Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of real-world scenarios necessitates DS with a higher degree of non-linearity, along with the ability to adapt to potential changes in environmental conditions, such as obstacles. Current learning strategies for DSs often involve a trade-off, sacrificing either stability guarantees or offline computational efficiency in order to enhance the capabilities of the learned DS. Online local adaptation to environmental changes is either not taken into consideration or treated as a separate problem. In this paper, our objective is to introduce a method that enhances the complexity of the learned DS without compromising efficiency during training or stability guarantees. Furthermore, we aim to provide a unified approach for seamlessly integrating the initially learned DS's non-linearity with any local non-linearities that may arise due to changes in the environment. We propose a geometrical approach to learn asymptotically stable non-linear DS for robotics control. Each DS is modeled as a harmonic damped oscillator on a latent manifold. By learning the manifold's Euclidean embedded representation, our approach encodes the non-linearity of the DS within the curvature of the space. Having an explicit embedded representation of the manifold allows us to showcase obstacle avoidance by directly inducing local deformations of the space. We demonstrate the effectiveness of our methodology through two scenarios: first, the 2D learning of synthetic vector fields, and second, the learning of 3D robotic end-effector motions in real-world settings.

Layout synthesis is mapping a quantum circuit to a quantum processor. SWAP gate insertions are needed for scheduling 2-qubit gates only on connected physical qubits. With the ever-increasing number of qubits in NISQ processors, scalable layout synthesis is of utmost importance. With large optimality gaps observed in heuristic approaches, scalable exact methods are needed. While recent exact and near-optimal approaches scale to moderate circuits, large deep circuits are still out of scope. In this work, we propose a SAT encoding based on parallel plans that apply 1 SWAP and a group of CNOTs at each time step. Using domain-specific information, we maintain optimality in parallel plans while scaling to large and deep circuits. From our results, we show the scalability of our approach which significantly outperforms leading exact and near-optimal approaches (up to 100x). For the first time, we can optimally map several 8, 14, and 16 qubit circuits onto 54, 80, and 127 qubit platforms with up to 17 SWAPs. While adding optimal SWAPs, we also report near-optimal depth in our mapped circuits.

We consider a dynamic system with multiple types of customers and servers. Each type of waiting customer or server joins a separate queue, forming a bipartite graph with customer-side queues and server-side queues. The platform can match the servers and customers if their types are compatible. The matched pairs then leave the system. The platform will charge a customer a price according to their type when they arrive and will pay a server a price according to their type. The arrival rate of each queue is determined by the price according to some unknown demand or supply functions. Our goal is to design pricing and matching algorithms to maximize the profit of the platform with unknown demand and supply functions, while keeping queue lengths of both customers and servers below a predetermined threshold. This system can be used to model two-sided markets such as ride-sharing markets with passengers and drivers. The difficulties of the problem include simultaneous learning and decision making, and the tradeoff between maximizing profit and minimizing queue length. We use a longest-queue-first matching algorithm and propose a learning-based pricing algorithm, which combines gradient-free stochastic projected gradient ascent with bisection search. We prove that our proposed algorithm yields a sublinear regret $\tilde{O}(T^{5/6})$ and queue-length bound $\tilde{O}(T^{2/3})$, where $T$ is the time horizon. We further establish a tradeoff between the regret bound and the queue-length bound: $\tilde{O}(T^{1-\gamma/4})$ versus $\tilde{O}(T^{\gamma})$ for $\gamma \in (0, 2/3].$

This paper presents a selective review of statistical computation methods for massive data analysis. A huge amount of statistical methods for massive data computation have been rapidly developed in the past decades. In this work, we focus on three categories of statistical computation methods: (1) distributed computing, (2) subsampling methods, and (3) minibatch gradient techniques. The first class of literature is about distributed computing and focuses on the situation, where the dataset size is too huge to be comfortably handled by one single computer. In this case, a distributed computation system with multiple computers has to be utilized. The second class of literature is about subsampling methods and concerns about the situation, where the sample size of dataset is small enough to be placed on one single computer but too large to be easily processed by its memory as a whole. The last class of literature studies those minibatch gradient related optimization techniques, which have been extensively used for optimizing various deep learning models.

Optimizing robotic action parameters is a significant challenge for manipulation tasks that demand high levels of precision and generalization. Using a model-based approach, the robot must quickly reason about the outcomes of different actions using a predictive model to find a set of parameters that will have the desired effect. The model may need to capture the behaviors of rigid and deformable objects, as well as objects of various shapes and sizes. Predictive models often need to trade-off speed for prediction accuracy and generalization. This paper proposes a framework that leverages the strengths of multiple predictive models, including analytical, learned, and simulation-based models, to enhance the efficiency and accuracy of action parameter optimization. Our approach uses Model Deviation Estimators (MDEs) to determine the most suitable predictive model for any given state-action parameters, allowing the robot to select models to make fast and precise predictions. We extend the MDE framework by not only learning sim-to-real MDEs, but also sim-to-sim MDEs. Our experiments show that these sim-to-sim MDEs provide significantly faster parameter optimization as well as a basis for efficiently learning sim-to-real MDEs through finetuning. The ease of collecting sim-to-sim training data also allows the robot to learn MDEs based directly on visual inputs and local material properties.

Modern robotic systems are required to operate in dense dynamic environments, requiring highly accurate real-time track identification and estimation. For 3D multi-object tracking, recent approaches process a single measurement frame recursively with greedy association and are prone to errors in ambiguous association decisions. Our method, Sliding Window Tracker (SWTrack), yields more accurate association and state estimation by batch processing many frames of sensor data while being capable of running online in real-time. The most probable track associations are identified by evaluating all possible track hypotheses across the temporal sliding window. A novel graph optimization approach is formulated to solve the multidimensional assignment problem with lifted graph edges introduced to account for missed detections and graph sparsity enforced to retain real-time efficiency. We evaluate our SWTrack implementation$^{2}$ on the NuScenes autonomous driving dataset to demonstrate improved tracking performance.

Optimal behaviours of a system to perform a specific task can be achieved by leveraging the coupling between trajectory optimization, stabilization, and design optimization. This approach is particularly advantageous for underactuated systems, which are systems that have fewer actuators than degrees of freedom and thus require for more elaborate control systems. This paper proposes a novel co-design algorithm, namely Robust Trajectory Control with Design optimization (RTC-D). An inner optimization layer (RTC) simultaneously performs direct transcription (DIRTRAN) to find a nominal trajectory while computing optimal hyperparameters for a stabilizing time-varying linear quadratic regulator (TVLQR). RTC-D augments RTC with a design optimization layer, maximizing the system's robustness through a time-varying Lyapunov-based region of attraction (ROA) analysis. This analysis provides a formal guarantee of stability for a set of off-nominal states. The proposed algorithm has been tested on two different underactuated systems: the torque-limited simple pendulum and the cart-pole. Extensive simulations of off-nominal initial conditions demonstrate improved robustness, while real-system experiments show increased insensitivity to torque disturbances.

We pose transductive classification as a matrix completion problem. By assuming the underlying matrix has a low rank, our formulation is able to handle three problems simultaneously: i) multi-label learning, where each item has more than one label, ii) transduction, where most of these labels are unspecified, and iii) missing data, where a large number of features are missing. We obtained satisfactory results on several real-world tasks, suggesting that the low rank assumption may not be as restrictive as it seems. Our method allows for different loss functions to apply on the feature and label entries of the matrix. The resulting nuclear norm minimization problem is solved with a modified fixed-point continuation method that is guaranteed to find the global optimum.

This paper proposes a principled extension of the traditional single-layer flat sparse coding scheme, where a two-layer coding scheme is derived based on theoretical analysis of nonlinear functional approximation that extends recent results for local coordinate coding. The two-layer approach can be easily generalized to deeper structures in a hierarchical multiple-layer manner. Empirically, it is shown that the deep coding approach yields improved performance in benchmark datasets.

A new algorithm for isotonic regression is presented based on recursively partitioning the solution space. We develop efficient methods for each partitioning subproblem through an equivalent representation as a network flow problem, and prove that this sequence of partitions converges to the global solution. These network flow problems can further be decomposed in order to solve very large problems. Success of isotonic regression in prediction and our algorithm's favorable computational properties are demonstrated through simulated examples as large as 2 10