Multimodal synthetic data generation is crucial in domains such as autonomous driving, robotics, augmented/virtual reality, and retail. We propose a novel approach, GenMM, for jointly editing RGB videos and LiDAR scans by inserting temporally and geometrically consistent 3D objects. Our method uses a reference image and 3D bounding boxes to seamlessly insert and blend new objects into target videos. We inpaint the 2D Regions of Interest (consistent with 3D boxes) using a diffusion-based video inpainting model. We then compute semantic boundaries of the object and estimate it's surface depth using state-of-the-art semantic segmentation and monocular depth estimation techniques. Subsequently, we employ a geometry-based optimization algorithm to recover the 3D shape of the object's surface, ensuring it fits precisely within the 3D bounding box. Finally, LiDAR rays intersecting with the new object surface are updated to reflect consistent depths with its geometry. Our experiments demonstrate the effectiveness of GenMM in inserting various 3D objects across video and LiDAR modalities.

We present AB-VINS, a different kind of visual-inertial SLAM system. Unlike most VINS systems which only use hand-crafted techniques, AB-VINS makes use of three different deep networks. Instead of estimating sparse feature positions, AB-VINS only estimates the scale and bias parameters (a and b) of monocular depth maps, as well as other terms to correct the depth using multi-view information which results in a compressed feature state. Despite being an optimization-based system, the main VIO thread of AB-VINS surpasses the efficiency of a state-of-the-art filter-based method while also providing dense depth. While state-of-the-art loop-closing SLAM systems have to relinearize a number of variables linear the number of keyframes, AB-VINS can perform loop closures while only affecting a constant number of variables. This is due to a novel data structure called the memory tree, in which the keyframe poses are defined relative to each other rather than all in one global frame, allowing for all but a few states to be fixed. AB-VINS is not as accurate as state-of-the-art VINS systems, but it is shown through careful experimentation to be more robust.

Adam (Kingma and Ba, 2015) is one of the most widely used optimization algorithms in deep learning. By entry-wisely adjusting the learning rate based on the magnitude of historical gradients, Adam has proven to be highly efficient in solving optimization tasks in machine learning. However, despite the remarkable empirical success of Adam, current theoretical understandings of Adam cannot fully explain its fundamental difference compared with other optimization algorithms. It has been recently pointed out that the implicit bias (Neyshabur et al., 2014; Soudry et al., 2018; Ji and Telgarsky, 2019b) of an optimization algorithm is essential in understanding the performance of the algorithm in machine learning. In over-parameterized learning tasks where the training objective function may have infinitely many solutions, the implicit bias of an optimization algorithm characterizes how the algorithm prioritizes converging towards a specific optimum with particular structures and properties. Several recent works studied the implicit bias of Adam and other adaptive gradient methods. Specifically, Qian and Qian (2019) studied the implicit bias of AdaGrad, and showed that AdaGrad converges to a direction that can be characterized as the solution of a quadratic optimization problem related to the limit of preconditioners. However, their results cannot be extended to Adam.

Differentiable causal discovery has made significant advancements in the learning of directed acyclic graphs. However, its application to real-world datasets remains restricted due to the ubiquity of latent confounders and the requirement to learn maximal ancestral graphs (MAGs). To date, existing differentiable MAG learning algorithms have been limited to small datasets and failed to scale to larger ones (e.g., with more than 50 variables). The key insight in this paper is that the causal skeleton, which is the undirected version of the causal graph, has potential for improving accuracy and reducing the search space of the optimization procedure, thereby enhancing the performance of differentiable causal discovery. Therefore, we seek to address a two-fold challenge to harness the potential of the causal skeleton for differentiable causal discovery in the presence of latent confounders: (1) scalable and accurate estimation of skeleton and (2) universal integration of skeleton estimation with differentiable causal discovery. To this end, we propose SPOT (Skeleton Posterior-guided OpTimization), a two-phase framework that harnesses skeleton posterior for differentiable causal discovery in the presence of latent confounders. On the contrary to a ``point-estimation'', SPOT seeks to estimate the posterior distribution of skeletons given the dataset. It first formulates the posterior inference as an instance of amortized inference problem and concretizes it with a supervised causal learning (SCL)-enabled solution to estimate the skeleton posterior. To incorporate the skeleton posterior with differentiable causal discovery, SPOT then features a skeleton posterior-guided stochastic optimization procedure to guide the optimization of MAGs. [abridged due to length limit]

In robot-assisted minimally invasive surgery (RMIS), inverse kinematics (IK) must satisfy a remote center of motion (RCM) constraint to prevent tissue damage at the incision point. However, most of existing IK methods do not account for the trade-offs between the RCM constraint and other objectives such as joint limits, task performance and manipulability optimization. This paper presents a novel method for manipulability maximization in constrained IK of surgical robots, which optimizes the robot's dexterity while respecting the RCM constraint and joint limits. Our method uses a hierarchical quadratic programming (HQP) framework that solves a series of quadratic programs with different priority levels. We evaluate our method in simulation on a 6D path tracking task for constrained and unconstrained IK scenarios for redundant kinematic chains. Our results show that our method enhances the manipulability index for all cases, with an important increase of more than 100% when a large number of degrees of freedom are available. The average computation time for solving the IK problems was under 1ms, making it suitable for real-time robot control. Our method offers a novel and effective solution to the constrained IK problem in RMIS applications.

This paper considers a consensus optimization problem, where all the nodes in a network, with access to the zeroth-order information of its local objective function only, attempt to cooperatively achieve a common minimizer of the sum of their local objectives. To address this problem, we develop ZoPro, a zeroth-order proximal algorithm, which incorporates a zeroth-order oracle for approximating Hessian and gradient into a recently proposed, high-performance distributed second-order proximal algorithm. We show that the proposed ZoPro algorithm, equipped with a dynamic stepsize, converges linearly to a neighborhood of the optimum in expectation, provided that each local objective function is strongly convex and smooth. Extensive simulations demonstrate that ZoPro converges faster than several state-of-the-art distributed zeroth-order algorithms and outperforms a few distributed second-order algorithms in terms of running time for reaching given accuracy.

Semidefinite programs (SDPs) and their solvers are powerful tools with many applications in machine learning and data science. Designing scalable SDP solvers is challenging because by standard the positive semidefinite decision variable is an $n \times n$ dense matrix, even though the input is often an $n \times n$ sparse matrix. However, the information in the solution may not correspond to a full-rank dense matrix as shown by Bavinok and Pataki. Two decades ago, Burer and Monterio developed an SDP solver $\texttt{SDPLR}$ that optimizes over a low-rank factorization instead of the full matrix. This greatly decreases the storage cost and works well for many problems. The original solver $\texttt{SDPLR}$ tracks only the primal infeasibility of the solution, limiting the technique's flexibility to produce moderate accuracy solutions. We use a suboptimality bound for trace-bounded SDP problems that enables us to track the progress better and perform early termination. We then develop $\texttt{SDPLR+}$, which starts the optimization with an extremely low-rank factorization and dynamically updates the rank based on the primal infeasibility and suboptimality. This further speeds up the computation and saves the storage cost. Numerical experiments on Max Cut, Minimum Bisection, Cut Norm, and Lov\'{a}sz Theta problems with many recent memory-efficient scalable SDP solvers demonstrate its scalability up to problems with million-by-million decision variables and it is often the fastest solver to a moderate accuracy of $10^{-2}$.

Temporal logic rules are often used in control and robotics to provide structured, human-interpretable descriptions of high-dimensional trajectory data. These rules have numerous applications including safety validation using formal methods, constraining motion planning among autonomous agents, and classifying data. However, existing methods for learning temporal logic predicates from data provide no assurances about the correctness of the resulting predicate. We present a novel method to learn temporal logic predicates from data with finite-sample correctness guarantees. Our approach leverages expression optimization and conformal prediction to learn predicates that correctly describe future trajectories under mild assumptions with a user-defined confidence level. We provide experimental results showing the performance of our approach on a simulated trajectory dataset and perform ablation studies to understand how each component of our algorithm contributes to its performance.

Sensor calibration is crucial for autonomous driving, providing the basis for accurate localization and consistent data fusion. Enabling the use of high-accuracy GNSS sensors, this work focuses on the antenna lever arm calibration. We propose a globally optimal multi-antenna lever arm calibration approach based on motion measurements. For this, we derive an optimization method that further allows the integration of a-priori knowledge. Globally optimal solutions are obtained by leveraging the Lagrangian dual problem and a primal recovery strategy. Generally, motion-based calibration for autonomous vehicles is known to be difficult due to cars' predominantly planar motion. Therefore, we first describe the motion requirements for a unique solution and then propose a planar motion extension to overcome this issue and enable a calibration based on the restricted motion of autonomous vehicles. Last we present and discuss the results of our thorough evaluation. Using simulated and augmented real-world data, we achieve accurate calibration results and fast run times that allow online deployment.

Quadrotor flight is an extremely challenging problem due to the limited control authority encountered at the limit of handling. Model Predictive Contouring Control (MPCC) has emerged as a promising model-based approach for time optimization problems such as drone racing. However, the standard MPCC formulation used in quadrotor racing introduces the notion of the gates directly in the cost function, creating a multi objective optimization that continuously trades off between maximizing progress and tracking the path accurately. This paper introduces three key components that enhance the state-of-the-art MPCC approach for drone racing. First and foremost, we provide safety guarantees in the form of a track constraint and terminal set. The track constraint is designed as a spatial constraint which prevents gate collisions while allowing for time optimization only in the cost function. Second, we augment the existing first principles dynamics with a residual term that captures complex aerodynamic effects and thrust forces learned directly from real-world data. Third, we use Trust Region Bayesian Optimization (TuRBO), a state-of-the-art global Bayesian Optimization algorithm, to tune the hyperparameters of the MPCC controller given a sparse reward based on lap time minimization. The proposed approach achieves similar lap times to the best-performing RL policy and outperforms the best model-based controller while satisfying constraints. In both simulation and real world, our approach consistently prevents gate crashes with 100% success rate, while pushing the quadrotor to its physical limits reaching speeds of more than 80km/h.