At the heart of both lossy compression and clustering is a trade-off between the fidelity and size of the learned representation. Our goal is to map out and study the Pareto frontier that quantifies this trade-off. We focus on the optimization of the Deterministic Information Bottleneck (DIB) objective over the space of hard clusterings. To this end, we introduce the primal DIB problem, which we show results in a much richer frontier than its previously studied Lagrangian relaxation when optimized over discrete search spaces. We present an algorithm for mapping out the Pareto frontier of the primal DIB trade-off that is also applicable to other two-objective clustering problems. We study general properties of the Pareto frontier, and we give both analytic and numerical evidence for logarithmic sparsity of the frontier in general. We provide evidence that our algorithm has polynomial scaling despite the super-exponential search space, and additionally, we propose a modification to the algorithm that can be used where sampling noise is expected to be significant. Finally, we use our algorithm to map the DIB frontier of three different tasks: compressing the English alphabet, extracting informative color classes from natural images, and compressing a group theory-inspired dataset, revealing interesting features of frontier, and demonstrating how the structure of the frontier can be used for model selection with a focus on points previously hidden by the cloak of the convex hull.

In the context of autonomous driving, the iterative linear quadratic regulator (iLQR) is known to be an efficient approach to deal with the nonlinear vehicle model in motion planning problems. Particularly, the constrained iLQR algorithm has shown noteworthy advantageous outcomes of computation efficiency in achieving motion planning tasks under general constraints of different types. However, the constrained iLQR methodology requires a feasible trajectory at the first iteration as a prerequisite when the logarithmic barrier function is used. Also, the methodology leaves open the possibility for incorporation of fast, efficient, and effective optimization methods to further speed up the optimization process such that the requirements of real-time implementation can be successfully fulfilled. In this paper, a well-defined motion planning problem is formulated under nonlinear vehicle dynamics and various constraints, and an alternating direction method of multipliers (ADMM) is utilized to determine the optimal control actions leveraging the iLQR. The approach is able to circumvent the feasibility requirement of the trajectory at the first iteration. An illustrative example of motion planning for autonomous vehicles is then investigated. A noteworthy achievement of high computation efficiency is attained with the proposed development; comparing with the constrained iLQR algorithm based on the logarithmic barrier function, our proposed method reduces the average computation time by 31.93%, 38.52%, and 44.57% in the three driving scenarios; compared with the optimization solver IPOPT, our proposed method reduces the average computation time by 46.02%, 53.26%, and 88.43% in the three driving scenarios. As a result, real-time computation and implementation can be realized through our proposed framework, and thus it provides additional safety to the on-road driving tasks.

High-precision camera re-localization technology in a pre-established 3D environment map is the basis for many tasks, such as Augmented Reality, Robotics and Autonomous Driving. The point-based visual re-localization approaches are well-developed in recent decades, but are insufficient in some feature-less cases. In this paper, we design a complete pipeline for camera pose refinement with points and lines, which contains the innovatively designed line extracting CNN named VLSE, the line matching and the pose optimization approaches. We adopt a novel line representation and customize a hybrid convolution block based on the Stacked Hourglass network, to detect accurate and stable line features on images. Then we apply a geometric-based strategy to obtain precise 2D-3D line correspondences using epipolar constraint and reprojection filtering. A following point-line joint cost function is constructed to optimize the camera pose with the initial coarse pose from the pure point-based localization. Sufficient experiments are conducted on open datasets, i.e, line extractor on Wireframe and YorkUrban, localization performance on InLoc duc1 and duc2, to confirm the effectiveness of our point-line joint pose optimization method.

This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems viewpoint of an optimization algorithm, accelerated convergence to a saddle point can be obtained. Instead of requiring the objective function to be strongly-convex--strongly-concave (as necessitated for accelerated convergence of several saddle-point algorithms), uniform fixed-time convergence is guaranteed for functions satisfying only the two-sided Polyak-{\L}ojasiewicz (PL) inequality. A large number of practical problems, including the robust least squares estimation, are known to satisfy the two-sided PL inequality. The proposed method achieves arbitrarily fast convergence compared to any other state-of-the-art method with linear or even super-linear convergence, as also corroborated in numerical case studies.

Although Simultaneous Localization and Mapping (SLAM) has been an active research topic for decades, current state-of-the-art methods still suffer from instability or inaccuracy due to feature insufficiency or its inherent estimation drift, in many civilian environments. To resolve these issues, we propose a navigation system combing the SLAM and prior-map-based localization. Specifically, we consider additional integration of line and plane features, which are ubiquitous and more structurally salient in civilian environments, into the SLAM to ensure feature sufficiency and localization robustness. More importantly, we incorporate general prior map information into the SLAM to restrain its drift and improve the accuracy. To avoid rigorous association between prior information and local observations, we parameterize the prior knowledge as low dimensional structural priors defined as relative distances/angles between different geometric primitives. The localization is formulated as a graph-based optimization problem that contains sliding-window-based variables and factors, including IMU, heterogeneous features, and structure priors. We also derive the analytical expressions of Jacobians of different factors to avoid the automatic differentiation overhead. To further alleviate the computation burden of incorporating structural prior factors, a selection mechanism is adopted based on the so-called information gain to incorporate only the most effective structure priors in the graph optimization. Finally, the proposed framework is extensively tested on synthetic data, public datasets, and, more importantly, on the real UAV flight data obtained from a building inspection task. The results show that the proposed scheme can effectively improve the accuracy and robustness of localization for autonomous robots in civilian applications.

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Federated learning (FL) is a promising distributed framework for collaborative artificial intelligence model training while protecting user privacy. A bootstrapping component that has attracted significant research attention is the design of incentive mechanism to stimulate user collaboration in FL. The majority of works adopt a broker-centric approach to help the central operator to attract participants and further obtain a well-trained model. Few works consider forging participant-centric collaboration among participants to pursue an FL model for their common interests, which induces dramatic differences in incentive mechanism design from the broker-centric FL. To coordinate the selfish and heterogeneous participants, we propose a novel analytic framework for incentivizing effective and efficient collaborations for participant-centric FL. Specifically, we respectively propose two novel game models for contribution-oblivious FL (COFL) and contribution-aware FL (CAFL), where the latter one implements a minimum contribution threshold mechanism. We further analyze the uniqueness and existence for Nash equilibrium of both COFL and CAFL games and design efficient algorithms to achieve equilibrium solutions. Extensive performance evaluations show that there exists free-riding phenomenon in COFL, which can be greatly alleviated through the adoption of CAFL model with the optimized minimum threshold.

This paper presents an optimal motion planning framework to generate versatile energy-optimal quadrupedal jumping motions automatically (e.g., flips, spin). The jumping motions via the centroidal dynamics are formulated as a 12-dimensional black-box optimization problem subject to the robot kino-dynamic constraints. Gradient-based approaches offer great success in addressing trajectory optimization (TO), yet, prior knowledge (e.g., reference motion, contact schedule) is required and results in sub-optimal solutions. The new proposed framework first employed a heuristics-based optimization method to avoid these problems. Moreover, a prioritization fitness function is created for heuristics-based algorithms in robot ground reaction force (GRF) planning, enhancing convergence and searching performance considerably. Since heuristics-based algorithms often require significant time, motions are planned offline and stored as a pre-motion library. A selector is designed to automatically choose motions with user-specified or perception information as input. The proposed framework has been successfully validated only with a simple continuously tracking PD controller in an open-source Mini-Cheetah by several challenging jumping motions, including jumping over a window-shaped obstacle with 30 cm height and left-flipping over a rectangle obstacle with 27 cm height.

With the continuous growth of the global economy and markets, resource imbalance has risen to be one of the central issues in real logistic scenarios. In marine transportation, this trade imbalance leads to Empty Container Repositioning (ECR) problems. Once the freight has been delivered from an exporting country to an importing one, the laden will turn into empty containers that need to be repositioned to satisfy new goods requests in exporting countries. In such problems, the performance that any cooperative repositioning policy can achieve strictly depends on the routes that vessels will follow (i.e., fleet deployment). Historically, Operation Research (OR) approaches were proposed to jointly optimize the repositioning policy along with the fleet of vessels. However, the stochasticity of future supply and demand of containers, together with black-box and non-linear constraints that are present within the environment, make these approaches unsuitable for these scenarios. In this paper, we introduce a novel framework, Configurable Semi-POMDPs, to model this type of problems. Furthermore, we provide a two-stage learning algorithm, "Configure & Conquer" (CC), that first configures the environment by finding an approximation of the optimal fleet deployment strategy, and then "conquers" it by learning an ECR policy in this tuned environmental setting. We validate our approach in large and real-world instances of the problem. Our experiments highlight that CC avoids the pitfalls of OR methods and that it is successful at optimizing both the ECR policy and the fleet of vessels, leading to superior performance in world trade environments.

Given the rapidly changing machine learning environments and expensive data labeling, semi-supervised domain adaptation (SSDA) is imperative when the labeled data from the source domain is statistically different from the partially labeled data from the target domain. Most prior SSDA research is centrally performed, requiring access to both source and target data. However, data in many fields nowadays is generated by distributed end devices. Due to privacy concerns, the data might be locally stored and cannot be shared, resulting in the ineffectiveness of existing SSDA research. This paper proposes an innovative approach to achieve SSDA over multiple distributed and confidential datasets, named by Federated Semi-Supervised Domain Adaptation (FSSDA). FSSDA integrates SSDA with federated learning based on strategically designed knowledge distillation techniques, whose efficiency is improved by performing source and target training in parallel. Moreover, FSSDA controls the amount of knowledge transferred across domains by properly selecting a key parameter, i.e., the imitation parameter. Further, the proposed FSSDA can be effectively generalized to multi-source domain adaptation scenarios. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of FSSDA design.