Research
Research
Research
Research
2,595+ open-access research outputs.
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in …
This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games. We reformulate the game as a regenerative problem with deterministic cycles, which allows polic…
A polynomial approximation of the minimum energy estimator, also called Mortensen observer, is discussed. The method relies on successive differentiations of an underlying value function and the Hamil…
In this paper, we propose a novel Physics-Informed Neural Network (PINN) framework based on the Cord\`{e}s condition for solving both linear and fully nonlinear partial differential equations (PDEs) i…
Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only…
Backward stochastic differential equation (BSDE) provides probabilistic solutions for a class of parabolic partial differential equations (PDEs). DeepBSDE and FBSNN are two deep learning approaches fo…
We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. I…
We study the control of finite-state systems driven by exogenous disturbances, and design causal policies that track the performance of a lookahead benchmark controller. This objective is formalized t…
We study a sequential coin-flipping game in which a player starts with~$n$ coins, each landing heads independently with probability~$p$. In each round the player flips all remaining coins and must set…
This paper addresses a Stackelberg stochastic linear-quadratic (LQ) differential game under closed-loop information, a problem inherently time-inconsistent. Existing approaches rely on solving two cou…
This paper investigates the $H_{2}/H_{\infty}$ control problem for linear stochastic differential systems under partial observation. Unlike existing studies that assume full state accessibility, we co…
This paper establishes a rigorous connection between regularized discrete-time reinforcement learning (RL) and continuous-time stochastic optimal control. Specifically, classical RL algorithms are typ…
This paper develops a co-state based fusion frame work for spacecraft navigation, consistency monitoring, and hazard forecasting. A differential algebraic co-state is introduced as an instantaneous La…
Electroencephalography (EEG) source imaging aims to infer brain activity from electrical potentials measured on the scalp. This is a difficult problem because many different source patterns can explai…
We extend classical evolutionary game dynamics based on the momentary action choices of agents by accounting for two elements: forward-looking behavior and exploration cost. We focus on pairwise compa…
Let $s > 1$ be a large integer, and let $f$ be a diffeomorphism sufficiently close in the $C^{s}$-topology to the time-1 map of a $C^{s}$ generic volume-preserving Anosov flow on a $3$-dimensional com…
An explicit solution is derived for the Bellman inequality corresponding to minimax optimal dual control. The minimizing player determines control action as a function of past state measurements and i…
Q-value iteration (Q-VI) is usually analyzed through the \(\gamma\)-contraction of the Bellman operator. This argument proves convergence to \(Q^*\), but it gives only a coarse account of when the ind…
This note studies the Burnside problem for homeomorphism groups of compact connected manifolds. For surfaces, we prove that the identity component of the homeomorphism group is torsion-free precisely …
In continuous-time portfolio selection for non-concave utility functions, the martingale duality approach is widely adopted in complete markets, while the dynamic programming approach may sometimes le…
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