The hierarchical structure of 3D scene graphs shows a high relevance for representations purposes, as it fits common patterns from man-made environments. But, additionally, the semantic and geometric information in such hierarchical representations could be leveraged to speed up the optimization and management of map elements and robot poses. In this direction, we present our work Situational Graphs 2.0 (S-Graphs 2.0), which leverages the hierarchical structure of indoor scenes for efficient data management and optimization. Our algorithm begins by constructing a situational graph that represents the environment into four layers: Keyframes, Walls, Rooms, and Floors. Our first novelty lies in the front-end, which includes a floor detection module capable of identifying stairways and assigning floor-level semantic relations to the underlying layers. Floor-level semantics allows us to propose a floor-based loop closure strategy, that effectively rejects false positive closures that typically appear due to aliasing between different floors of a building. Our second novelty lies in leveraging our representation hierarchy in the optimization. Our proposal consists of: (1) local optimization over a window of recent keyframes and their connected components across the four representation layers, (2) floor-level global optimization, which focuses only on keyframes and their connections within the current floor during loop closures, and (3) room-level local optimization, marginalizing redundant keyframes that share observations within the room, which reduces the computational footprint. We validate our algorithm extensively in different real multi-floor environments. Our approach shows state-of-art-art accuracy metrics in large-scale multi-floor environments, estimating hierarchical representations up to 10x faster, in average, than competing baselines
Asynchronous federated learning mitigates the inefficiency of conventional synchronous aggregation by integrating updates as they arrive and adjusting their influence based on staleness. Due to asynchrony and data heterogeneity, learning objectives at the global and local levels are inherently inconsistent -- global optimization trajectories may conflict with ongoing local updates. Existing asynchronous methods simply distribute the latest global weights to clients, which can overwrite local progress and cause model drift. In this paper, we propose OrthoFL, an orthogonal calibration framework that decouples global and local learning progress and adjusts global shifts to minimize interference before merging them into local models. In OrthoFL, clients and the server maintain separate model weights. Upon receiving an update, the server aggregates it into the global weights via a moving average. For client weights, the server computes the global weight shift accumulated during the client's delay and removes the components aligned with the direction of the received update. The resulting parameters lie in a subspace orthogonal to the client update and preserve the maximal information from the global progress. The calibrated global shift is then merged into the client weights for further training. Extensive experiments show that OrthoFL improves accuracy by 9.6% and achieves a 12$\times$ speedup compared to synchronous methods. Moreover, it consistently outperforms state-of-the-art asynchronous baselines under various delay patterns and heterogeneity scenarios.
The LLM-as-a-Judge paradigm shows promise for evaluating generative content but lacks reliability in reasoning-intensive scenarios, such as programming. Inspired by recent advances in reasoning models and shifts in scaling laws, we pioneer bringing test-time computation into LLM-as-a-Judge, proposing MCTS-Judge, a resource-efficient, System-2 thinking framework for code correctness evaluation. MCTS-Judge leverages Monte Carlo Tree Search (MCTS) to decompose problems into simpler, multi-perspective evaluations. Through a node-selection strategy that combines self-assessment based on historical actions in the current trajectory and the Upper Confidence Bound for Trees based on prior rollouts, MCTS-Judge balances global optimization and refinement of the current trajectory. We further designed a high-precision, unit-test-level reward mechanism to encourage the Large Language Model (LLM) to perform line-by-line analysis. Extensive experiments on three benchmarks and five LLMs demonstrate the effectiveness of MCTS-Judge, which improves the base model's accuracy from 41% to 80%, surpassing the o1-series models with 3x fewer tokens. Further evaluations validate the superiority of its reasoning trajectory in logic, analytics, thoroughness, and overall quality, while revealing the test-time scaling law of the LLM-as-a-Judge paradigm.
The Cuckoo Search Algorithm (CSA), while effective in solving complex optimization problems, faces limitations in random population initialization and reliance on fixed parameters. Random initialization of the population often results in clustered solutions, resulting in uneven exploration of the search space and hindering effective global optimization. Furthermore, the use of fixed values for discovery rate and step size creates a trade-off between solution accuracy and convergence speed. To address these limitations, an Enhanced Cuckoo Search Algorithm (ECSA) is proposed. This algorithm utilizes the Sobol Sequence to generate a more uniformly distributed initial population and incorporates Cosine Annealing with Warm Restarts to dynamically adjust the parameters. The performance of the algorithms was evaluated on 13 benchmark functions (7 unimodal, 6 multimodal). Statistical analyses were conducted to determine the significance and consistency of the results. The ECSA outperforms the CSA in 11 out of 13 benchmark functions with a mean fitness improvement of 30% across all functions, achieving 35% for unimodal functions and 24% for multimodal functions. The enhanced algorithm demonstrated increased convergence efficiency, indicating its superiority to the CSA in solving a variety of optimization problems. The ECSA is subsequently applied to optimize earthquake evacuation space allocation in Intramuros, Manila.
Optimizing expensive, non-convex, black-box Lipschitz continuous functions presents significant challenges, particularly when the Lipschitz constant of the underlying function is unknown. Such problems often demand numerous function evaluations to approximate the global optimum, which can be prohibitive in terms of time, energy, or resources. In this work, we introduce Every Call is Precious (ECP), a novel global optimization algorithm that minimizes unpromising evaluations by strategically focusing on potentially optimal regions. Unlike previous approaches, ECP eliminates the need to estimate the Lipschitz constant, thereby avoiding additional function evaluations. ECP guarantees no-regret performance for infinite evaluation budgets and achieves minimax-optimal regret bounds within finite budgets. Extensive ablation studies validate the algorithm's robustness, while empirical evaluations show that ECP outperforms 10 benchmark algorithms including Lipschitz, Bayesian, bandits, and evolutionary methods across 30 multi-dimensional non-convex synthetic and real-world optimization problems, which positions ECP as a competitive approach for global optimization.
With the growing penetration of distributed renewable energy, distributed control approaches are widely utilized in voltage control of active distribution networks (ADNs), suffering from limited applicability for control devices or heavy communication burden. This paper develops an innovative distributed voltage control strategy of ADNs with global sensitivities (DVC-GS), which integrates network information from a global optimization view to coordinate energy storages, PV inverters and the OLTC with little communication and computing time. The global sensitivities of voltage violations across all buses with respect to nodal voltage and active/reactive power injection are formulated to quantify the ability of each controllable resource for alleviating voltage violations in the entire ADN. The back-and-forth communication combined with the modified DistFlow model is newly developed for the real-time update of global sensitivities at each bus with high accuracy and no iteration. Then the coordinated control of various devices is implemented on basis of global sensitivities to effectively ensure voltage security of ADNs. Comprehensive simulations based on modified 11-bus and 123-bus systems demonstrate the significant efficiency and superiority of the global sensitivities and DVC-GS.
Non-smooth and non-convex global optimization poses significant challenges across various applications, where standard gradient-based methods often struggle. We propose the Ball-Proximal Point Method, Broximal Point Method, or Ball Point Method (BPM) for short - a novel algorithmic framework inspired by the classical Proximal Point Method (PPM) (Rockafellar, 1976), which, as we show, sheds new light on several foundational optimization paradigms and phenomena, including non-convex and non-smooth optimization, acceleration, smoothing, adaptive stepsize selection, and trust-region methods. At the core of BPM lies the ball-proximal ("broximal") operator, which arises from the classical proximal operator by replacing the quadratic distance penalty by a ball constraint. Surprisingly, and in sharp contrast with the sublinear rate of PPM in the nonsmooth convex regime, we prove that BPM converges linearly and in a finite number of steps in the same regime. Furthermore, by introducing the concept of ball-convexity, we prove that BPM retains the same global convergence guarantees under weaker assumptions, making it a powerful tool for a broader class of potentially non-convex optimization problems. Just like PPM plays the role of a conceptual method inspiring the development of practically efficient algorithms and algorithmic elements, e.g., gradient descent, adaptive step sizes, acceleration (Ahn & Sra, 2020), and "W" in AdamW (Zhuang et al., 2022), we believe that BPM should be understood in the same manner: as a blueprint and inspiration for further development.
We present Light3R-SfM, a feed-forward, end-to-end learnable framework for efficient large-scale Structure-from-Motion (SfM) from unconstrained image collections. Unlike existing SfM solutions that rely on costly matching and global optimization to achieve accurate 3D reconstructions, Light3R-SfM addresses this limitation through a novel latent global alignment module. This module replaces traditional global optimization with a learnable attention mechanism, effectively capturing multi-view constraints across images for robust and precise camera pose estimation. Light3R-SfM constructs a sparse scene graph via retrieval-score-guided shortest path tree to dramatically reduce memory usage and computational overhead compared to the naive approach. Extensive experiments demonstrate that Light3R-SfM achieves competitive accuracy while significantly reducing runtime, making it ideal for 3D reconstruction tasks in real-world applications with a runtime constraint. This work pioneers a data-driven, feed-forward SfM approach, paving the way toward scalable, accurate, and efficient 3D reconstruction in the wild.
The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We devise a problem instance generator and pick 56 representative instances, which we compare to established benchmarking suits through Exploratory Landscape Analysis to show their uniqueness. For the computational comparison, we select twelve well-performing global optimization techniques from both subfields of stochastic algorithms (evolutionary computation methods) and deterministic algorithms (Dividing RECTangles, or DIRECT-type methods). The experiments were conducted in settings with varying dimensionality and computational budgets. The results were analyzed through several criteria (number of best-found solutions, mean relative error, Friedman ranks) and utilized established statistical tests. The best-ranking methods for the UAV problems were almost universally the top-performing evolutionary techniques from recent competitions on numerical optimization at the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation. Lastly, we discussed the variable dimension characteristics of the studied UAV problems that remain still largely under-investigated.
Bayesian optimization (BO) is well known to be sample-efficient for solving black-box problems. However, the BO algorithms can sometimes get stuck in suboptimal solutions even with plenty of samples. Intrinsically, such suboptimal problem of BO can attribute to the poor surrogate accuracy of the trained Gaussian process (GP), particularly that in the regions where the optimal solutions locate. Hence, we propose to build multiple GP models instead of a single GP surrogate to complement each other and thus resolving the suboptimal problem of BO. Nevertheless, according to the bias-variance tradeoff equation, the individual prediction errors can increase when increasing the diversity of models, which may lead to even worse overall surrogate accuracy. On the other hand, based on the theory of Rademacher complexity, it has been proved that exploiting the agreement of models on unlabeled information can help to reduce the complexity of the hypothesis space, and therefore achieving the required surrogate accuracy with fewer samples. Such value of model agreement has been extensively demonstrated for co-training style algorithms to boost model accuracy with a small portion of samples. Inspired by the above, we propose a novel BO algorithm labeled as co-learning BO (CLBO), which exploits both model diversity and agreement on unlabeled information to improve the overall surrogate accuracy with limited samples, and therefore achieving more efficient global optimization. Through tests on five numerical toy problems and three engineering benchmarks, the effectiveness of proposed CLBO has been well demonstrated.
We describe a global optimization technique using `basin-hopping' in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features which recent work suggests must be present in an energy landscape for efficient relaxation to the global minimum. The transformation associates any point in configuration space with the local minimum obtained by a geometry optimization started from that point, effectively removing transition state regions from the problem. However, unlike other methods based upon hypersurface deformation, this transformation does not change the global minimum. The lowest known structures are located for all Lennard-Jones clusters up to 110 atoms, including a number that have never been found before in unbiased searches.
As urbanization accelerates, open spaces are increasingly recognized for their role in enhancing sustainability and well-being, yet they remain underexplored compared to built spaces. This study introduces an AI-driven framework that integrates machine learning models (MLMs) and explainable AI techniques to optimize Sky View Factor (SVF) and visibility, key spatial metrics influencing thermal comfort and perceived safety in urban spaces. Unlike global optimization methods, which are computationally intensive and impractical for localized adjustments, this framework supports incremental design improvements with lower computational costs and greater flexibility. The framework employs SHapley Adaptive Explanations (SHAP) to analyze feature importance and Counterfactual Explanations (CFXs) to propose minimal design changes. Simulations tested five MLMs, identifying XGBoost as the most accurate, with building width, park area, and heights of surrounding buildings as critical for SVF, and distances from southern buildings as key for visibility. Compared to Genetic Algorithms, which required approximately 15/30 minutes across 3/4 generations to converge, the tested CFX approach achieved optimized results in 1 minute with a 5% RMSE error, demonstrating significantly faster performance and suitability for scalable retrofitting strategies. This interpretable and computationally efficient framework advances urban performance optimization, providing data-driven insights and practical retrofitting solutions for enhancing usability and environmental quality across diverse urban contexts.
Typical LiDAR SLAM architectures feature a front-end for odometry estimation and a back-end for refining and optimizing the trajectory and map, commonly through loop closures. However, loop closure detection in large-scale missions presents significant computational challenges due to the need to identify, verify, and process numerous candidate pairs for pose graph optimization. Keyframe sampling bridges the front-end and back-end by selecting frames for storing and processing during global optimization. This article proposes an online keyframe sampling approach that constructs the pose graph using the most impactful keyframes for loop closure. We introduce the Minimal Subset Approach (MSA), which optimizes two key objectives: redundancy minimization and information preservation, implemented within a sliding window framework. By operating in the feature space rather than 3-D space, MSA efficiently reduces redundant keyframes while retaining essential information. In sum, evaluations on diverse public datasets show that the proposed approach outperforms naive methods in reducing false positive rates in place recognition, while delivering superior ATE and RPE in metric localization, without the need for manual parameter tuning. Additionally, MSA demonstrates efficiency and scalability by reducing memory usage and computational overhead during loop closure detection and pose graph optimization.
In this paper, we present an intuitive analysis of the optimization technique based on the quantization of an objective function. Quantization of an objective function is an effective optimization methodology that decreases the measure of a level set containing several saddle points and local minima and finds the optimal point at the limit level set. To investigate the dynamics of quantization-based optimization, we derive an overdamped Langevin dynamics model from an intuitive analysis to minimize the level set by iterative quantization. We claim that quantization-based optimization involves the quantities of thermodynamical and quantum mechanical optimization as the core methodologies of global optimization. Furthermore, on the basis of the proposed SDE, we provide thermodynamic and quantum mechanical analysis with Witten-Laplacian. The simulation results with the benchmark functions, which compare the performance of the nonlinear optimization, demonstrate the validity of the quantization-based optimization.
Real-time bidding (RTB) plays a pivotal role in online advertising ecosystems. Advertisers employ strategic bidding to optimize their advertising impact while adhering to various financial constraints, such as the return-on-investment (ROI) and cost-per-click (CPC). Primarily focusing on bidding with fixed budget constraints, traditional approaches cannot effectively manage the dynamic budget allocation problem where the goal is to achieve global optimization of bidding performance across multiple channels with a shared budget. In this paper, we propose a hierarchical multi-agent reinforcement learning framework for multi-channel bidding optimization. In this framework, the top-level strategy applies a CPC constrained diffusion model to dynamically allocate budgets among the channels according to their distinct features and complex interdependencies, while the bottom-level strategy adopts a state-action decoupled actor-critic method to address the problem of extrapolation errors in offline learning caused by out-of-distribution actions and a context-based meta-channel knowledge learning method to improve the state representation capability of the policy based on the shared knowledge among different channels. Comprehensive experiments conducted on a large scale real-world industrial dataset from the Meituan ad bidding platform demonstrate that our method achieves a state-of-the-art performance.
We present an application of a single-qubit Data Re-Uploading (QRU) quantum model for particle classification in calorimetric experiments. Optimized for Noisy Intermediate-Scale Quantum (NISQ) devices, this model requires minimal qubits while delivering strong classification performance. Evaluated on a novel simulated dataset specific to particle physics, the QRU model achieves high accuracy in classifying particle types. Through a systematic exploration of model hyperparameters -- such as circuit depth, rotation gates, input normalization and the number of trainable parameters per input -- and training parameters like batch size, optimizer, loss function and learning rate, we assess their individual impacts on model accuracy and efficiency. Additionally, we apply global optimization methods, uncovering hyperparameter correlations that further enhance performance. Our results indicate that the QRU model attains significant accuracy with efficient computational costs, underscoring its potential for practical quantum machine learning applications.
Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the performance of the explicit graduated optimization algorithm with an optimal noise scheduling derived from a previous study and discusses its limitations. It uses traditional benchmark functions and empirical loss functions for modern neural network architectures for evaluating. In addition, this paper extends the implicit graduated optimization algorithm, which is based on the fact that stochastic noise in the optimization process of SGD implicitly smooths the objective function, to SGD with momentum, analyzes its convergence, and demonstrates its effectiveness through experiments on image classification tasks with ResNet architectures.
Bayesian Optimisation (BO) is a state-of-the-art global optimisation technique for black-box problems where derivative information is unavailable, and sample efficiency is crucial. However, improving the general scalability of BO has proved challenging. Here, we explore Latent Space Bayesian Optimisation (LSBO), that applies dimensionality reduction to perform BO in a reduced-dimensional subspace. While early LSBO methods used (linear) random projections (Wang et al., 2013), we employ Variational Autoencoders (VAEs) to manage more complex data structures and general DR tasks. Building on Grosnit et. al. (2021), we analyse the VAE-based LSBO framework, focusing on VAE retraining and deep metric loss. We suggest a few key corrections in their implementation, originally designed for tasks such as molecule generation, and reformulate the algorithm for broader optimisation purposes. Our numerical results show that structured latent manifolds improve BO performance. Additionally, we examine the use of the Mat\'{e}rn-$\frac{5}{2}$ kernel for Gaussian Processes in this LSBO context. We also integrate Sequential Domain Reduction (SDR), a standard global optimization efficiency strategy, into BO. SDR is included in a GPU-based environment using \textit{BoTorch}, both in the original and VAE-generated latent spaces, marking the first application of SDR within LSBO.
Recent sparse multi-view scene reconstruction advances like DUSt3R and MASt3R no longer require camera calibration and camera pose estimation. However, they only process a pair of views at a time to infer pixel-aligned pointmaps. When dealing with more than two views, a combinatorial number of error prone pairwise reconstructions are usually followed by an expensive global optimization, which often fails to rectify the pairwise reconstruction errors. To handle more views, reduce errors, and improve inference time, we propose the fast single-stage feed-forward network MV-DUSt3R. At its core are multi-view decoder blocks which exchange information across any number of views while considering one reference view. To make our method robust to reference view selection, we further propose MV-DUSt3R+, which employs cross-reference-view blocks to fuse information across different reference view choices. To further enable novel view synthesis, we extend both by adding and jointly training Gaussian splatting heads. Experiments on multi-view stereo reconstruction, multi-view pose estimation, and novel view synthesis confirm that our methods improve significantly upon prior art. Code will be released.
Recent advances in learning decision-making policies can largely be attributed to training expressive policy models, largely via imitation learning. While imitation learning discards non-expert data, reinforcement learning (RL) can still learn from suboptimal data. However, instantiating RL training of a new policy class often presents a different challenge: most deep RL machinery is co-developed with assumptions on the policy class and backbone, resulting in poor performance when the policy class changes. For instance, SAC utilizes a low-variance reparameterization policy gradient for Gaussian policies, but this is unstable for diffusion policies and intractable for autoregressive categorical policies. To address this issue, we develop an offline RL and online fine-tuning approach called policy-agnostic RL (PA-RL) that can effectively train multiple policy classes, with varying architectures and sizes. We build off the basic idea that a universal supervised learning loss can replace the policy improvement step in RL, as long as it is applied on "optimized" actions. To obtain these optimized actions, we first sample multiple actions from a base policy, and run global optimization (i.e., re-ranking multiple action samples using the Q-function) and local optimization (i.e., running gradient steps on an action sample) to maximize the critic on these candidates. PA-RL enables fine-tuning diffusion and transformer policies with either autoregressive tokens or continuous action outputs, at different sizes, entirely via actor-critic RL. Moreover, PA-RL improves the performance and sample-efficiency by up to 2 times compared to existing offline RL and online fine-tuning methods. We show the first result that successfully fine-tunes OpenVLA, a 7B generalist robot policy, autonomously with Cal-QL, an online RL fine-tuning algorithm, improving from 40% to 70% in the real world in 40 minutes.