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}.

Online optimization with multiple budget constraints is challenging since the online decisions over a short time horizon are coupled together by strict inventory constraints. The existing manually-designed algorithms cannot achieve satisfactory average performance for this setting because they often need a large number of time steps for convergence and/or may violate the inventory constraints. In this paper, we propose a new machine learning (ML) assisted unrolling approach, called LAAU (Learning-Assisted Algorithm Unrolling), which unrolls the online decision pipeline and leverages an ML model for updating the Lagrangian multiplier online. For efficient training via backpropagation, we derive gradients of the decision pipeline over time. We also provide the average cost bounds for two cases when training data is available offline and collected online, respectively. Finally, we present numerical results to highlight that LAAU can outperform the existing baselines.

Express companies are deploying more robotic sorting systems, where mobile robots are used to sort incoming parcels by destination. In this study, we propose an integrated assignment and path-finding method for robots in such sorting systems. The method has two parts: offline and online. In the offline part, we represent the system as a traffic flow network, develop an approximate delay function using stochastic models, and solve the min-cost network flow problem. In the online part, robots are guided through the system according to the calculated optimal flow split probability. The online calculation of the method is decentralized and has linear complexity. Our method outperforms fast multi-agent path planning algorithms like prioritized planning because such algorithms lead to stochastic user equilibrium traffic assignment. In contrast, our method gives the approximated system-optimal traffic assignment. According to our simulations, our method can achieve 10%--20% higher throughput than zoning or random assignment. We also show that our method is robust even if the initial demand estimation is inaccurate.

When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called "neural collapse" phenomenon. More specifically, for the output features of the penultimate layer, for each class the within-class features converge to their means, and the means of different classes exhibit a certain tight frame structure, which is also aligned with the last layer's classifier. As feature normalization in the last layer becomes a common practice in modern representation learning, in this work we theoretically justify the neural collapse phenomenon for normalized features. Based on an unconstrained feature model, we simplify the empirical loss function in a multi-class classification task into a nonconvex optimization problem over the Riemannian manifold by constraining all features and classifiers over the sphere. In this context, we analyze the nonconvex landscape of the Riemannian optimization problem over the product of spheres, showing a benign global landscape in the sense that the only global minimizers are the neural collapse solutions while all other critical points are strict saddles with negative curvature. Experimental results on practical deep networks corroborate our theory and demonstrate that better representations can be learned faster via feature normalization.