PyPose is an open-source library for robot learning. It combines a learning-based approach with physics-based optimization, which enables seamless end-to-end robot learning. It has been used in many tasks due to its meticulously designed application programming interface (API) and efficient implementation. From its initial launch in early 2022, PyPose has experienced significant enhancements, incorporating a wide variety of new features into its platform. To satisfy the growing demand for understanding and utilizing the library and reduce the learning curve of new users, we present the fundamental design principle of the imperative programming interface, and showcase the flexible usage of diverse functionalities and modules using an extremely simple Dubins car example. We also demonstrate that the PyPose can be easily used to navigate a real quadruped robot with a few lines of code.

The rising usage of AI and ML-based processing across application domains has exacerbated the need for low-cost ML implementation, specifically for resource-constrained embedded systems. To this end, approximate computing, an approach that explores the power, performance, area (PPA), and behavioral accuracy (BEHAV) trade-offs, has emerged as a possible solution for implementing embedded machine learning. Due to the predominance of MAC operations in ML, designing platform-specific approximate arithmetic operators forms one of the major research problems in approximate computing. Recently there has been a rising usage of AI/ML-based design space exploration techniques for implementing approximate operators. However, most of these approaches are limited to using ML-based surrogate functions for predicting the PPA and BEHAV impact of a set of related design decisions. While this approach leverages the regression capabilities of ML methods, it does not exploit the more advanced approaches in ML. To this end, we propose AxOCS, a methodology for designing approximate arithmetic operators through ML-based supersampling. Specifically, we present a method to leverage the correlation of PPA and BEHAV metrics across operators of varying bit-widths for generating larger bit-width operators. The proposed approach involves traversing the relatively smaller design space of smaller bit-width operators and employing its associated Design-PPA-BEHAV relationship to generate initial solutions for metaheuristics-based optimization for larger operators. The experimental evaluation of AxOCS for FPGA-optimized approximate operators shows that the proposed approach significantly improves the quality-resulting hypervolume for multi-objective optimization-of 8x8 signed approximate multipliers.

Users of public permissionless blockchains can modify the shared state of the network through transactions that are executed by a set of nodes with limited computational resources. To allocate resources among competing transactions most blockchains use transaction fees. Initial transaction fee mechanisms in the Bitcoin and Ethereum blockchains relied on users bidding for transaction inclusion as the main way of pricing congestion. Moreover, all computational resources were bundled into a unique virtual resource ("gas") with fixed relative prices hardcoded in the protocol. Current R&D efforts are focused on improving transaction fee markets along two directions: (1) setting a minimum dynamic base fee (henceforth also called price) that is adjusted by the protocol as function of user demand and (2) unbundling resources so that different resources can be individually priced and their relative prices can also efficiently adjust with demand. In this paper, we propose a new framework for choosing a resource pricing policy that makes significant progress across both directions. We consider the practical problem of a blockchain protocol that has to jointly update the prices of multiple resources at every block. We assume that the type of resources being metered and priced, as well as the block limits and sustainable targets for each resource, are pre-determined.

Performative prediction is a recently proposed framework where predictions guide decision-making and hence influence future data distributions. Such performative phenomena are ubiquitous in various areas, such as transportation, finance, public policy, and recommendation systems. To date, work on performative prediction has only focused on unconstrained scenarios, neglecting the fact that many real-world learning problems are subject to constraints. This paper bridges this gap by studying performative prediction under inequality constraints. Unlike most existing work that provides only performative stable points, we aim to find the optimal solutions. Anticipating performative gradients is a challenging task, due to the agnostic performative effect on data distributions. To address this issue, we first develop a robust primal-dual framework that requires only approximate gradients up to a certain accuracy, yet delivers the same order of performance as the stochastic primal-dual algorithm without performativity. Based on this framework, we then propose an adaptive primal-dual algorithm for location families. Our analysis demonstrates that the proposed adaptive primal-dual algorithm attains $\ca{O}(\sqrt{T})$ regret and constraint violations, using only $\sqrt{T} + 2T$ samples, where $T$ is the time horizon. To our best knowledge, this is the first study and analysis on the optimality of the performative prediction problem under inequality constraints. Finally, we validate the effectiveness of our algorithm and theoretical results through numerical simulations.

A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy management, stealth, or implicit coordination. We formulate the problem of planning under uncertainty when the robot's observations are intermittent but their timing is known via a pre-declared schedule. After having established the appropriate notion of an optimal policy for such settings, we tackle the problem of joint optimization of the cumulative execution cost and the number of state observations, both in expectation under discounts. To approach this multi-objective optimization problem, we introduce an algorithm that can identify the Pareto front for a class of schedules that are advantageous in the discounted setting. The algorithm proceeds in an accumulative fashion, prepending additions to a working set of schedules and then computing incremental changes to the value functions. Because full exhaustive construction becomes computationally prohibitive for moderate-sized problems, we propose a filtering approach to prune the working set. Empirical results demonstrate that this filtering is effective at reducing computation while incurring only negligible reduction in quality. In summarizing our findings, we provide a characterization of the run-time vs quality trade-off involved.

Traditional optimization methods rely on the use of single-precision floating point arithmetic, which can be costly in terms of memory size and computing power. However, mixed precision optimization techniques leverage the use of both single and half-precision floating point arithmetic to reduce memory requirements while maintaining model accuracy. We provide here an algorithm to further reduce memory usage during the training of a model by getting rid of the floating point copy of the parameters, virtually keeping only half-precision numbers. We also explore the benefits of getting rid of the gradient's value by executing the optimizer step during the back-propagation. In practice, we achieve up to 25% lower peak memory use and 15% faster training while maintaining the same level of accuracy.

Stochastic Gradient Descent (SGD), a widely used optimization algorithm in deep learning, is often limited to converging to local optima due to the non-convex nature of the problem. Leveraging these local optima to improve model performance remains a challenging task. Given the inherent complexity of neural networks, the simple arithmetic averaging of the obtained local optima models in undesirable results. This paper proposes a {\em soft merging} method that facilitates rapid merging of multiple models, simplifies the merging of specific parts of neural networks, and enhances robustness against malicious models with extreme values. This is achieved by learning gate parameters through a surrogate of the $l_0$ norm using hard concrete distribution without modifying the model weights of the given local optima models. This merging process not only enhances the model performance by converging to a better local optimum, but also minimizes computational costs, offering an efficient and explicit learning process integrated with stochastic gradient descent. Thorough experiments underscore the effectiveness and superior performance of the merged neural networks.

We present a distributed conjugate gradient method for distributed optimization problems, where each agent computes an optimal solution of the problem locally without any central computation or coordination, while communicating with its immediate, one-hop neighbors over a communication network. Each agent updates its local problem variable using an estimate of the average conjugate direction across the network, computed via a dynamic consensus approach. Our algorithm enables the agents to use uncoordinated step-sizes. We prove convergence of the local variable of each agent to the optimal solution of the aggregate optimization problem, without requiring decreasing step-sizes. In addition, we demonstrate the efficacy of our algorithm in distributed state estimation problems, and its robust counterparts, where we show its performance compared to existing distributed first-order optimization methods.

It is well-known that parallel manipulators are prone to singularities. However, there is still a lack of distance evaluation functions, referred to as metrics, for computing the distance between two 3-RPR configurations. The proposed extrinsic metrics take the combinatorial structure of the manipulator into account as well as different design options. Utilizing these extrinsic metrics, we formulate constrained optimization problems. These problems are aimed at identifying the closest singular configurations for a given non-singular configuration. The solution to the associated system of polynomial equations relies on algorithms from numerical algebraic geometry implemented in the software package \texttt{Bertini}. Furthermore, we have developed a computational pipeline for determining the distance to singularity during a one-parametric motion of the manipulator. To facilitate these computations for the user, an open-source interface is developed between software packages \texttt{Maple}, \texttt{Bertini}, and \texttt{Paramotopy}. The effectiveness of the presented approach is demonstrated based on numerical examples and compared with existing indices evaluating the singularity closeness.

Bayesian Optimization (BO) is an effective approach for global optimization of black-box functions when function evaluations are expensive. Most prior works use Gaussian processes to model the black-box function, however, the use of kernels in Gaussian processes leads to two problems: first, the kernel-based methods scale poorly with the number of data points and second, kernel methods are usually not effective on complex structured high dimensional data due to curse of dimensionality. Therefore, we propose a novel black-box optimization algorithm where the black-box function is modeled using a neural network. Our algorithm does not need a Bayesian neural network to estimate predictive uncertainty and is therefore computationally favorable. We analyze the theoretical behavior of our algorithm in terms of regret bound using advances in NTK theory showing its efficient convergence. We perform experiments with both synthetic and real-world optimization tasks and show that our algorithm is more sample efficient compared to existing methods.