model by estimating posterior distributions and managing uncertainty from limited information. Second, we propose an adaptive questioning policy that maximizes cumulative uncertainty reduction, formulating questioning as a finite Markov decision process and using Monte Carlo Tree Search to prioritize promising question trajectories. By considering long-term effects and leveraging the efficiency of the Bayesian approach, the policy avoids shortsightedness. Third, we apply the framework to Multiple Criteria Decision Aiding, with pairwise comparison as the preference information and an additive value function as the preference model. We integrate the reparameterization trick to address high-variance issues, enhancing robustness and efficiency. Computational studies on real-world and synthetic datasets demonstrate the framework's practical usability, outperforming baselines in capturing preferences and achieving superior uncertainty reduction within limited interactions.

We study a search problem on capturing a moving target on an infinite real line. Two autonomous mobile robots (which can move with a maximum speed of 1) are initially placed at the origin, while an oblivious moving target is initially placed at a distance $d$ away from the origin. The robots can move along the line in any direction, but the target is oblivious, cannot change direction, and moves either away from or toward the origin at a constant speed $v$. Our aim is to design efficient algorithms for the two robots to capture the target. The target is captured only when both robots are co-located with it. The robots communicate with each other only face-to-face (F2F), meaning they can exchange information only when co-located, while the target remains oblivious and has no communication capabilities. We design algorithms under various knowledge scenarios, which take into account the prior knowledge the robots have about the starting distance $d$, the direction of movement (either toward or away from the origin), and the speed $v$ of the target. As a measure of the efficiency of the algorithms, we use the competitive ratio, which is the ratio of the capture time of an algorithm with limited knowledge to the capture time in the full-knowledge model. In our analysis, we are mindful of the cost of changing direction of movement, and show how to accomplish the capture of the target with at most three direction changes (turns).

Decision trees are a crucial class of models offering robust predictive performance and inherent interpretability across various domains, including healthcare, finance, and logistics. However, current tree induction methods often face limitations such as suboptimal solutions from greedy methods or prohibitive computational costs and limited applicability of exact optimization approaches. To address these challenges, we propose an evolutionary optimization method for decision tree induction based on genetic programming (GP). Our key innovation is the integration of semantic priors and domain-specific knowledge about the search space into the optimization algorithm. To this end, we introduce $\texttt{LLEGO}$, a framework that incorporates semantic priors into genetic search operators through the use of Large Language Models (LLMs), thereby enhancing search efficiency and targeting regions of the search space that yield decision trees with superior generalization performance. This is operationalized through novel genetic operators that work with structured natural language prompts, effectively utilizing LLMs as conditional generative models and sources of semantic knowledge. Specifically, we introduce $\textit{fitness-guided}$ crossover to exploit high-performing regions, and $\textit{diversity-guided}$ mutation for efficient global exploration of the search space. These operators are controlled by corresponding hyperparameters that enable a more nuanced balance between exploration and exploitation across the search space. Empirically, we demonstrate across various benchmarks that $\texttt{LLEGO}$ evolves superior-performing trees compared to existing tree induction methods, and exhibits significantly more efficient search performance compared to conventional GP approaches.

Retrieval-Augmented Generation (RAG) has gained significant attention in recent years for its potential to enhance natural language understanding and generation by combining large-scale retrieval systems with generative models. RAG leverages external knowledge sources, such as documents, databases, or structured data, to improve model performance and generate more accurate and contextually relevant outputs. This survey aims to provide a comprehensive overview of RAG by examining its fundamental components, including retrieval mechanisms, generation processes, and the integration between the two. We discuss the key characteristics of RAG, such as its ability to augment generative models with dynamic external knowledge, and the challenges associated with aligning retrieved information with generative objectives. We also present a taxonomy that categorizes RAG methods, ranging from basic retrieval-augmented approaches to more advanced models incorporating multi-modal data and reasoning capabilities. Additionally, we review the evaluation benchmarks and datasets commonly used to assess RAG systems, along with a detailed exploration of its applications in fields such as question answering, summarization, and information retrieval. Finally, we highlight emerging research directions and opportunities for improving RAG systems, such as enhanced retrieval efficiency, model interpretability, and domain-specific adaptations. This paper concludes by outlining the prospects for RAG in addressing real-world challenges and its potential to drive further advancements in natural language processing.

Understanding long video content is a complex endeavor that often relies on densely sampled frame captions or end-to-end feature selectors, yet these techniques commonly overlook the logical relationships between textual queries and visual elements. In practice, computational constraints necessitate coarse frame subsampling, a challenge analogous to ``finding a needle in a haystack.'' To address this issue, we introduce a semantics-driven search framework that reformulates keyframe selection under the paradigm of Visual Semantic-Logical Search. Specifically, we systematically define four fundamental logical dependencies: 1) spatial co-occurrence, 2) temporal proximity, 3) attribute dependency, and 4) causal order. These relations dynamically update frame sampling distributions through an iterative refinement process, enabling context-aware identification of semantically critical frames tailored to specific query requirements. Our method establishes new SOTA performance on the manually annotated benchmark in key-frame selection metrics. Furthermore, when applied to downstream video question-answering tasks, the proposed approach demonstrates the best performance gains over existing methods on LongVideoBench and Video-MME, validating its effectiveness in bridging the logical gap between textual queries and visual-temporal reasoning. The code will be publicly available.

This paper introduces TuneNSearch, a hybrid transfer learning and local search approach for addressing different variants of vehicle routing problems (VRP). Recently, multi-task learning has gained much attention for solving VRP variants. However, this adaptability often compromises the performance of the models. To address this challenge, we first pre-train a reinforcement learning model on the multi-depot VRP, followed by a short fine-tuning phase to adapt it to different variants. By leveraging the complexity of the multi-depot VRP, the pre-trained model learns richer node representations and gains more transferable knowledge compared to models trained on simpler routing problems, such as the traveling salesman problem. TuneNSearch employs, in the first stage, a Transformer-based architecture, augmented with a residual edge-graph attention network to capture the impact of edge distances and residual connections between layers. This architecture allows for a more precise capture of graph-structured data, improving the encoding of VRP's features. After inference, our model is also coupled with a second stage composed of a local search algorithm, which yields substantial performance gains with minimal computational overhead added. Results show that TuneNSearch outperforms many existing state-of-the-art models trained for each VRP variant, requiring only one-fifth of the training epochs. Our approach demonstrates strong generalization, achieving high performance across different tasks, distributions and problem sizes, thus addressing a long-standing gap in the literature.

We introduce Siege, a multi-turn adversarial framework that models the gradual erosion of Large Language Model (LLM) safety through a tree search perspective. Unlike single-turn jailbreaks that rely on one meticulously engineered prompt, Siege expands the conversation at each turn in a breadth-first fashion, branching out multiple adversarial prompts that exploit partial compliance from previous responses. By tracking these incremental policy leaks and re-injecting them into subsequent queries, Siege reveals how minor concessions can accumulate into fully disallowed outputs. Evaluations on the JailbreakBench dataset show that Siege achieves a 100% success rate on GPT-3.5-turbo and 97% on GPT-4 in a single multi-turn run, using fewer queries than baselines such as Crescendo or GOAT. This tree search methodology offers an in-depth view of how model safeguards degrade over successive dialogue turns, underscoring the urgency of robust multi-turn testing procedures for language models.