Frederike Dümbgen

Avinash Subramanian, Connor Holmes, Timothy D. Barfoot et al.

Robust and efficient state estimation is crucial for perception, navigation, and control in robotics. State estimation problems are conveniently modeled using the factor-graph framework as enabled by modern software packages such as GTSAM or g2o. However, the standard solvers included in such frameworks are local and may converge to poor local minima, posing significant safety concerns. Conversely, techniques based on convex relaxations have been shown to provide a means of globally solving or certifying many state estimation problems. However, these relaxations 1) often require substantial effort to formulate, and 2) may incur significantly higher cost compared to efficient local solvers, as they require solving a large semidefinite program (SDP). In this work, we address both shortcomings by 1) creating a new procedure within the GTSAM framework for automatically constructing convex SDP relaxations for any factor graphs with common factor and variable types, and by 2) exploiting the Bayes tree constructions native to GTSAM to decompose the SDP problem, leading to significant speedup in solver time for chordally sparse problems. We demonstrate the favorable scaling of this structure-exploiting global estimator compared to standard local solvers for two case studies: A 3D pose-graph SLAM problem with a ring factor graph and a 2D localization problem with a chain factor graph. The software framework is available at https://github.com/borglab/gtsam.

Buqing Ou, Frederike Dümbgen

Bayesian Optimization (BO) is an effective framework for globally optimizing functions whose evaluations are expensive. It is particularly effective for optimizing functions defined over continuous domains and explicitly handles stochastic noise in evaluations. As a result, it is widely applied in areas such as hyperparameter tuning, robotics policy search, and scientific experiment design, where sample efficiency is essential. Its two-step procedure consists of model fitting followed by optimization of the acquisition function, which is often treated as a generic black-box problem despite its structured nature. In this work, we introduce KSOS-BO, a kernel-based derivative-free framework for BO acquisition optimization. KSOS-BO formulates the optimization of the acquisition function as a semidefinite program with kernel-induced representations, enabling a structured global search. Across a diverse set of benchmark functions with varying landscape properties, KSOS-BO consistently outperforms derivative-free baselines using Sobol Search, Differential Evolution, or CMA-ES to optimize the acquisition function, achieving an average regret improvement of 81.16% on 10/15 benchmarks. In particular, KSOS-BO demonstrates strong performance in highly multimodal and unimodal but ill-conditioned functions, indicating its applicability to diverse landscape structures. Despite a higher per-iteration computational cost, it converges faster in wall-clock time with an average improvement of 93.55% on 10/15 benchmarks, as it reaches high-quality solutions with fewer evaluations. Limitations include reduced effectiveness on functions with steep drops or plate-shaped regions.

Antoine Groudiev, Fabian Schramm, Éloïse Berthier et al.

Global optimization has gained attraction over the past decades, thanks to the development of both theoretical foundations and efficient numerical routines. Among recent advances, Kernel Sum of Squares (KernelSOS) provides a powerful theoretical framework, combining the expressivity of kernel methods with the guarantees of SOS optimization. In this paper, we take KernelSOS from theory to practice and demonstrate its use on challenging control and robotics problems. We identify and address the practical considerations required to make the method work in applied settings: restarting strategies, systematic calibration of hyperparameters, methods for recovering minimizers, and the combination with fast local solvers. As a proof of concept, the application of KernelSOS to robot localization highlights its competitiveness with existing SOS approaches that rely on heuristics and handcrafted reformulations to render the problem polynomial. Even in the high-dimensional, non-parametric setting of trajectory optimization with simulators treated as black boxes, we demonstrate how KernelSOS can be combined with fast local solvers to uncover higher-quality solutions without compromising overall runtimes.

Zhongqi Wei, Frederike Dümbgen

Contact-rich manipulation is challenging due to its high dimensionality, the requirement for long time horizons, and the presence of hybrid contact dynamics. Sampling-based methods have become a popular approach for this class of problems, but without explicit mechanisms for global exploration, they are susceptible to converging to poor local minima. In this paper, we introduce Global-MPPI, a unified trajectory optimization framework that integrates global exploration and local refinement. At the global level, we leverage kernel sum-of-squares optimization to identify globally promising regions of the solution space. To enable reliable performance for the non-smooth landscapes inherent to contact-rich manipulation, we introduce a graduated non-convexity strategy based on log-sum-exp smoothing, which transitions the optimization landscape from a smoothed surrogate to the original non-smooth objective. Finally, we employ the model-predictive path integral method to locally refine the solution. We evaluate Global-MPPI on high-dimensional, long-horizon contact-rich tasks, including the PushT task and dexterous in-hand manipulation. Experimental results demonstrate that our approach robustly uncovers high-quality solutions, achieving faster convergence and lower final costs compared to existing baseline methods.

Buqing Ou, Frederike Dümbgen

Policy optimization in high-dimensional continuous control for robotics remains a challenging problem. Predominant methods are inherently local and often require extensive tuning and carefully chosen initial guesses for good performance, whereas more global and less initialization-sensitive search methods typically incur high rollout costs. We propose TFM-S3, a tabular hybrid local-global method for improving global exploration in robot policy learning with limited rollout cost. We interleave high-frequency local updates with intermittent rounds of global search. In each search round, we construct a dynamically updated low-dimensional policy subspace via SVD and perform iterative surrogate-guided refinement within this space. A pretrained tabular foundation model predicts candidate returns from a small context set, enabling large-scale screening with limited rollout cost. Experiments on continuous control benchmarks show that TFM-S3 consistently accelerates early-stage convergence and improves final performance compared to TD3 and population-based baselines under an identical rollout budget. These results demonstrate that foundation models are a powerful new tool for creating sample-efficient policy learning methods for continuous control in robotics.

Frederike Dümbgen, Majed El Helou, Adam Scholefield

Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case where no anchor locations are known. Inspired by Euclidean distance matrices, we investigate when a set of inner angles corresponds to a realizable point set. In particular, we find linear and non-linear constraints that are provably necessary, and we conjecture also sufficient for characterizing realizable angle sets. We confirm this in extensive numerical simulations, and we illustrate the use of these constraints for denoising angle measurements along with the reconstruction of a valid point set.

Majed El Helou, Frederike Dümbgen, Sabine Süsstrunk

The large capacity of neural networks enables them to learn complex functions. To avoid overfitting, networks however require a lot of training data that can be expensive and time-consuming to collect. A common practical approach to attenuate overfitting is the use of network regularization techniques. We propose a novel regularization method that progressively penalizes the magnitude of activations during training. The combined activation signals produced by all neurons in a given layer form the representation of the input image in that feature space. We propose to regularize this representation in the last feature layer before classification layers. Our method's effect on generalization is analyzed with label randomization tests and cumulative ablations. Experimental results show the advantages of our approach in comparison with commonly-used regularizers on standard benchmark datasets.

Majed El Helou, Frederike Dümbgen, Radhakrishna Achanta et al.

Image optimization problems encompass many applications such as spectral fusion, deblurring, deconvolution, dehazing, matting, reflection removal and image interpolation, among others. With current image sizes in the order of megabytes, it is extremely expensive to run conventional algorithms such as gradient descent, making them unfavorable especially when closed-form solutions can be derived and computed efficiently. This paper explains in detail the framework for solving convex image optimization and deconvolution in the Fourier domain. We begin by explaining the mathematical background and motivating why the presented setups can be transformed and solved very efficiently in the Fourier domain. We also show how to practically use these solutions, by providing the corresponding implementations. The explanations are aimed at a broad audience with minimal knowledge of convolution and image optimization. The eager reader can jump to Section 3 for a footprint of how to solve and implement a sample optimization function, and Section 5 for the more complex cases.