arXiv subjects

Chih-Fan Pai

Publications and source records attributed to Chih-Fan Pai.

5 recordsLinked to original sources

arXiv2026

Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squares

We study online prediction for marginally stable, partially observed linear dynamical systems under nonstochastic disturbances. Our objective is to minimize the cumulative squared prediction loss and compete with the best-in-hindsight Luenberger predictor. Standard online learning methods typically rely on bounded domains/gradients, and thus their guarantees may fail to deal with potentially unbounded trajectories in marginally stable systems. In this paper, we introduce an unconstrained online least squares method that stabilizes the learning process via tailored predictive hints. With model knowledge, we prove that hints constructed from any stabilizing Luenberger predictor render the hint residuals uniformly bounded, achieving logarithmic regret despite unbounded trajectory growth. We also discuss model-free prediction and introduce a simple universal hint for symmetric systems, under which logarithmic regret is maintained without model knowledge. Our results provide an adaptive, instance-wise optimal online predictor compared to classical fixed-gain observers under nonstochastic disturbances.

cs.LG↗

arXiv2026

Online Tracking with Predictions for Nonlinear Systems with Koopman Linear Embedding

We study the problem of online tracking in unknown nonlinear dynamical systems, where only short-horizon predictions of future target states are available. This setting arises in practical scenarios where full future information and exact system dynamics are unavailable. We focus on a class of nonlinear systems that admit a Koopman linear embedding, enabling the dynamics to evolve linearly in a lifted space. Exploiting this structure, we analyze a model-free predictive tracking algorithm based on Willems' fundamental lemma, which imposes dynamic constraints using only past data within a receding-horizon control framework. We show that, for Koopman-linearizable systems, the cumulative cost and dynamic regret of the nonlinear tracking problem coincide with those of the lifted linear counterpart. Moreover, we prove that the dynamic regret of our algorithm decays exponentially with the prediction horizon, as validated by numerical experiments.

math.OC↗

arXiv2026

Policy Optimization of Mixed H2/H-infinity Control: Benign Nonconvexity and Global Optimality

Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer limited insight into the nonconvex optimization landscape and do not readily scale to large-scale or data-driven settings. In this paper, we revisit mixed H2/H-infinity control from a modern policy optimization viewpoint, including the general two-channel and single-channel cases. One central result is that both cases enjoy a benign nonconvex structure: every stationary point is globally optimal. We characterize the H-infinity-constrained feasible set, which is open, path-connected, with boundary given exactly by policies saturating the H-infinity constraint. We also show that the mixed objective is real analytic in the interior with explicit gradient formulas. Our key analysis builds on an Extended Convex Lifting (ECL) framework that bridges nonconvex policy optimization and convex reformulations. The ECL constructions rely on non-strict Riccati inequalities that allow us to characterize global optimality. These insights reveal hidden convexity in mixed H2/H-infinity control and facilitate the design of scalable policy iteration methods in large-scale settings.

math.OC↗

arXiv2025

Semidefinite Programming Duality in Infinite-Horizon Linear Quadratic Differential Games

Semidefinite programs (SDPs) play a crucial role in control theory, traditionally as a computational tool. Beyond computation, the duality theory in convex optimization also provides valuable analytical insights and new proofs of classical results in control. In this work, we extend this analytical use of SDPs to study the infinite-horizon linear-quadratic (LQ) differential game in continuous time. Under standard assumptions, we introduce a new SDP-based primal-dual approach to establish the saddle point characterized by linear static policies in LQ games. For this, we leverage the Gramian representation technique, which elegantly transforms linear quadratic control problems into tractable convex programs. We also extend this duality-based proof to the $\mathcal{H}_\infty$ suboptimal control problem. To our knowledge, this work provides the first primal-dual analysis using Gramian representations for the LQ game and $\mathcal{H}_\infty$ control beyond LQ optimal control and $\mathcal{H}_\infty$ analysis.

math.OC↗

arXiv2024

Benign Nonconvex Landscapes in Optimal and Robust Control, Part II: Extended Convex Lifting

Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In Part II of this paper, we introduce a new and unified Extended Convex Lifting (ECL) framework to reveal hidden convexity in classical optimal and robust control problems from a modern optimization perspective. Our ECL offers a bridge between nonconvex policy optimization and convex reformulations, enabling convex analysis for nonconvex problems. Despite non-convexity and non-smoothness, the existence of an ECL not only reveals that minimizing the original function is equivalent to a convex problem but also certifies a class of first-order non-degenerate stationary points to be globally optimal. Therefore, no spurious stationarity exists in the set of non-degenerate policies. This ECL framework can cover many benchmark control problems, including state feedback linear quadratic regulator (LQR), dynamic output feedback linear quadratic Gaussian (LQG) control, and $\mathcal{H}_\infty$ robust control. ECL can also handle a class of distributed control problems when the notion of quadratic invariance (QI) holds. We further show that all static stabilizing policies are non-degenerate for state feedback LQR and $\mathcal{H}_\infty$ control under standard assumptions. We believe that the new ECL framework may be of independent interest for analyzing nonconvex problems beyond control.

math.OC↗