As the use of robotics becomes more widespread, the huge amount of vision data leads to a dramatic increase in data dimensionality. Although deep learning methods can effectively process these high-dimensional vision data. Due to the limitation of computational resources, some special scenarios still rely on traditional machine learning methods. However, these high-dimensional visual data lead to great challenges for traditional machine learning methods. Therefore, we propose a Lite Fireworks Algorithm with Fractal Dimension constraint for feature selection (LFWA+FD) and use it to solve the feature selection problem driven by robot vision. The "LFWA+FD" focuses on searching the ideal feature subset by simplifying the fireworks algorithm and constraining the dimensionality of selected features by fractal dimensionality, which in turn reduces the approximate features and reduces the noise in the original data to improve the accuracy of the model. The comparative experimental results of two publicly available datasets from UCI show that the proposed method can effectively select a subset of features useful for model inference and remove a large amount of noise noise present in the original data to improve the performance.

This paper presents a scalable online algorithm to generate safe and kinematically feasible trajectories for quadrotor swarms. Existing approaches rely on linearizing Euclidean distance-based collision constraints and on axis-wise decoupling of kinematic constraints to reduce the trajectory optimization problem for each quadrotor to a quadratic program (QP). This conservative approximation often fails to find a solution in cluttered environments. We present a novel alternative that handles collision constraints without linearization and kinematic constraints in their quadratic form while still retaining the QP form. We achieve this by reformulating the constraints in a polar form and applying an Alternating Minimization algorithm to the resulting problem. Through extensive simulation results, we demonstrate that, as compared to Sequential Convex Programming (SCP) baselines, our approach achieves on average a 72% improvement in success rate, a 36% reduction in mission time, and a 42 times faster per-agent computation time. We also show that collision constraints derived from discrete-time barrier functions (BF) can be incorporated, leading to different safety behaviours without significant computational overhead. Moreover, our optimizer outperforms the state-of-the-art optimal control solver ACADO in handling BF constraints with a 31 times faster per-agent computation time and a 44% reduction in mission time on average. We experimentally validated our approach on a Crazyflie quadrotor swarm of up to 12 quadrotors. The code with supplementary material and video are released for reference.

Federated sampling algorithms have recently gained great popularity in the community of machine learning and statistics. This paper studies variants of such algorithms called Error Feedback Langevin algorithms (ELF). In particular, we analyze the combinations of EF21 and EF21-P with the federated Langevin Monte-Carlo. We propose three algorithms: P-ELF, D-ELF, and B-ELF that use, respectively, primal, dual, and bidirectional compressors. We analyze the proposed methods under Log-Sobolev inequality and provide non-asymptotic convergence guarantees.

It is often overlooked by roboticists when designing locomotion controllers for their legged machines, that energy consumption plays an important role in selecting the best gaits for locomotion at high speeds or over long distances. The purpose of this study is to examine four similar asymmetrical quadrupedal gaits that are frequently observed in legged animals in nature. To understand how a specific footfall pattern will change the energetics of a legged system, we first developed a full body model of a quadrupedal robot called A1. And for each gait we created a hybrid system with desired footfall sequence and rigid impacts. In order to find the most energy efficient gait, we used optimal control methods to formulate the problem as a trajectory optimization problem with proper constraints and objective function. This problem was implemented and solved in a nonlinear programming framework called FROST. Based on the optimized trajectories for each gait, we investigated the values of cost of transport and the work done by all joints. Moreover, we analyzed the exchange of angular momentum in different components of the system during the whole stride cycle. According to the simulation results, bounding with two flight phases is likely to be the most energy efficient gait for A1 across a wide range of speed.

In this paper, we address the lack of datasets for - and the issue of reproducibility in - collaborative SLAM pose graph optimizers by providing a novel pose graph generator. Our pose graph generator, kollagen, is based on a random walk in a planar grid world, similar to the popular M3500 dataset for single agent SLAM. It is simple to use and the user can set several parameters, e.g., the number of agents, the number of nodes, loop closure generation probabilities, and standard deviations of the measurement noise. Furthermore, a qualitative execution time analysis of our pose graph generator showcases the speed of the generator in the tunable parameters. In addition to the pose graph generator, our paper provides two example datasets that researchers can use out-of-the-box to evaluate their algorithms. One of the datasets has 8 agents, each with 3500 nodes, and 67645 constraints in the pose graphs, while the other has 5 agents, each with 10000 nodes, and 76134 constraints. In addition, we show that current state-of-the-art pose graph optimizers are able to process our generated datasets and perform pose graph optimization. The data generator can be found at https://github.com/EricssonResearch/kollagen.

Monitoring the Covid19 pandemic constitutes a critical societal stake that received considerable research efforts. The intensity of the pandemic on a given territory is efficiently measured by the reproduction number, quantifying the rate of growth of daily new infections. Recently, estimates for the time evolution of the reproduction number were produced using an inverse problem formulation with a nonsmooth functional minimization. While it was designed to be robust to the limited quality of the Covid19 data (outliers, missing counts), the procedure lacks the ability to output credibility interval based estimates. This remains a severe limitation for practical use in actual pandemic monitoring by epidemiologists that the present work aims to overcome by use of Monte Carlo sampling. After interpretation of the nonsmooth functional into a Bayesian framework, several sampling schemes are tailored to adjust the nonsmooth nature of the resulting posterior distribution. The originality of the devised algorithms stems from combining a Langevin Monte Carlo sampling scheme with Proximal operators. Performance of the new algorithms in producing relevant credibility intervals for the reproduction number estimates and denoised counts are compared. Assessment is conducted on real daily new infection counts made available by the Johns Hopkins University. The interest of the devised monitoring tools are illustrated on Covid19 data from several different countries.

Auditing large language models for unexpected behaviors is critical to preempt catastrophic deployments, yet remains challenging. In this work, we cast auditing as an optimization problem, where we automatically search for input-output pairs that match a desired target behavior. For example, we might aim to find a non-toxic input that starts with "Barack Obama" that a model maps to a toxic output. This optimization problem is difficult to solve as the set of feasible points is sparse, the space is discrete, and the language models we audit are non-linear and high-dimensional. To combat these challenges, we introduce a discrete optimization algorithm, ARCA, that jointly and efficiently optimizes over inputs and outputs. Our approach automatically uncovers derogatory completions about celebrities (e.g. "Barack Obama is a legalized unborn" -> "child murderer"), produces French inputs that complete to English outputs, and finds inputs that generate a specific name. Our work offers a promising new tool to uncover models' failure-modes before deployment.

Before delving into optimization methods, it's critical to understand the various types of functions utilised in machine learning. Constrained functions are mathematical expressions that are subject to certain constraints or rules. These restrictions can take the form of equalities or inequalities that the function's input and output must satisfy. A limitation could, for example, be that the function's input must be inside a certain range. The two most prevalent types of constrained functions are Linear programming, in which both the objective function and constraints are linear, and quadratic programming, in which the objective function is quadratic in form.

This impact is estimated about 50% of the total energy consumption in the chip [1]. This places the memory subsystem as one of the most important sources to improve both performance and energy consumption. Concerns such as thermal issues or high energy consumption can cause a significant performance degradation, as well as irreversible damages to the devices therefore increasing the energy cost. Previous works have shown that saving energy in the memory subsystem can effectively control transistors aging effect and can significantly extend lifetime of the internal structures [2]. Technological changes combined with the development of communications have led to the great expansion of mobile devices such as smartphones, tablets, etc. Mobile devices have evolved rapidly to adapt to the new requirements, giving support to multimedia applications. These devices are supplied with embedded systems, which are mainly battery-powered and usually have less computing resources than desktop systems. Additionally, multimedia applications are usually memory intensive, so they have high performance requirements which implies a high energy consumption. These features increase the pressure on the whole memory subsystem. Processor registers, smaller in size, work at the same speed than the processor and consume less energy compared with other levels of the memory subsystem.

In this paper, we focus on a novel optimization problem in which the objective function is a black-box and can only be evaluated through a ranking oracle. This problem is common in real-world applications, particularly in cases where the function is assessed by human judges. Reinforcement Learning with Human Feedback (RLHF) is a prominent example of such an application, which is adopted by the recent works \cite{ouyang2022training,liu2023languages,chatgpt,bai2022training} to improve the quality of Large Language Models (LLMs) with human guidance. We propose ZO-RankSGD, a first-of-its-kind zeroth-order optimization algorithm, to solve this optimization problem with a theoretical guarantee. Specifically, our algorithm employs a new rank-based random estimator for the descent direction and is proven to converge to a stationary point. ZO-RankSGD can also be directly applied to the policy search problem in reinforcement learning when only a ranking oracle of the episode reward is available. This makes ZO-RankSGD a promising alternative to existing RLHF methods, as it optimizes in an online fashion and thus can work without any pre-collected data. Furthermore, we demonstrate the effectiveness of ZO-RankSGD in a novel application: improving the quality of images generated by a diffusion generative model with human ranking feedback. Throughout experiments, we found that ZO-RankSGD can significantly enhance the detail of generated images with only a few rounds of human feedback. Overall, our work advances the field of zeroth-order optimization by addressing the problem of optimizing functions with only ranking feedback, and offers an effective approach for aligning human and machine intentions in a wide range of domains. Our code is released here \url{https://github.com/TZW1998/Taming-Stable-Diffusion-with-Human-Ranking-Feedback}.