Continuum robots, made from flexible materials with continuous backbones, have several advantages over traditional rigid robots. Some of them are the ability to navigate through narrow or confined spaces, adapt to irregular or changing environments, and perform tasks in proximity to humans. However, one of the challenges in using continuum robots is the difficulty in accurately estimating their state, such as their tip position and curvature. This is due to the complexity of their kinematics and the inherent uncertainty in their measurement and control. This paper proposes a moving horizon estimation (MHE) approach for estimating the robot's state, including its tip position and shape parameters. Our approach involves minimizing the error between measurement samples from an IMU attached to the robot's tip and the estimated state along the estimation horizon using an inline optimization problem. We demonstrate the effectiveness of our approach through simulation and experimental results. Our approach can potentially improve the accuracy and robustness of state estimation and control for continuum robots. It can be applied to various applications such as surgery, manufacturing, and inspection.

Nonparametric two-sample tests such as the Maximum Mean Discrepancy (MMD) are often used to detect differences between two distributions in machine learning applications. However, the majority of existing literature assumes that error-free samples from the two distributions of interest are available.We relax this assumption and study the estimation of the MMD under $\epsilon$-contamination, where a possibly non-random $\epsilon$ proportion of one distribution is erroneously grouped with the other. We show that under $\epsilon$-contamination, the typical estimate of the MMD is unreliable. Instead, we study partial identification of the MMD, and characterize sharp upper and lower bounds that contain the true, unknown MMD. We propose a method to estimate these bounds, and show that it gives estimates that converge to the sharpest possible bounds on the MMD as sample size increases, with a convergence rate that is faster than alternative approaches. Using three datasets, we empirically validate that our approach is superior to the alternatives: it gives tight bounds with a low false coverage rate.

This short paper outlines two recent works on multi-contact teleoperation and the development of the SEIKO (Sequential Equilibrium Inverse Kinematic Optimization) framework. SEIKO adapts commands from the operator in real-time and ensures that the reference configuration sent to the underlying controller is feasible. Additionally, an admittance scheme is used to implement physical interaction, which is then combined with the operator's command and retargeted. SEIKO has been applied in simulations on various robots, including humanoid and quadruped robots designed for loco-manipulation. Furthermore, SEIKO has been tested on real hardware for bimanual heavy object carrying tasks.

Machine learning has achieved remarkable success over the past couple of decades, often attributed to a combination of algorithmic innovations and the availability of high-quality data available at scale. However, a third critical component is the fine-tuning of hyperparameters, which plays a pivotal role in achieving optimal model performance. Despite its significance, hyperparameter optimization (HPO) remains a challenging task for several reasons. Many HPO techniques rely on naive search methods or assume that the loss function is smooth and continuous, which may not always be the case. Traditional methods, like grid search and Bayesian optimization, often struggle to quickly adapt and efficiently search the loss landscape. Grid search is computationally expensive, while Bayesian optimization can be slow to prime. Since the search space for HPO is frequently high-dimensional and non-convex, it is often challenging to efficiently find a global minimum. Moreover, optimal hyperparameters can be sensitive to the specific dataset or task, further complicating the search process. To address these issues, we propose a new hyperparameter optimization method, HomOpt, using a data-driven approach based on a generalized additive model (GAM) surrogate combined with homotopy optimization. This strategy augments established optimization methodologies to boost the performance and effectiveness of any given method with faster convergence to the optimum on continuous, discrete, and categorical domain spaces. We compare the effectiveness of HomOpt applied to multiple optimization techniques (e.g., Random Search, TPE, Bayes, and SMAC) showing improved objective performance on many standardized machine learning benchmarks and challenging open-set recognition tasks.

We consider the nonconvex optimization problem associated with the decomposition of a real symmetric tensor into a sum of rank one terms. Use is made of the rich symmetry structure to construct infinite families of critical points represented by Puiseux series in the problem dimension, and so obtain precise analytic estimates on the value of the objective function and the Hessian spectrum. The results allow an analytic characterization of various obstructions to using local optimization methods, revealing in particular a complex array of saddles and minima differing by their symmetry, structure and analytic properties. A desirable phenomenon, occurring for all critical points considered, concerns the number of negative Hessian eigenvalues increasing with the value of the objective function. Our approach makes use of Newton polyhedra as well as results from real algebraic geometry, notably the Curve Selection Lemma, to determine the extremal character of degenerate critical points, establishing in particular the existence of infinite families of third-order saddles which can significantly slow down the optimization process.

Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation monitoring. However, there are limitations; satellites are difficult to manufacture, expensive to maintain, and tricky to launch into orbit. Therefore, satellites must be employed efficiently. This poses a challenge known as the satellite mission planning problem, which could be computationally prohibitive to solve on large scales. However, close-to-optimal algorithms, such as greedy reinforcement learning and optimization algorithms, can often provide satisfactory resolutions. This paper introduces a set of quantum algorithms to solve the mission planning problem and demonstrate an advantage over the classical algorithms implemented thus far. The problem is formulated as maximizing the number of high-priority tasks completed on real datasets containing thousands of tasks and multiple satellites. This work demonstrates that through solution-chaining and clustering, optimization and machine learning algorithms offer the greatest potential for optimal solutions. This paper notably illustrates that a hybridized quantum-enhanced reinforcement learning agent can achieve a completion percentage of 98.5% over high-priority tasks, significantly improving over the baseline greedy methods with a completion rate of 75.8%. The results presented in this work pave the way to quantum-enabled solutions in the space industry and, more generally, future mission planning problems across industries.

Screening classifiers are increasingly used to identify qualified candidates in a variety of selection processes. In this context, it has been recently shown that, if a classifier is calibrated, one can identify the smallest set of candidates which contains, in expectation, a desired number of qualified candidates using a threshold decision rule. This lends support to focusing on calibration as the only requirement for screening classifiers. In this paper, we argue that screening policies that use calibrated classifiers may suffer from an understudied type of within-group unfairness -- they may unfairly treat qualified members within demographic groups of interest. Further, we argue that this type of unfairness can be avoided if classifiers satisfy within-group monotonicity, a natural monotonicity property within each of the groups. Then, we introduce an efficient post-processing algorithm based on dynamic programming to minimally modify a given calibrated classifier so that its probability estimates satisfy within-group monotonicity. We validate our algorithm using US Census survey data and show that within-group monotonicity can be often achieved at a small cost in terms of prediction granularity and shortlist size.

Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its application. Optimal Partial Transport (OPT) is a recently proposed solution to this limitation. Similar to the OT problem, the computation of OPT relies on solving a linear programming problem (often in high dimensions), which can become computationally prohibitive. In this paper, we propose an efficient algorithm for calculating the OPT problem between two non-negative measures in one dimension. Next, following the idea of sliced OT distances, we utilize slicing to define the sliced OPT distance. Finally, we demonstrate the computational and accuracy benefits of the sliced OPT-based method in various numerical experiments. In particular, we show an application of our proposed Sliced-OPT in noisy point cloud registration.

Formation flight has a vast potential for aerial robot swarms in various applications. However, existing methods lack the capability to achieve fully autonomous large-scale formation flight in dense environments. To bridge the gap, we present a complete formation flight system that effectively integrates real-world constraints into aerial formation navigation. This paper proposes a differentiable graph-based metric to quantify the overall similarity error between formations. This metric is invariant to rotation, translation, and scaling, providing more freedom for formation coordination. We design a distributed trajectory optimization framework that considers formation similarity, obstacle avoidance, and dynamic feasibility. The optimization is decoupled to make large-scale formation flights computationally feasible. To improve the elasticity of formation navigation in highly constrained scenes, we present a swarm reorganization method that adaptively adjusts the formation parameters and task assignments by generating local navigation goals. A novel swarm agreement strategy called global-remap-local-replan and a formation-level path planner is proposed in this work to coordinate the global planning and local trajectory optimizations. To validate the proposed method, we design comprehensive benchmarks and simulations with other cutting-edge works in terms of adaptability, predictability, elasticity, resilience, and efficiency. Finally, integrated with palm-sized swarm platforms with onboard computers and sensors, the proposed method demonstrates its efficiency and robustness by achieving the largest scale formation flight in dense outdoor environments.

This report investigates the problem of learning rate optimisation, focusing on techniques that remove the programmer's burden to choose a proper initial learning rate. The report aims to satisfy two purposes: 1. Acting as an intuition-led guide to Defazio and Mishchenko's 2023 Learning-Rate-Free Learning by D-Adaptation [2] and Mahsereci and Hennig's 2015 Probabilistic Line Searches for Stochastic Optimisation [5]. 2. Presenting a unified notation to discuss optimisation techniques, allowing us to bring together the two learning-rate-free approaches and introduce probabilistics to D-Adaptation in the Discussion section (4). We will begin by recapping the general problem of optimisation. This will establish a common language through which to discuss optimisation algorithms, and introduce the notation used in Defazio et al's D-Adaptation paper.