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This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
We study the equilibrium of a liquid film on an attractive spherical substrate for an intermolecular interaction model exhibiting both fluid-fluid and fluid-wall long-range forces. We first reexamine the wetting properties of the model in…
Recent studies have highlighted the potential of Lipschitz-based methods for training certifiably robust neural networks against adversarial attacks. A key challenge, supported both theoretically and empirically, is that robustness demands…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…
For optimal control of diffusions under several criteria, due to computational or analytical reasons, many studies have a apriori assumed control policies to be Lipschitz or smooth, often with no rigorous analysis on whether this…
Game-theoretic MPC (or Receding Horizon Games) is an emerging control methodology for multi-agent systems that generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion. This control…
Our work focuses on the design of a scalable permissionless blockchain in the proof-of-stake setting. In particular, we use a distributed hash table as a building block to set up randomized shards, and then leverage the sharded architecture…
In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a DC (Difference of Convex functions) function, where the differentiable function is not restricted to the global Lipschitz gradient…
Certified defenses such as randomized smoothing have shown promise towards building reliable machine learning systems against $\ell_p$-norm bounded attacks. However, existing methods are insufficient or unable to provably defend against…
Illumination variation remains a central challenge in object detection and recognition. Existing analyses of illumination variation typically pertain to convex, Lambertian objects, and guarantee quality of approximation in an average case…
The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as…
We develop a new simulation method for multidimensional diffusions with sticky boundaries. The challenge comes from simulating the sticky boundary behavior, for which standard methods like the Euler scheme fail. We approximate the sticky…
Diffusion models have made significant strides in recent years, exhibiting strong generalization capabilities in planning and control tasks. However, most diffusion-based policies remain focused on reward maximization or cost minimization,…
In this paper, we focus on finding the global minimizer of a general unconstrained nonsmooth nonconvex optimization problem. Taking advantage of the smoothing method and the consensus-based optimization (CBO) method, we propose a novel…
Model attribution is a popular tool to explain the rationales behind model predictions. However, recent work suggests that the attributions are vulnerable to minute perturbations, which can be added to input samples to fool the attributions…
Many safety-critical control systems must operate under latent uncertainty that sensors cannot directly resolve at decision time. Such uncertainty, arising from unknown physical properties, exogenous disturbances, or unobserved environment…
We study vortex matter in layered superconductors in the limit of zero Josephson coupling. The long range of the interaction between pancake vortices in the c-direction allows us to employ a mean-field method: all attractive inter-layer…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
We consider the problem of verifying safety for continuous-time dynamical systems. Developing upon recent advancements in data-driven verification, we use only a finite number of sampled trajectories to learn a barrier certificate, namely a…
In this paper, we address robust static anti-windup compensator design and performance analysis for saturated linear closed loops in the presence of nonlinear probabilistic parameter uncertainties via randomized techniques. The proposed…