Perception algorithms that provide estimates of their uncertainty are crucial to the development of autonomous robots that can operate in challenging and uncontrolled environments. Such perception algorithms provide the means for having risk-aware robots that reason about the probability of successfully completing a task when planning. There exist perception algorithms that come with models of their uncertainty; however, these models are often developed with assumptions, such as perfect data associations, that do not hold in the real world. Hence the resultant estimated uncertainty is a weak lower bound. To tackle this problem we present introspective perception - a novel approach for predicting accurate estimates of the uncertainty of perception algorithms deployed on mobile robots. By exploiting sensing redundancy and consistency constraints naturally present in the data collected by a mobile robot, introspective perception learns an empirical model of the error distribution of perception algorithms in the deployment environment and in an autonomously supervised manner. In this paper, we present the general theory of introspective perception and demonstrate successful implementations for two different perception tasks. We provide empirical results on challenging real-robot data for introspective stereo depth estimation and introspective visual simultaneous localization and mapping and show that they learn to predict their uncertainty with high accuracy and leverage this information to significantly reduce state estimation errors for an autonomous mobile robot.

--V ertical Federated Learning (VFL) attracts increasing attention because it empowers multiple parties to jointly train a privacy-preserving model over vertically partitioned data. Recent research has shown that applying zeroth-order optimization (ZOO) has many advantages in building a practical VFL algorithm. However, a vital problem with the ZOO-based VFL is its slow convergence rate, which limits its application in handling modern large models. T o address this problem, we propose a cascaded hybrid optimization method in VFL. In this method, the downstream models (clients) are trained with ZOO to protect privacy and ensure that no internal information is shared. Meanwhile, the upstream model (server) is updated with first-order optimization (FOO) locally, which significantly improves the convergence rate, making it feasible to train the large models without compromising privacy and security. We theoretically prove that our VFL framework converges faster than the ZOO-based VFL, as the convergence of our framework is not limited by the size of the server model, making it effective for training large models with the major part on the server . Extensive experiments demonstrate that our method achieves faster convergence than the ZOO-based VFL framework, while maintaining an equivalent level of privacy protection. Moreover, we show that the convergence of our VFL is comparable to the unsafe FOO-based VFL baseline. Additionally, we demonstrate that our method makes the training of a large model feasible. Data availability is essential for machine learning, however, privacy concerns often prevent the direct sharing of data among different parties. This approach allows multiple parties to leverage their data while adhering to the privacy protection measure and the government regulation, such as the General Data Protection Regulation (GDPR) [4]. Bin Gu is with Department of machine learning, Mohamed Bin Za-yed University of Artificial Intelligence, Abu Dhabi, UAE (e-mail: jsgu-bin@gmail.com). Charles Ling, Boyu Wang, Xiang Li, Ganyu Wang is with Department of Computer Science of Western University, London, Ontario, Canada. Qingsong Zhang is with School of Electronic Engineering, Xidian University, Xi'an, China (email: qszhang1995@gmail.com).

Reconfigurable robot swarms are capable of connecting with each other to form complex structures. Current mechanical or magnetic connection mechanisms can be complicated to manufacture, consume high power, have a limited load-bearing capacity, or can only form rigid structures. In this paper, we present our low-cost soft anchor design that enables flexible coupling and decoupling between robots. Our asymmetric anchor requires minimal force to be pushed into the opening of another robot while having a strong pulling force so that the connection between robots can be secured. To maintain this flexible coupling mechanism as an assembled structure, we present our Model Predictive Control (MPC) frameworks with polygon constraints to model the geometric relationship between robots. We conducted experiments on the soft anchor to obtain its force profile, which informed the three-bar linkage model of the anchor in the simulations. We show that the proposed mechanism and MPC frameworks enable the robots to couple, decouple, and perform various behaviors in both the simulation environment and hardware platform. Our code is available at https://github.com/ZoomLabCMU/puzzlebot_anchor . Video is available at https://www.youtube.com/watch?v=R3gFplorCJg .

Numerous applications in machine learning and data analytics can be formulated as equilibrium computation over Riemannian manifolds. Despite the extensive investigation of their Euclidean counterparts, the performance of Riemannian gradient-based algorithms remain opaque and poorly understood. We revisit the original scheme of Riemannian gradient descent (RGD) and analyze it under a geodesic monotonicity assumption, which includes the well-studied geodesically convex-concave min-max optimization problem as a special case. Our main contribution is to show that, despite the phenomenon of distance distortion, the RGD scheme, with a step size that is agnostic to the manifold's curvature, achieves a curvature-independent and linear last-iterate convergence rate in the geodesically strongly monotone setting. To the best of our knowledge, the possibility of curvature-independent rates and/or last-iterate convergence in the Riemannian setting has not been considered before.

For min-max optimization and variational inequalities problems (VIP) encountered in diverse machine learning tasks, Stochastic Extragradient (SEG) and Stochastic Gradient Descent Ascent (SGDA) have emerged as preeminent algorithms. Constant step-size variants of SEG/SGDA have gained popularity, with appealing benefits such as easy tuning and rapid forgiveness of initial conditions, but their convergence behaviors are more complicated even in rudimentary bilinear models. Our work endeavors to elucidate and quantify the probabilistic structures intrinsic to these algorithms. By recasting the constant step-size SEG/SGDA as time-homogeneous Markov Chains, we establish a first-of-its-kind Law of Large Numbers and a Central Limit Theorem, demonstrating that the average iterate is asymptotically normal with a unique invariant distribution for an extensive range of monotone and non-monotone VIPs. Specializing to convex-concave min-max optimization, we characterize the relationship between the step-size and the induced bias with respect to the Von-Neumann's value. Finally, we establish that Richardson-Romberg extrapolation can improve proximity of the average iterate to the global solution for VIPs. Our probabilistic analysis, underpinned by experiments corroborating our theoretical discoveries, harnesses techniques from optimization, Markov chains, and operator theory.

For letting mobile robots travel flexibly through complicated environments, increasing attention has been paid to the whole-body collision evaluation. Most existing works either opt for the conservative corridor-based methods that impose strict requirements on the corridor generation, or ESDF-based methods that suffer from high computational overhead. It is still a great challenge to achieve fast and accurate whole-body collision evaluation. In this paper, we propose a Robo-centric ESDF (RC-ESDF) that is pre-built in the robot body frame and is capable of seamlessly applied to any-shape mobile robots, even for those with non-convex shapes. RC-ESDF enjoys lazy collision evaluation, which retains only the minimum information sufficient for whole-body safety constraint and significantly speeds up trajectory optimization. Based on the analytical gradients provided by RC-ESDF, we optimize the position and rotation of robot jointly, with whole-body safety, smoothness, and dynamical feasibility taken into account. Extensive simulation and real-world experiments verified the reliability and generalizability of our method.

In the pursuit of efficient optimization of expensive-to-evaluate systems, this paper investigates a novel approach to Bayesian multi-objective and multi-fidelity (MOMF) optimization. Traditional optimization methods, while effective, often encounter prohibitively high costs in multi-dimensional optimizations of one or more objectives. Multi-fidelity approaches offer potential remedies by utilizing multiple, less costly information sources, such as low-resolution simulations. However, integrating these two strategies presents a significant challenge. We suggest the innovative use of a trust metric to support simultaneous optimization of multiple objectives and data sources. Our method modifies a multi-objective optimization policy to incorporate the trust gain per evaluation cost as one objective in a Pareto optimization problem, enabling simultaneous MOMF at lower costs. We present and compare two MOMF optimization methods: a holistic approach selecting both the input parameters and the trust parameter jointly, and a sequential approach for benchmarking. Through benchmarks on synthetic test functions, our approach is shown to yield significant cost reductions - up to an order of magnitude compared to pure multi-objective optimization. Furthermore, we find that joint optimization of the trust and objective domains outperforms addressing them in sequential manner. We validate our results using the use case of optimizing laser-plasma acceleration simulations, demonstrating our method's potential in Pareto optimization of high-cost black-box functions. Implementing these methods in existing Bayesian frameworks is simple, and they can be readily extended to batch optimization. With their capability to handle various continuous or discrete fidelity dimensions, our techniques offer broad applicability in solving simulation problems in fields such as plasma physics and fluid dynamics.

In this article, a tutorial introduction to visual-inertial navigation(VIN) is presented. Visual and inertial perception are two complementary sensing modalities. Cameras and inertial measurement units (IMU) are the corresponding sensors for these two modalities. The low cost and light weight of camera-IMU sensor combinations make them ubiquitous in robotic navigation. Visual-inertial Navigation is a state estimation problem, that estimates the ego-motion and local environment of the sensor platform. This paper presents visual-inertial navigation in the classical state estimation framework, first illustrating the estimation problem in terms of state variables and system models, including related quantities representations (Parameterizations), IMU dynamic and camera measurement models, and corresponding general probabilistic graphical models (Factor Graph). Secondly, we investigate the existing model-based estimation methodologies, these involve filter-based and optimization-based frameworks and related on-manifold operations. We also discuss the calibration of some relevant parameters, also initialization of state of interest in optimization-based frameworks. Then the evaluation and improvement of VIN in terms of accuracy, efficiency, and robustness are discussed. Finally, we briefly mention the recent development of learning-based methods that may become alternatives to traditional model-based methods.

One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only started to gain attention theoretically in recent years. With different convergence rates developed for random shuffling and incremental gradient descent, we seek to find an ordering that can improve the convergence rates for the non-replacement form of the algorithm. Based on existing bounds of the distance between the optimal and current iterate, we derive an upper bound that is dependent on the gradients at the beginning of the epoch. Through analysis of the bound, we are able to develop optimal orderings for constant and decreasing step sizes for strongly convex and convex functions. We further test and verify our results through experiments on synthesis and real data sets. In addition, we are able to combine the ordering with mini-batch and further apply it to more complex neural networks, which show promising results.

PyBADS is a Python implementation of the Bayesian Adaptive Direct Search (BADS) algorithm for fast and robust black-box optimization (Acerbi and Ma 2017). BADS is an optimization algorithm designed to efficiently solve difficult optimization problems where the objective function is rough (non-convex, non-smooth), mildly expensive (e.g., the function evaluation requires more than 0.1 seconds), possibly noisy, and gradient information is unavailable. With BADS, these issues are well addressed, making it an excellent choice for fitting computational models using methods such as maximum-likelihood estimation. The algorithm scales efficiently to black-box functions with up to $D \approx 20$ continuous input parameters and supports bounds or no constraints. PyBADS comes along with an easy-to-use Pythonic interface for running the algorithm and inspecting its results. PyBADS only requires the user to provide a Python function for evaluating the target function, and optionally other constraints. Extensive benchmarks on both artificial test problems and large real model-fitting problems models drawn from cognitive, behavioral and computational neuroscience, show that BADS performs on par with or better than many other common and state-of-the-art optimizers (Acerbi and Ma 2017), making it a general model-fitting tool which provides fast and robust solutions.