This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization problem, aiming to minimize the output prediction error. This formulation provides a direct bridge between data-driven optimal control and, its dual, optimal filtering.

This paper presents a real-time control framework for nonlinear pure-feedback systems with unknown dynamics to satisfy reach-avoid-stay tasks within a prescribed time in dynamic environments. To achieve this, we introduce a real-time spatiotemporal tube (STT) framework. An STT is defined as a time-varying ball in the state space whose center and radius adapt online using only real-time sensory input. A closed-form, approximation-free control law is then derived to constrain the system output within the STT, ensuring safety and task satisfaction. We provide formal guarantees for obstacle avoidance and on-time task completion. The effectiveness and scalability of the framework are demonstrated through simulations and hardware experiments on a mobile robot and an aerial vehicle, navigating in cluttered dynamic environments.

Neural Information Processing Systems http://nips.cc/

Abstract-- We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounde d norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measur ed data and these prior bounds in a purely data-driven manner . This characterization enables data-consistency verification, inference, and one-step-ahead prediction, which can be leverage d for safety verification and cost minimization. Ultimately, thi s work represents a preliminary step toward exploiting interpola tion conditions in data-driven control, offering a systematic w ay to characterize trajectories consistent with a dynamical sys tem within a given class and enabling their use in control design . Data-driven control has become a crucial aspect of modern control theory, offering powerful tools for system analysis and design [1].

We expect this technique to be of broader interest.

Wasserstein distributionally robust control (DRC) recently emerges as a principled paradigm for handling uncertainty in stochastic dynamical systems. However, it constructs data-driven ambiguity sets via uniform distribution shifts before sequentially incorporating them into downstream control synthesis. This segregation between ambiguity set construction and control objectives inherently introduces a structural misalignment, which undesirably leads to conservative control policies with sub-optimal performance. To address this limitation, we propose a novel end-to-end finite-horizon Wasserstein DRC framework that integrates the learning of anisotropic Wasserstein metrics with downstream control tasks in a closed-loop manner, thus enabling ambiguity sets to be systematically adjusted along performance-critical directions and yielding more effective control policies. This framework is formulated as a bilevel program: the inner level characterizes dynamical system evolution under DRC, while the outer level refines the anisotropic metric leveraging control-performance feedback across a range of initial conditions. To solve this program efficiently, we develop a stochastic augmented Lagrangian algorithm tailored to the bilevel structure. Theoretically, we prove that the learned ambiguity sets preserve statistical finite-sample guarantees under a novel radius adjustment mechanism, and we establish the well-posedness of the bilevel formulation by demonstrating its continuity with respect to the learnable metric. Furthermore, we show that the algorithm converges to stationary points of the outer level problem, which are statistically consistent with the optimal metric at a non-asymptotic convergence rate. Experiments on both numerical and inventory control tasks verify that the proposed framework achieves superior closed-loop performance and robustness compared against state-of-the-art methods.

This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization problem, aiming to minimize the output prediction error. This formulation provides a direct bridge between data-driven optimal control and, its dual, optimal filtering.

We expect this technique to be of broader interest.

This paper investigates the privacy-preserving distributed optimization problem, aiming to protect agents' private information from potential attackers during the optimization process. Gradient tracking, an advanced technique for improving the convergence rate in distributed optimization, has been applied to most first-order algorithms in recent years. We first reveal the inherent privacy leakage risk associated with gradient tracking. Building upon this insight, we propose a weighted gradient tracking distributed privacy-preserving algorithm, eliminating the privacy leakage risk in gradient tracking using decaying weight factors. Then, we characterize the convergence of the proposed algorithm under time-varying heterogeneous step sizes. We prove the proposed algorithm converges precisely to the optimal solution under mild assumptions. Finally, numerical simulations validate the algorithm's effectiveness through a classical distributed estimation problem and the distributed training of a convolutional neural network.