arXiv subjects

Botao Jin

Publications and source records attributed to Botao Jin.

2 recordsLinked to original sources

arXiv2026

The Price of Covertness: Dual-Control Navigation in Uncertain Flows under Adversarial Sensing

Covert navigation in an uncertain flow couples motion planning with information acquisition. A vehicle must estimate the local flow to navigate, while estimation error induces corrective maneuvers that increase statistical distinguishability, or leakage, and hence the vehicle's detectability. We model this coupling by augmenting position with the estimation-error variance, whose evolution depends on the route through the local information rate. A small-error expansion shows that estimation uncertainty contributes a leading-order correction to the expected detectability rate. The resulting route-planning problem is characterized by a first-order Hamilton--Jacobi--Bellman (HJB) equation. The deadline-indexed value determines the covert-time frontier, while an exact sensitivity formula with respect to sensing quality shows that information acquired earlier along the route can reduce leakage incurred later, whereas information acquired later cannot reduce leakage already incurred. We then formulate a zero-sum sensing-allocation game, show that the leakage rate is convex in the sensing allocation, and prove that the defender may restrict attention to randomization over extreme single-site allocations. The resulting equilibrium is computed by column generation, with vehicle best responses obtained from the HJB equation. Numerical experiments illustrate the learning detour, the deadline--leakage tradeoff, the spatial-ordering effect, and the benefit of randomized sensing allocations.

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arXiv2025

Deep Signature Approach for McKean-Vlasov FBSDEs in a Random Environment

Mean-field games with common noise provide a powerful framework for modeling the collective behavior of large populations subject to shared randomness, such as systemic risk in finance or environmental shocks in economics. These problems can be reformulated as McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) in a random environment, where the coefficients depend on the conditional law of the state given the common noise. Existing numerical methods, however, are largely limited to cases where interactions depend only on expectations or low-order moments, and therefore cannot address the general setting of full distributional dependence. In this work, we introduce a deep learning-based algorithm for solving MV-FBSDEs with common noise and general mean-field interactions. Building on fictitious play, our method iteratively solves conditional FBSDEs with fixed distributions, where the conditional law is efficiently represented using signatures, and then updates the distribution through supervised learning. Deep neural networks are employed both to solve the conditional FBSDEs and to approximate the distribution-dependent coefficients, enabling scalability to high-dimensional problems. Under suitable assumptions, we establish convergence in terms of the fictitious play iterations, with error controlled by the supervised learning step. Numerical experiments, including a distribution-dependent mean-field game with common noise, demonstrate the effectiveness of the proposed approach.

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