1. M.K. Wafi, A.C.B de Oliveira, and E.D. Sontag. On the (almost) global exponential convergence of overparameterized policy optimization for the LQR problem. In 2026 American Control Conference (ACC), 2026. Note: To appear. See also 2025 arXiv:2510.02140. [PDF] Keyword(s): gradient dynamics, gradient descent, gradient systems, numerical methods, dynamics of algorithms, gradient dominance, gradient flows, machine learning, artificial intelligence, dynamics of algorithms, LQR, reinforcement learning. Abstract:

   In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple example that, surprisingly, the gradient flow solution can be exponentially or asymptotically convergent, depending on how the problem is formulated. We then deepen the analysis and show that a policy optimization strategy for the continuous-time linear quadratic regulator (LQR) (which is known to present only asymptotic convergence globally) presents almost global exponential convergence if the problem is overparameterized through a linear feed-forward neural network (LFFNN). We prove this qualitative improvement always happens for a simplified version of the LQR problem and derive explicit convergence rates for the gradient flow. Finally, we show that both the qualitative improvement and the quantitative rate gains persist in the general LQR through numerical simulations.




2. M.K. Wafi, A.C.B de Oliveira, and E.D. Sontag. When is cumulative dose response monotonic? Analysis of incoherent feedforward motifs. In Proc. 65th IEEE Conference on Decision and Control (CDC), 2026. Note: Submitted. Also arXiv:2604.01573. Keyword(s): dose response, perfect adaptation, systems biology, incoherent feedforward loops, transient behavior. Abstract:

   We study the monotonicity of the cumulative dose response (cDR) for a class of incoherent feedforward motif (IFFMs) systems with linear intermediate dynamics and nonlinear output dynamics. While the instantaneous dose response (DR) may be nonmonotone with respect to the input, the cDR can still be monotone. To analyze this phenomenon, we derive an integral representation of the sensitivity of cDR with respect to the input and establish general sufficient conditions for both monotonicity and non-monotonicity. These results reduce the problem to verifying qualitative sign properties along system trajectories. We apply this framework to four canonical IFFM systems and obtain a complete characterization of their behavior. In particular, IFFM1 and IFFM3 exhibit monotone cDR despite potentially non-monotone DR, while IFFM2 is monotone already at the level of DR, which implies monotonicity of cDR. In contrast, IFFM4 violates these conditions, leading to a loss of monotonicity. Numerical simulations indicate that these properties persist beyond the structured initial conditions used in the analysis. Overall, our results provide a unified framework for understanding how network structure governs monotonicity in cumulative input–output responses.

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