Understanding the geometry of collision-free configuration space (C-free) in the presence of task-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing C-free regions with rigorous certificates due to the complexity of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge rigorous method for approximately decomposing a rational parametrization of C-free into certified polyhedral regions. Our method, called C-IRIS (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parameterization of the configuration space which are rigorously certified to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Based on convex optimization, our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and is fast enough to scale to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in several 2-DOF examples where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa, a 6-DOF UR3e and 12-DOF bimanual manipulators. An implementation of our algorithm is open-sourced in Drake. We furthermore provide examples of our algorithm in interactive Python notebooks.

Data-driven automated laboratories, also called self-driving laboratories, can significantly accelerate molecular synthesis and materials discovery. A key technical challenge of fully autonomous and artificial intelligenceassisted laboratory design is to effectively collect and utilize data from multiple complex processes in order to inform future experimentation. One long-standing template for utilizing experimental and simulation data is the multiresponse surface methodology (RSM) [13], whereby initial data sets are gathered through design of experiments and then statistical models are built for each quantity of interest, analyzed, and hypothesis tested iteratively. In modern scientific and engineering settings, several common paradigms could be considered as specific implementations of this discovery framework, the most common of which are active learning and modelbased optimization techniques such as Bayesian optimization. To account for multiple competing criteria, we utilize an active learning framework based in multiobjective optimization, which utilizes surrogates (such as Gaussian processes), optimization solvers, and multicriteria data acquisition in a closed feedback loop.

We introduce Delta Denoising Score (DDS), a novel scoring function for text-based image editing that guides minimal modifications of an input image towards the content described in a target prompt. DDS leverages the rich generative prior of text-to-image diffusion models and can be used as a loss term in an optimization problem to steer an image towards a desired direction dictated by a text. DDS utilizes the Score Distillation Sampling (SDS) mechanism for the purpose of image editing. We show that using only SDS often produces non-detailed and blurry outputs due to noisy gradients. To address this issue, DDS uses a prompt that matches the input image to identify and remove undesired erroneous directions of SDS. Our key premise is that SDS should be zero when calculated on pairs of matched prompts and images, meaning that if the score is non-zero, its gradients can be attributed to the erroneous component of SDS. Our analysis demonstrates the competence of DDS for text based image-to-image translation. We further show that DDS can be used to train an effective zero-shot image translation model. Experimental results indicate that DDS outperforms existing methods in terms of stability and quality, highlighting its potential for real-world applications in text-based image editing.

Penetration depth (PD) is essential for robotics due to its extensive applications in dynamic simulation, motion planning, haptic rendering, etc. The Expanding Polytope Algorithm (EPA) is the de facto standard for this problem, which estimates PD by expanding an inner polyhedral approximation of an implicit set. In this paper, we propose a novel optimization-based algorithm that incrementally estimates minimum penetration depth and its direction. One major advantage of our method is that it can be warm-started by exploiting the spatial and temporal coherence, which emerges naturally in many robotic applications (e.g., the temporal coherence between adjacent simulation time knots). As a result, our algorithm achieves substantial speedup -- we demonstrate it is 5-30x faster than EPA on several benchmarks. Moreover, our approach is built upon the same implicit geometry representation as EPA, which enables easy integration and deployment into existing software stacks. We also provide an open-source implementation for further evaluations and experiments.

Traditional revenue management relies on long and stable historical data and predictable demand patterns. However, meeting those requirements is not always possible. Many industries face demand volatility on an ongoing basis, an example would be air cargo which has much shorter booking horizon with highly variable batch arrivals. Even for passenger airlines where revenue management (RM) is well-established, reacting to external shocks is a well-known challenge that requires user monitoring and manual intervention. Moreover, traditional RM comes with strict data requirements including historical bookings and pricing even in the absence of any bookings, spanning multiple years. For companies that have not established a practice in RM, that type of extensive data is usually not available. We present a data-driven approach to RM which eliminates the need for demand forecasting and optimization techniques. We develop a methodology to generate bid prices using historical booking data only. Our approach is an ex-post greedy heuristic to estimate proxies for marginal opportunity costs as a function of remaining capacity and time-to-departure solely based on historical booking data. We utilize a neural network algorithm to project bid price estimations into the future. We conduct an extensive simulation study where we measure performance of our methodology compared to that of an optimally generated bid price using dynamic programming (DP). We also extend our simulations to measure performance of both data-driven and DP generated bid prices under the presence of demand misspecification. Our results show that our data-driven methodology stays near a theoretical optimum (<1% revenue gap) for a wide-range of settings, whereas DP deviates more significantly from the optimal as the magnitude of misspecification is increased. This highlights the robustness of our data-driven approach.

The large-scale multiobjective optimization problem (LSMOP) is characterized by simultaneously optimizing multiple conflicting objectives and involving hundreds of decision variables. Many real-world applications in engineering fields can be modeled as LSMOPs; simultaneously, engineering applications require insensitivity in performance. This requirement usually means that the results from the algorithm runs should not only be good for every run in terms of performance but also that the performance of multiple runs should not fluctuate too much, i.e., the algorithm shows good insensitivity. Considering that substantial computational resources are requested for each run, it is essential to improve upon the performance of the large-scale multiobjective optimization algorithm, as well as the insensitivity of the algorithm. However, existing large-scale multiobjective optimization algorithms solely focus on improving the performance of the algorithms, leaving the insensitivity characteristics unattended. In this work, we propose an evolutionary algorithm for solving LSMOPs based on Monte Carlo tree search, the so-called LMMOCTS, which aims to improve the performance and insensitivity for large-scale multiobjective optimization problems. The proposed method samples the decision variables to construct new nodes on the Monte Carlo tree for optimization and evaluation. It selects nodes with good evaluation for further search to reduce the performance sensitivity caused by large-scale decision variables. We compare the proposed algorithm with several state-of-the-art designs on different benchmark functions. We also propose two metrics to measure the sensitivity of the algorithm. The experimental results confirm the effectiveness and performance insensitivity of the proposed design for solving large-scale multiobjective optimization problems.

Recent years have seen a rise in the popularity of quality diversity (QD) optimization, a branch of optimization that seeks to find a collection of diverse, high-performing solutions to a given problem. To grow further, we believe the QD community faces two challenges: developing a framework to represent the field's growing array of algorithms, and implementing that framework in software that supports a range of researchers and practitioners. To address these challenges, we have developed pyribs, a library built on a highly modular conceptual QD framework. By replacing components in the conceptual framework, and hence in pyribs, users can compose algorithms from across the QD literature; equally important, they can identify unexplored algorithm variations. Furthermore, pyribs makes this framework simple, flexible, and accessible, with a user-friendly API supported by extensive documentation and tutorials. This paper overviews the creation of pyribs, focusing on the conceptual framework that it implements and the design principles that have guided the library's development.

Classical paradigms for distributed learning, such as federated or decentralized gradient descent, employ consensus mechanisms to enforce homogeneity among agents. While these strategies have proven effective in i.i.d. scenarios, they can result in significant performance degradation when agents follow heterogeneous objectives or data. Distributed strategies for multitask learning, on the other hand, induce relationships between agents in a more nuanced manner, and encourage collaboration without enforcing consensus. We develop a generalization of the exact diffusion algorithm for subspace constrained multitask learning over networks, and derive an accurate expression for its mean-squared deviation when utilizing noisy gradient approximations. We verify numerically the accuracy of the predicted performance expressions, as well as the improved performance of the proposed approach over alternatives based on approximate projections.

This paper presents a non-iterative approach for finding the assignment of heterogeneous robots to efficiently execute online Pickup and Just-In-Time Delivery (PJITD) tasks with optimal resource utilization. The PJITD assignments problem is formulated as a spatio-temporal multi-task assignment (STMTA) problem. The physical constraints on the map and vehicle dynamics are incorporated in the cost formulation. The linear sum assignment problem is formulated for the heterogeneous STMTA problem. The recently proposed Dynamic Resource Allocation with Multi-task assignments (DREAM) approach has been modified to solve the heterogeneous PJITD problem. At the start, it computes the minimum number of robots required (with their types) to execute given heterogeneous PJITD tasks. These required robots are added to the team to guarantee the feasibility of all PJITD tasks. Then robots in an updated team are assigned to execute the PJITD tasks while minimizing the total cost for the team to execute all PJITD tasks. The performance of the proposed non-iterative approach has been validated using high-fidelity software-in-loop simulations and hardware experiments. The simulations and experimental results clearly indicate that the proposed approach is scalable and provides optimal resource utilization.

The Iterative Closest Point (ICP) algorithm and its variants are a fundamental technique for rigid registration between two point sets, with wide applications in different areas from robotics to 3D reconstruction. The main drawbacks for ICP are its slow convergence as well as its sensitivity to outliers, missing data, and partial overlaps. Recent work such as Sparse ICP achieves robustness via sparsity optimization at the cost of computational speed. In this paper, we propose a new method for robust registration with fast convergence. First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to speed up its convergence. In addition, we introduce a robust error metric based on the Welsch's function, which is minimized efficiently using the MM algorithm with Anderson acceleration. On challenging datasets with noises and partial overlaps, we achieve similar or better accuracy than Sparse ICP while being at least an order of magnitude faster. Finally, we extend the robust formulation to point-to-plane ICP, and solve the resulting problem using a similar Anderson-accelerated MM strategy. Our robust ICP methods improve the registration accuracy on benchmark datasets while being competitive in computational time.