CLOSURE: Fast Quantification of Pose Uncertainty Sets

We investigate uncertainty quantification of 6D pose estimation from keypoint measurements. Assuming unknown-but-bounded measurement noises, a pose uncertainty set (PURSE) is a subset of SE(3) that contains all possible 6D poses compatible with the measurements. Despite being simple to formulate and its ability to embed uncertainty, the PURSE is difficult to manipulate and interpret due to the many abstract nonconvex polynomial constraints. An appealing simplification of PURSE is to find its minimum enclosing geodesic ball (MEGB), i.e., a point pose estimation with minimum worst-case error bound. We contribute (i) a dynamical system perspective, and (ii) a fast algorithm to inner approximate the MEGB. Particularly, we show the PURSE corresponds to the feasible set of a constrained dynamical system, and this perspective allows us to design an algorithm to densely sample the boundary of the PURSE through strategic random walks. We then use the miniball algorithm to compute the MEGB of PURSE samples, leading to an inner approximation. Our algorithm is named CLOSURE (enClosing baLl frOm purSe boUndaRy samplEs) and it enables computing a certificate of approximation tightness by calculating the relative size ratio between the inner approximation and the outer approximation. Running on a single RTX 3090 GPU, CLOSURE achieves the relative ratio of 92.8% on the LM-O object pose estimation dataset and 91.4% on the 3DMatch point cloud registration dataset with the average runtime less than 0.2 second. Obtaining comparable worst-case error bound but 398x and 833x faster than the outer approximation GRCC, CLOSURE enables uncertainty quantification of 6D pose estimation to be implemented in real-time robot perception applications.

Q-SLAM: Quadric Representations for Monocular SLAM

Monocular SLAM has long grappled with the challenge of accurately modeling 3D geometries. Recent advances in Neural Radiance Fields (NeRF)-based monocular SLAM have shown promise, yet these methods typically focus on novel view synthesis rather than precise 3D geometry modeling. This focus results in a significant disconnect between NeRF applications, i.e., novel-view synthesis and the requirements of SLAM. We identify that the gap results from the volumetric representations used in NeRF, which are often dense and noisy. In this study, we propose a novel approach that reimagines volumetric representations through the lens of quadric forms. We posit that most scene components can be effectively represented as quadric planes. Leveraging this assumption, we reshape the volumetric representations with million of cubes by several quadric planes, which leads to more accurate and efficient modeling of 3D scenes in SLAM contexts. Our method involves two key steps: First, we use the quadric assumption to enhance coarse depth estimations obtained from tracking modules, e.g., Droid-SLAM. This step alone significantly improves depth estimation accuracy. Second, in the subsequent mapping phase, we diverge from previous NeRF-based SLAM methods that distribute sampling points across the entire volume space. Instead, we concentrate sampling points around quadric planes and aggregate them using a novel quadric-decomposed Transformer. Additionally, we introduce an end-to-end joint optimization strategy that synchronizes pose estimation with 3D reconstruction.

Discounted Adaptive Online Prediction

Online learning is not always about memorizing everything. Since the future can be statistically very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the classical notion of discounted regret using recently developed techniques in adaptive online learning. Our main result is a new algorithm that adapts to the complexity of both the loss sequence and the comparator, improving the widespread non-adaptive algorithm - gradient descent with a constant learning rate. In particular, our theoretical guarantee does not require any structural assumption beyond convexity, and the algorithm is provably robust to suboptimal hyperparameter tuning. We further demonstrate such benefits through online conformal prediction, a downstream online learning task with set-membership decisions.

PAC-Bayes Generalization Certificates for Learned Inductive Conformal Prediction

Inductive Conformal Prediction (ICP) provides a practical and effective approach for equipping deep learning models with uncertainty estimates in the form of set-valued predictions which are guaranteed to contain the ground truth with high probability. Despite the appeal of this coverage guarantee, these sets may not be efficient: the size and contents of the prediction sets are not directly controlled, and instead depend on the underlying model and choice of score function. To remedy this, recent work has proposed learning model and score function parameters using data to directly optimize the efficiency of the ICP prediction sets. While appealing, the generalization theory for such an approach is lacking: direct optimization of empirical efficiency may yield prediction sets that are either no longer efficient on test data, or no longer obtain the required coverage on test data. In this work, we use PAC-Bayes theory to obtain generalization bounds on both the coverage and the efficiency of set-valued predictors which can be directly optimized to maximize efficiency while satisfying a desired test coverage. In contrast to prior work, our framework allows us to utilize the entire calibration dataset to learn the parameters of the model and score function, instead of requiring a separate hold-out set for obtaining test-time coverage guarantees. We leverage these theoretical results to provide a practical algorithm for using calibration data to simultaneously fine-tune the parameters of a model and score function while guaranteeing test-time coverage and efficiency of the resulting prediction sets. We evaluate the approach on regression and classification tasks, and outperform baselines calibrated using a Hoeffding bound-based PAC guarantee on ICP, especially in the low-data regime.

Uncertainty Quantification of Set-Membership Estimation in Control and Perception: Revisiting the Minimum Enclosing Ellipsoid

Set-membership estimation (SME) outputs a set estimator that guarantees to cover the groundtruth. Such sets are, however, defined by (many) abstract (and potentially nonconvex) constraints and therefore difficult to manipulate. We present tractable algorithms to compute simple and tight overapproximations of SME in the form of minimum enclosing ellipsoids (MEE). We first introduce the hierarchy of enclosing ellipsoids proposed by Nie and Demmel (2005), based on sums-ofsquares relaxations, that asymptotically converge to the MEE of a basic semialgebraic set. This framework, however, struggles in modern control and perception problems due to computational challenges. We contribute three computational enhancements to make this framework practical, namely constraints pruning, generalized relaxed Chebyshev center, and handling non-Euclidean geometry. We showcase numerical examples on system identification and object pose estimation.

InstOptima: Evolutionary Multi-objective Instruction Optimization via Large Language Model-based Instruction Operators

Instruction-based language modeling has received significant attention in pretrained language models. However, the efficiency of instruction engineering remains low and hinders the development of instruction studies. Recent studies have focused on automating instruction generation, but they primarily aim to improve performance without considering other crucial objectives that impact instruction quality, such as instruction length and perplexity. Therefore, we propose a novel approach (i.e., InstOptima) that treats instruction generation as an evolutionary multi-objective optimization problem. In contrast to text edition-based methods, our approach utilizes a large language model (LLM) to simulate instruction operators, including mutation and crossover. Furthermore, we introduce an objective-guided mechanism for these operators, allowing the LLM to comprehend the objectives and enhance the quality of the generated instructions. Experimental results demonstrate improved fine-tuning performance and the generation of a diverse set of high-quality instructions.

Improving Adaptive Online Learning Using Refined Discretization

We study unconstrained Online Linear Optimization with Lipschitz losses. The goal is to simultaneously achieve ($i$) second order gradient adaptivity; and ($ii$) comparator norm adaptivity also known as "parameter freeness" in the literature. Existing regret bounds (Cutkosky and Orabona, 2018; Mhammedi and Koolen, 2020; Jacobsen and Cutkosky, 2022) have the suboptimal $O(\sqrt{V_T\log V_T})$ dependence on the gradient variance $V_T$, while the present work improves it to the optimal rate $O(\sqrt{V_T})$ using a novel continuous-time-inspired algorithm, without any impractical doubling trick. This result can be extended to the setting with unknown Lipschitz constant, eliminating the range ratio problem from prior works (Mhammedi and Koolen, 2020). Concretely, we first show that the aimed simultaneous adaptivity can be achieved fairly easily in a continuous time analogue of the problem, where the environment is modeled by an arbitrary continuous semimartingale. Then, our key innovation is a new discretization argument that preserves such adaptivity in the discrete time adversarial setting. This refines a non-gradient-adaptive discretization argument from (Harvey et al., 2023), both algorithmically and analytically, which could be of independent interest.

SIM-Sync: From Certifiably Optimal Synchronization over the 3D Similarity Group to Scene Reconstruction with Learned Depth

This paper presents SIM-Sync, a certifiably optimal algorithm that estimates camera trajectory and 3D scene structure directly from multiview image keypoints. SIM-Sync fills the gap between pose graph optimization and bundle adjustment; the former admits efficient global optimization but requires relative pose measurements and the latter directly consumes image keypoints but is difficult to optimize globally (due to camera projective geometry). The bridge to this gap is a pretrained depth prediction network. Given a graph with nodes representing monocular images taken at unknown camera poses and edges containing pairwise image keypoint correspondences, SIM-Sync first uses a pretrained depth prediction network to lift the 2D keypoints into 3D scaled point clouds, where the scaling of the per-image point cloud is unknown due to the scale ambiguity in monocular depth prediction. SIM-Sync then seeks to synchronize jointly the unknown camera poses and scaling factors (i.e., over the 3D similarity group). The SIM-Sync formulation, despite nonconvex, allows designing an efficient certifiably optimal solver that is almost identical to the SE-Sync algorithm. We demonstrate the tightness, robustness, and practical usefulness of SIM-Sync in both simulated and real experiments. In simulation, we show (i) SIM-Sync compares favorably with SE-Sync in scale-free synchronization, and (ii) SIM-Sync can be used together with robust estimators to tolerate a high amount of outliers. In real experiments, we show (a) SIM-Sync achieves similar performance as Ceres on bundle adjustment datasets, and (b) SIM-Sync performs on par with ORB-SLAM3 on the TUM dataset with zero-shot depth prediction.

Topology-Aware Resilient Routing Protocol for FANETs: An Adaptive Q-Learning Approach

Flying ad hoc networks (FANETs) play a crucial role in numerous military and civil applications since it shortens mission duration and enhances coverage significantly compared with a single unmanned aerial vehicle (UAV). Whereas, designing an energy-efficient FANET routing protocol with a high packet delivery rate (PDR) and low delay is challenging owing to the dynamic topology changes. In this article, we propose a topology-aware resilient routing strategy based on adaptive Q-learning (TARRAQ) to accurately capture topology changes with low overhead and make routing decisions in a distributed and autonomous way. First, we analyze the dynamic behavior of UAV nodes via the queuing theory, and then the closed-form solutions of neighbors' change rate (NCR) and neighbors' change interarrival time (NCIT) distribution are derived. Based on the real-time NCR and NCIT, a resilient sensing interval (SI) is determined by defining the expected sensing delay of network events. Besides, we also present an adaptive Q-learning approach that enables UAVs to make distributed, autonomous, and adaptive routing decisions, where the above SI ensures that the action space can be updated in time at a low cost. The simulation results verify the accuracy of the topology dynamic analysis model and also prove that our TARRAQ outperforms the Q-learning-based topology-aware routing (QTAR), mobility prediction-based virtual routing (MPVR), and greedy perimeter stateless routing based on energy-efficient hello (EE-Hello) in terms of 25.23%, 20.24%, and 13.73% lower overhead, 9.41%, 14.77%, and 16.70% higher PDR, and 5.12%, 15.65%, and 11.31% lower energy consumption, respectively.

Toward Intelligent and Efficient 6G Networks: JCSC Enabled On-Purpose Machine Communications

Driven by the vision of "intelligent connection of everything" toward 6G, the collective intelligence of networked machines can be fully exploited to improve system efficiency by shifting the paradigm of wireless communication design from naive maximalist approaches to intelligent value-based approaches. In this article, we propose an on-purpose machine communication framework enabled by joint communication, sensing, and computation (JCSC) technology, which employs machine semantics as the interactive information flow. Naturally, there are potential technical barriers to be solved before the widespread adoption of on-purpose communications, including the conception of machine purpose, fast and concise networking strategy, and semantics-aware information exchange mechanism during the process of task-oriented cooperation. Hence, we discuss enabling technologies complemented by a range of open challenges. The simulation result shows that the proposed framework can significantly reduce networking overhead and improve communication efficiency.