Planning collision free trajectories in complex environments remains a core challenge in robotics. Existing corridor based planners which rely on decomposition of the free space into collision free subsets scale poorly with environmental complexity and require explicit allocations of time windows to trajectory segments. We introduce a new trajectory parameterization that represents trajectories in a nonconvex collision free corridor as being in a convex cartesian product of balls. This parameterization allows us to decouple problem size from geometric complexity of the solution and naturally avoids explicit time allocation by allowing trajectories to evolve continuously inside ellipsoidal corridors. Building on this representation, we formulate the Orthogonal Trust Region Problem (Orth-TRP), a specialized convex program with separable block constraints, and develop a solver that exploits this parallel structure and the unique structure of each parallel subproblem for efficient optimization. Experiments on a quadrotor trajectory planning benchmark show that our approach produces smoother trajectories and lower runtimes than state-of-the-art corridor based planners, especially in highly complicated environments.

Counterfactual explanation (CE) is a widely used post-hoc method that provides individuals with actionable changes to alter an unfavorable prediction from a machine learning model. Plausible CE methods improve realism by considering data distribution characteristics, but their optimization models introduce a large number of constraints, leading to high computational cost. In this work, we revisit the DACE framework and propose a refined Mixed-Integer Linear Programming (MILP) formulation that significantly reduces the number of constraints in the local outlier factor (LOF) objective component. We also apply the method to a linear SVM classifier with standard scaler. The experimental results show that our approach achieves faster solving times while maintaining explanation quality. These results demonstrate the promise of more efficient LOF modeling in counterfactual explanation and data science applications.

Training robust bimanual manipulation policies via imitation learning requires demonstration data with broad coverage over robot poses, contacts, and scene contexts. However, collecting diverse and precise real-world demonstrations is costly and time-consuming, which hinders scalability. Prior works have addressed this with data augmentation, typically for either eye-in-hand (wrist camera) setups with RGB inputs or for generating novel images without paired actions, leaving augmentation for eye-to-hand (third-person) RGB-D training with new action labels less explored. In this paper, we propose Synthetic Robot Pose Generation for RGB-D Bimanual Data Augmentation (ROPA), an offline imitation learning data augmentation method that fine-tunes Stable Diffusion to synthesize third-person RGB and RGB-D observations of novel robot poses. Our approach simultaneously generates corresponding joint-space action labels while employing constrained optimization to enforce physical consistency through appropriate gripper-to-object contact constraints in bimanual scenarios. We evaluate our method on 5 simulated and 3 real-world tasks. Our results across 2625 simulation trials and 300 real-world trials demonstrate that ROPA outperforms baselines and ablations, showing its potential for scalable RGB and RGB-D data augmentation in eye-to-hand bimanual manipulation. Our project website is available at: https://ropaaug.github.io/.

Classifying hadronic jets using their constituents' kinematic information is a critical task in modern high-energy collider physics. Often, classifiers are designed by targeting the best performance using metrics such as accuracy, AUC, or rejection rates. However, the use of a single metric can lead to the use of architectures that are more model-dependent than competitive alternatives, leading to potential uncertainty and bias in analysis. We explore such trade-offs and demonstrate the consequences of using networks with high performance metrics but low resilience.

Edge intelligence has emerged as a promising strategy to deliver low-latency and ubiquitous services for mobile devices. Recent advances in fine-tuning mechanisms of foundation models have enabled edge intelligence by integrating low-rank adaptation (LoRA) with federated learning. However, in wireless networks, the device heterogeneity and resource constraints on edge devices pose great threats to the performance of federated fine-tuning. To tackle these issues, we propose to optimize federated fine-tuning in heterogenous wireless networks via online learning. First, the framework of switching-based federated fine-tuning in wireless networks is provided. The edge devices switches to LoRA modules dynamically for federated fine-tuning with base station to jointly mitigate the impact of device heterogeneity and transmission unreliability. Second, a tractable upper bound on the inference risk gap is derived based on theoretical analysis. To improve the generalization capability, we formulate a non-convex mixed-integer programming problem with long-term constraints, and decouple it into model switching, transmit power control, and bandwidth allocation subproblems. An online optimization algorithm is developed to solve the problems with polynomial computational complexity. Finally, the simulation results on the SST-2 and QNLI data sets demonstrate the performance gains in test accuracy and energy efficiency.

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a relationship between the observed and unobserved entries of the tensor. The low-rank tensor completion problem is typically solved using numerical optimization techniques, where the rank information is used either implicitly (in the rank minimization approach) or explicitly (in the error minimization approach). Current theories concerning these techniques often study probabilistic recovery guarantees under conditions such as random uniform observations and incoherence requirements. However, if an observation pattern exhibits some low-rank structure that can be exploited, more efficient algorithms with deterministic recovery guarantees can be designed by leveraging this structure. This work shows how to use only standard linear algebra operations to compute the tensor train decomposition of a specific type of ``fiber-wise" observed tensor, where some of the fibers of a tensor (along a single specific mode) are either fully observed or entirely missing, unlike the usual entry-wise observations. From an application viewpoint, this setting is relevant when it is easier to sample or collect a multiway data tensor along a specific mode (e.g., temporal). The proposed completion method is fast and is guaranteed to work under reasonable deterministic conditions on the observation pattern. Through numerical experiments, we showcase interesting applications and use cases that illustrate the effectiveness of the proposed approach.