There are many different nature-inspired algorithms in the literature, and almost all such algorithms have algorithm-dependent parameters that need to be tuned. The proper setting and parameter tuning should be carried out to maximize the performance of the algorithm under consideration. This work is the extension of the recent work on parameter tuning by Joy et al. (2024) presented at the International Conference on Computational Science (ICCS 2024), and the Firefly Algorithm (FA) is tuned using three different methods: the Monte Carlo method, the Quasi-Monte Carlo method and the Latin Hypercube Sampling. The FA with the tuned parameters is then used to solve a set of six different optimization problems, and the possible effect of parameter setting on the quality of the optimal solutions is analyzed. Rigorous statistical hypothesis tests have been carried out, including Student's t-tests, F-tests, non-parametric Friedman tests and ANOVA. Results show that the performance of the FA is not influenced by the tuning methods used. In addition, the tuned parameter values are largely independent of the tuning methods used. This indicates that the FA can be flexible and equally effective in solving optimization problems, and any of the three tuning methods can be used to tune its parameters effectively.

Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under structured corruptions. In this paper, we propose a self-guided data augmentation approach that employs adaptive weighting to suppress outlier influence, reformulating the original TRPCA problem into a standard Tensor Principal Component Analysis (TPCA) problem. The proposed model involves an optimization-driven weighting scheme that dynamically identifies and downweights outlier contributions during tensor augmentation. We develop an efficient proximal block coordinate descent algorithm with closed-form updates to solve the resulting optimization problem, ensuring computational efficiency. Theoretical convergence is guaranteed through a framework combining block coordinate descent with majorization-minimization principles. Numerical experiments on synthetic and real-world datasets, including face recovery, background subtraction, and hyperspectral denoising, demonstrate that our method effectively handles various corruption patterns. The results show the improvements in both accuracy and computational efficiency compared to state-of-the-art methods.

Grokking is proposed and widely studied as an intricate phenomenon in which generalization is achieved after a long-lasting period of overfitting. In this work, we propose NeuralGrok, a novel gradient-based approach that learns an optimal gradient transformation to accelerate the generalization of transformers in arithmetic tasks. Specifically, NeuralGrok trains an auxiliary module (e.g., an MLP block) in conjunction with the base model. This module dynamically modulates the influence of individual gradient components based on their contribution to generalization, guided by a bilevel optimization algorithm. Our extensive experiments demonstrate that NeuralGrok significantly accelerates generalization, particularly in challenging arithmetic tasks. We also show that NeuralGrok promotes a more stable training paradigm, constantly reducing the model's complexity, while traditional regularization methods, such as weight decay, can introduce substantial instability and impede generalization. We further investigate the intrinsic model complexity leveraging a novel Absolute Gradient Entropy (AGE) metric, which explains that NeuralGrok effectively facilitates generalization by reducing the model complexity. We offer valuable insights on the grokking phenomenon of Transformer models, which encourages a deeper understanding of the fundamental principles governing generalization ability.

Right, the changes in metrics between the original poses (in blue) and the poses optimized with MOISST (in red) for each dataset, grouped in 3 categories: Novel View Synthesis, Structure-from-Motion, Geometric. Abstract --Autonomous driving systems rely on accurate perception and localization of the ego car to ensure safety and reliability in challenging real-world driving scenarios. Public datasets play a vital role in benchmarking and guiding advancement in research by providing standardized resources for model development and evaluation. However, potential inaccuracies in sensor calibration and vehicle poses within these datasets can lead to erroneous evaluations of downstream tasks, adversely impacting the reliability and performance of the autonomous systems. T o address this challenge, we propose a robust optimization method based on Neural Radiance Fields (NeRF) to refine sensor poses and calibration parameters, enhancing the integrity of dataset benchmarks. T o validate improvement in accuracy of our optimized poses without ground truth, we present a thorough evaluation process, relying on reprojection metrics, Novel View Synthesis rendering quality, and geometric alignment. We demonstrate that our method achieves significant improvements in sensor pose accuracy. By optimizing these critical parameters, our approach not only improves the utility of existing datasets but also paves the way for more reliable 1 Noah's Ark Lab, Huawei. T o foster continued progress in this field, we make the optimized sensor poses publicly available, providing a valuable resource for the research community. I NTRODUCTION A UTONOMOUS driving presents unique challenges that set it apart from other domains. Safety stands as the cornerstone of this field, requiring systems to reliably protect passengers in a wide variety of conditions, including rare and critical edge cases. The complexity of road environments, characterized by dynamic interactions, unpredictable agent behaviors, and diverse environmental conditions, further amplifies the difficulty. Autonomous driving systems must accurately perceive their surroundings, predict the movements of other agents, and make split-second decisions to navigate safely and efficiently.

Generative information retrieval (GenIR) is a promising neural retrieval paradigm that formulates document retrieval as a document identifier (docid) generation task, allowing for end-to-end optimization toward a unified global retrieval objective. However, existing GenIR models suffer from token-level misalignment, where models trained to predict the next token often fail to capture document-level relevance effectively. While reinforcement learning-based methods, such as reinforcement learning from relevance feedback (RLRF), aim to address this misalignment through reward modeling, they introduce significant complexity, requiring the optimization of an auxiliary reward function followed by reinforcement fine-tuning, which is computationally expensive and often unstable. To address these challenges, we propose direct document relevance optimization (DDRO), which aligns token-level docid generation with document-level relevance estimation through direct optimization via pairwise ranking, eliminating the need for explicit reward modeling and reinforcement learning. Experimental results on benchmark datasets, including MS MARCO document and Natural Questions, show that DDRO outperforms reinforcement learning-based methods, achieving a 7.4% improvement in MRR@10 for MS MARCO and a 19.9% improvement for Natural Questions. These findings highlight DDRO's potential to enhance retrieval effectiveness with a simplified optimization approach. By framing alignment as a direct optimization problem, DDRO simplifies the ranking optimization pipeline of GenIR models while offering a viable alternative to reinforcement learning-based methods.

Ergodic coverage effectively generates exploratory behaviors for embodied agents by aligning the spatial distribution of the agent's trajectory with a target distribution, where the difference between these two distributions is measured by the ergodic metric. However, existing ergodic coverage methods are constrained by the limited set of ergodic metrics available for control synthesis, fundamentally limiting their performance. In this work, we propose an alternative approach to ergodic coverage based on flow matching, a technique widely used in generative inference for efficient and scalable sampling. We formally derive the flow matching problem for ergodic coverage and show that it is equivalent to a linear quadratic regulator problem with a closed-form solution. Our formulation enables alternative ergodic metrics from generative inference that overcome the limitations of existing ones. These metrics were previously infeasible for control synthesis but can now be supported with no computational overhead. Specifically, flow matching with the Stein variational gradient flow enables control synthesis directly over the score function of the target distribution, improving robustness to the unnormalized distributions; on the other hand, flow matching with the Sinkhorn divergence flow enables an optimal transport-based ergodic metric, improving coverage performance on non-smooth distributions with irregular supports. We validate the improved performance and competitive computational efficiency of our method through comprehensive numerical benchmarks and across different nonlinear dynamics. We further demonstrate the practicality of our method through a series of drawing and erasing tasks on a Franka robot.

Optimization algorithms are widely employed to tackle complex problems, but designing them manually is often labor-intensive and requires significant expertise. Global placement is a fundamental step in electronic design automation (EDA). While analytical approaches represent the state-of-the-art (SOTA) in global placement, their core optimization algorithms remain heavily dependent on heuristics and customized components, such as initialization strategies, preconditioning methods, and line search techniques. This paper presents an automated framework that leverages large language models (LLM) to evolve optimization algorithms for global placement. We first generate diverse candidate algorithms using LLM through carefully crafted prompts. Then we introduce an LLM-based genetic flow to evolve selected candidate algorithms. The discovered optimization algorithms exhibit substantial performance improvements across many benchmarks. Specifically, Our design-case-specific discovered algorithms achieve average HPWL improvements of \textbf{5.05\%}, \text{5.29\%} and \textbf{8.30\%} on MMS, ISPD2005 and ISPD2019 benchmarks, and up to \textbf{17\%} improvements on individual cases. Additionally, the discovered algorithms demonstrate good generalization ability and are complementary to existing parameter-tuning methods.

Local optima networks (LONs) capture fitness landscape information. They are typically constructed in a black-box manner; information about the problem structure is not utilised. This also applies to the analysis of LONs: knowledge about the problem, such as interaction between variables, is not considered. We challenge this status-quo with an alternative approach: we consider how LON analysis can be improved by incorporating subfunction-based information - this can either be known a-priori or learned during search. To this end, LONs are constructed for several benchmark pseudo-boolean problems using three approaches: firstly, the standard algorithm; a second algorithm which uses deterministic grey-box crossover; and a third algorithm which selects perturbations based on learned information about variable interactions. Metrics related to subfunction changes in a LON are proposed and compared with metrics from previous literature which capture other aspects of a LON. Incorporating problem structure in LON construction and analysing it can bring enriched insight into optimisation dynamics. Such information may be crucial to understanding the difficulty of solving a given problem with state-of-the-art linkage learning optimisers. In light of the results, we suggest incorporation of problem structure as an alternative paradigm in landscape analysis for problems with known or suspected subfunction structure.

Two-time-scale stochastic approximation is an algorithm with coupled iterations which has found broad applications in reinforcement learning, optimization and game control. While several prior works have obtained a mean square error bound of $O(1/k)$ for linear two-time-scale iterations, the best known bound in the non-linear contractive setting has been $O(1/k^{2/3})$. In this work, we obtain an improved bound of $O(1/k)$ for non-linear two-time-scale stochastic approximation. Our result applies to algorithms such as gradient descent-ascent and two-time-scale Lagrangian optimization. The key step in our analysis involves rewriting the original iteration in terms of an averaged noise sequence which decays sufficiently fast. Additionally, we use an induction-based approach to show that the iterates are bounded in expectation.

We study the problem of Active Simple Hypothesis Testing (ASHT) whe re an agent is faced with the problem of choosing between m different simple hypotheses after observing T samples. At the end of T samples, it has to output one of the m hypothesis. The distinguishing difference from the usual hypothes is testing scenario is the ability to choose one of K actions and observe the corresponding sample for that action. Th is ability to control the samples in this way makes the problem more interesting and difficult compared to the usual hypothesis testing with no control over the sample generation. The performance of the agent is meas ured in terms of the error probability its decision incurs. The above theoretical problem is a model for many practica l scenarios-A cosmetic drug trial often involve a testing period where the outcome of interest is to identify the best product after the trial period, choosing a channel from a set of channels before commencing communications, placeme nt of sensors in certain set of positions so as to minimize signal error. Any situation which require a period of testing b efore committing to a final decision with only certain fixed budget of samples (that is an inability to request additio nal samples) can be modeled effectively using ASHT and its more general version - Fixed Budget Best Arm Identific ation (FB-BAI). We intend to study the ASHT problem in the large deviation setting with the quantity of interest being the minimax error exponent over the hypotheses, that is, the worst case er ror exponent over the hypotheses.