Yuan‐Hua Ni

Lechen Feng, Yuan-Hua Ni

Linear-quadratic regulator (LQR) is a landmark problem in the field of optimal control, which is the concern of this paper. Generally, LQR is classified into state-feedback LQR (SLQR) and output-feedback LQR (OLQR) based on whether the full state is obtained. It has been suggested in existing literature that both SLQR and OLQR could be viewed as \textit{constrained nonconvex matrix optimization} problems in which the only variable to be optimized is the feedback gain matrix. In this paper, we introduce a first-order accelerated optimization framework of handling the LQR problem, and give its convergence analysis for the cases of SLQR and OLQR, respectively. Specifically, a Lipschiz Hessian property of LQR performance criterion is presented, which turns out to be a crucial property for the application of modern optimization techniques. For the SLQR problem, a continuous-time hybrid dynamic system is introduced, whose solution trajectory is shown to converge exponentially to the optimal feedback gain with Nesterov-optimal order $1-\frac{1}{\sqrtκ}$ ($κ$ the condition number). Then, the symplectic Euler scheme is utilized to discretize the hybrid dynamic system, and a Nesterov-type method with a restarting rule is proposed that preserves the continuous-time convergence rate, i.e., the discretized algorithm admits the Nesterov-optimal convergence order. For the OLQR problem, a Hessian-free accelerated framework is proposed, which is a two-procedure method consisting of semiconvex function optimization and negative curvature exploitation. In a time $\mathcal{O}(ε^{-7/4}\log(1/ε))$, the method can find an $ε$-stationary point of the performance criterion; this entails that the method improves upon the $\mathcal{O}(ε^{-2})$ complexity of vanilla gradient descent. Moreover, our method provides the second-order guarantee of stationary point.

Xiyun Li, Yining Ding, Yuhua Jiang et al.

Real-time human-artificial intelligence (AI) collaboration is crucial yet challenging, especially when AI agents must adapt to diverse and unseen human behaviors in dynamic scenarios. Existing large language model (LLM) agents often fail to accurately model the complex human mental characteristics such as domain intentions, especially in the absence of direct communication. To address this limitation, we propose a novel dual process multi-scale theory of mind (DPMT) framework, drawing inspiration from cognitive science dual process theory. Our DPMT framework incorporates a multi-scale theory of mind (ToM) module to facilitate robust human partner modeling through mental characteristic reasoning. Experimental results demonstrate that DPMT significantly enhances human-AI collaboration, and ablation studies further validate the contributions of our multi-scale ToM in the slow system.

Lechen Feng, Yuan-Hua Ni, Xuebo Zhang

A $\mathcal{H}_2$-guaranteed sparse-feedback linear-quadratic (LQ) optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where $\ell_0$-penalty is added into the $\mathcal{H}_2$ cost to penalize the number of communication links among distributed controllers. Then, the sparse-feedback gain is investigated to minimize the modified $\mathcal{H}_2$ cost together with the stability guarantee, and the corresponding main results are of three parts. First, the $\ell_1$ relaxation sparse-feedback LQ problem is of concern, and a two-timescale algorithm is developed based on proximal coordinate descent and primal-dual splitting approach. Second, piecewise quadratic relaxation sparse-feedback LQ control is investigated, which exhibits an accelerated convergence rate. Third, sparse-feedback LQ problem with $\ell_0$-penalty is directly studied through BSUM (Block Successive Upper-bound Minimization) framework, and precise approximation method and variational properties are introduced.