Related papers: Finite-sample guarantees for data-driven forward-b…
This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…
The problem of belief tracking in the presence of stochastic actions and observations is pervasive and yet computationally intractable. In this work we show however that probabilistic beliefs can be maintained in factored form exactly and…
This is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T.…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
This paper considers the general problem of transitioning theoretically safe controllers to hardware. Concretely, we explore the application of control barrier functions (CBFs) to sampled-data systems: systems that evolve continuously but…
Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs…
A backward stable numerical calculation of a function with condition number $\kappa$ will have a relative accuracy of $\kappa\epsilon_{\text{machine}}$. Standard formulations and software implementations of finite-strain elastic materials…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
This paper studies finite-time safety and reach-avoid verification for stochastic discrete-time dynamical systems. The aim is to ascertain lower and upper bounds of the probability that, within a predefined finite-time horizon, a system…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…
Ensuring safety for autonomous systems under uncertainty remains challenging, particularly when safety of the true state is required despite the true state not being fully known. Control barrier functions (CBFs) have become widely adopted…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite…
High-probability guarantees in stochastic optimization are often obtained only under strong noise assumptions such as sub-Gaussian tails. We show that such guarantees can also be achieved under the weaker assumption of bounded variance by…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
We present a federated learning framework that is designed to robustly deliver good predictive performance across individual clients with heterogeneous data. The proposed approach hinges upon a superquantile-based learning objective that…
This work establishes a crucial step toward advancing data-driven trajectory-based methods for stochastic systems with unknown mathematical dynamics. In contrast to scenario-based approaches that rely on independent and identically…
This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations…
The advent of fault-tolerant quantum computing (FTQC) promises to tackle classically intractable problems. A key milestone is solving the Navier-Stokes equations (NSE), which has remained formidable for quantum algorithms due to their high…