When greedy search algorithms encounter a local minima or plateau, the search typically devolves into a breadth-first search (BrFS), or a local search technique is used in an attempt to find a way out. In this work, we formally analyze the performance of BrFS and constant-depth restarting random walks (RRW) -- two methods often used for finding exits to a plateau/local minima -- to better understand when each is best suited. In particular, we formally derive the expected runtime for BrFS in the case of a uniformly distributed set of goals at a given goal depth. We then prove RRW will be faster than BrFS on trees if there are enough goals at that goal depth. We refer to this threshold as the crossover point. Our bound shows that the crossover point grows linearly with the branching factor of the tree, the goal depth, and the error in the random walk depth, while the size of the tree grows exponentially in branching factor and goal depth. Finally, we discuss the practical implications and applicability of this bound.

Cyber-physical systems (CPS) with reinforcement learning (RL)-based controllers are increasingly being deployed in complex physical environments such as autonomous vehicles, the Internet-of-Things(IoT), and smart cities. An important property of a CPS is tolerance; i.e., its ability to function safely under possible disturbances and uncertainties in the actual operation. In this paper, we introduce a new, expressive notion of tolerance that describes how well a controller is capable of satisfying a desired system requirement, specified using Signal Temporal Logic (STL), under possible deviations in the system. Based on this definition, we propose a novel analysis problem, called the tolerance falsification problem, which involves finding small deviations that result in a violation of the given requirement. We present a novel, two-layer simulation-based analysis framework and a novel search heuristic for finding small tolerance violations. To evaluate our approach, we construct a set of benchmark problems where system parameters can be configured to represent different types of uncertainties and disturbancesin the system. Our evaluation shows that our falsification approach and heuristic can effectively find small tolerance violations.

Combinatorial Optimization is crucial to numerous real-world applications, yet still presents challenges due to its (NP-)hard nature. Amongst existing approaches, heuristics often offer the best trade-off between quality and scalability, making them suitable for industrial use. While Reinforcement Learning (RL) offers a flexible framework for designing heuristics, its adoption over handcrafted heuristics remains incomplete within industrial solvers. Existing learned methods still lack the ability to adapt to specific instances and fully leverage the available computational budget. The current best methods either rely on a collection of pre-trained policies, or on data-inefficient fine-tuning; hence failing to fully utilize newly available information within the constraints of the budget. In response, we present MEMENTO, an RL approach that leverages memory to improve the adaptation of neural solvers at inference time. MEMENTO enables updating the action distribution dynamically based on the outcome of previous decisions. We validate its effectiveness on benchmark problems, in particular Traveling Salesman and Capacitated Vehicle Routing, demonstrating it can successfully be combined with standard methods to boost their performance under a given budget, both in and out-of-distribution, improving their performance on all 12 evaluated tasks.

The challenge of efficient target searching in vast natural environments has driven the need for advanced multi-UAV active search strategies. This paper introduces a novel method in which global and local information is adeptly merged to avoid issues such as myopia and redundant back-and-forth movements. In addition, a trajectory generation method is used to ensure the search pattern within continuous space. To further optimize multi-agent cooperation, the Voronoi partition technique is employed, ensuring a reduction in repetitive flight patterns and making the control of multiple agents in a decentralized way. Through a series of experiments, the evaluation and comparison results demonstrate the efficiency of our approach in various environments. The primary application of this innovative approach is demonstrated in the search for horseshoe crabs within their wild habitats, showcasing its potential to revolutionize ecological survey and conservation efforts.

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during inference. This survey focuses on these inference-time approaches. We explore three areas under a unified mathematical formalism: token-level generation algorithms, meta-generation algorithms, and efficient generation. Token-level generation algorithms, often called decoding algorithms, operate by sampling a single token at a time or constructing a token-level search space and then selecting an output. These methods typically assume access to a language model's logits, next-token distributions, or probability scores. Meta-generation algorithms work on partial or full sequences, incorporating domain knowledge, enabling backtracking, and integrating external information. Efficient generation methods aim to reduce token costs and improve the speed of generation.

Dynamic pricing, the practice of adjusting prices based on contextual factors, has gained significant attention due to its impact on revenue maximization. In this paper, we address the contextual dynamic pricing problem, which involves pricing decisions based on observable product features and customer characteristics. We propose a novel algorithm that achieves improved regret bounds while minimizing assumptions about the problem. Our algorithm discretizes the unknown noise distribution and combines the upper confidence bounds with a layered data partitioning technique to effectively regulate regret in each episode. These techniques effectively control the regret associated with pricing decisions, leading to the minimax optimality. Specifically, our algorithm achieves a regret upper bound of $\tilde{\mathcal{O}}(\rho_{\mathcal{V}}^{\frac{1}{3}}(\delta) T^{\frac{2}{3}})$, where $\rho_{\mathcal{V}}(\delta)$ represents the estimation error of the valuation function. Importantly, this bound matches the lower bound up to logarithmic terms, demonstrating the minimax optimality of our approach. Furthermore, our method extends beyond linear valuation models commonly used in dynamic pricing by considering general function spaces. We simplify the estimation process by reducing it to general offline regression oracles, making implementation more straightforward.

Recent studies show that existing training-free metrics have several limitations, such as limited correlation and poor generalisation across different search spaces and tasks. Hence, we propose Sample-Wise Activation Patterns and its derivative, SWAP-Score, a novel high-performance training-free metric. It measures the expressivity of networks over a batch of input samples. The SWAP-Score is strongly correlated with ground-truth performance across various search spaces and tasks, outperforming 15 existing training-free metrics on NAS-Bench-101/201/301 and TransNAS-Bench-101. The SWAP-Score can be further enhanced by regularisation, which leads to even higher correlations in cell-based search space and enables model size control during the search. For example, Spearman's rank correlation coefficient between regularised SWAP-Score and CIFAR-100 validation accuracies on NAS-Bench-201 networks is 0.90, significantly higher than 0.80 from the second-best metric, NWOT. When integrated with an evolutionary algorithm for NAS, our SWAP-NAS achieves competitive performance on CIFAR-10 and ImageNet in approximately 6 minutes and 9 minutes of GPU time respectively. Performance evaluation of neural networks is critical, especially in Neural Architecture Search (NAS) which aims to automatically construct high-performing neural networks for a given task. The conventional approach evaluates candidate networks by feed-forward and back-propagation training. This process typically requires every candidate to be trained on the target dataset until convergence (Liu et al., 2019; Zoph & Le, 2017), and often leads to prohibitively high computational cost (Ren et al., 2022; White et al., 2023). To mitigate this cost, several alternatives have been introduced, such as performance predictors, architecture comparators and weight-sharing strategies. A divergent approach is the use of training-free metrics, also known as zero-cost proxies (Chen et al., 2021a; Lin et al., 2021; Lopes et al., 2021; Mellor et al., 2021; Mok et al., 2022; Tanaka et al., 2020b; Li et al., 2023). The aim is to eliminate the need for network training entirely. These metrics are either positively or negatively correlated with the networks' ground-truth performance.

One of the hallmark achievements of the theory of graphical models and Bayesian model selection is the celebrated greedy equivalence search (GES) algorithm due to Chickering and Meek. GES is known to consistently estimate the structure of directed acyclic graph (DAG) models in various special cases including Gaussian and discrete models, which are in particular curved exponential families. A general theory that covers general nonparametric DAG models, however, is missing. Here, we establish the consistency of greedy equivalence search for general families of DAG models that satisfy smoothness conditions on the Markov factorization, and hence may not be curved exponential families, or even parametric. The proof leverages recent advances in nonparametric Bayes to construct a test for comparing misspecified DAG models that avoids arguments based on the Laplace approximation. Nonetheless, when the Laplace approximation is valid and a consistent scoring function exists, we recover the classical result. As a result, we obtain a general consistency theorem for GES applied to general DAG models.

The Grover search algorithm is a pivotal advancement in quantum computing, promising a remarkable speedup over classical algorithms in searching unstructured large databases. Here, we report results for the implementation and characterization of a three-qubit Grover search algorithm using the state-of-the-art scalable quantum computing technology of superconducting quantum architectures. To delve into the algorithm's scalability and performance metrics, our investigation spans the execution of the algorithm across all eight conceivable single-result oracles, alongside nine two-result oracles, employing IBM Quantum's 127-qubit quantum computers. Moreover, we conduct five quantum state tomography experiments to precisely gauge the behavior and efficiency of our implemented algorithm under diverse conditions; ranging from noisy, noise-free environments to the complexities of real-world quantum hardware. By connecting theoretical concepts with real-world experiments, this study not only shed light on the potential of NISQ (Noisy Intermediate-Scale Quantum) computers in facilitating large-scale database searches but also offer valuable insights into the practical application of the Grover search algorithm in real-world quantum computing applications.

Low-rank Adaption (LoRA) has been the de-facto parameter-efficient fine-tuning technique for large language models. We present HeteroLoRA, a light-weight search algorithm that leverages zero-cost proxies to allocate the limited LoRA trainable parameters across the model for better fine-tuned performance. In addition to the allocation for the standard LoRA-adapted models, we also demonstrate the efficacy of HeteroLoRA by performing the allocation in a more challenging search space that includes LoRA modules and LoRA-adapted shortcut connections. Experiments show that HeteroLoRA enables improvements in model performance given the same parameter budge. For example, on MRPC, we see an improvement of 1.6% in accuracy with similar training parameter budget. We will open-source our algorithm once the paper is accepted.