Fangji Wang

Fangji Wang, Siddhartha Ganguly, Panagiotis Tsiotras

We study a finite-horizon covariance steering problem for discrete-time Markov jump linear systems (MJLS) with both state- and control-dependent multiplicative noise. The objective is to minimize a quadratic running cost while steering the system from given mode-conditioned initial means and covariances to a prescribed terminal mean and covariance. We first show that, without loss of generality, feasible controls may be represented by mode-dependent linear feedback together with feedforward and independent random components, and we highlight that, in contrast to the case without multiplicative noise, a purely affine state-feedback law does not in general suffice. To this end, we introduce a lifted-state formulation that embeds the mean and covariance information into a unified second-moment description, and we prove that the resulting lifted problem is equivalent to the original covariance steering problem formulation. This leads to a lossless relaxation in moment variables and an SDP reformulation for the unconstrained case. We further study chance-constrained covariance steering with ball and half-space constraints on the state and control, derive tractable sufficient convex surrogates, and establish an iterative reference-update scheme to reduce conservatism. Numerical experiments on a finance application illustrate our results.

Fangji Wang, Panagiotis Tsiotras

Branch-and-bound with preactivation splitting has been shown highly effective for deterministic verification of neural networks. In this paper, we extend this framework to the probabilistic setting. We propose BaB-prob that iteratively divides the original problem into subproblems by splitting preactivations and leverages linear bounds computed by linear bound propagation to bound the probability for each subproblem. We prove soundness and completeness of BaB-prob for feedforward-ReLU neural networks. Furthermore, we introduce the notion of uncertainty level and design two efficient strategies for preactivation splitting, yielding BaB-prob-ordered and BaB+BaBSR-prob. We evaluate BaB-prob on untrained networks, MNIST and CIFAR-10 models, respectively, and VNN-COMP 2025 benchmarks. Across these settings, our approach consistently outperforms state-of-the-art approaches in medium- to high-dimensional input problems.