10 problems

Let $V(t,x)$ be the value function of the linear-quadratic stochastic control problem, with state dimension $d$ and time-dependent coefficients. Introduce a symmetric matrix-valued…

Consider stabilizable multidimensional linear quadratic regulator systems, and let Thompson Sampling (TS) denote an adaptive control strategy that samples a model from a posterior…

Feedback representation conjecture. The state admits the representation

Robust finite-data convergence conjecture. Such robust, finite-data convergence properties should admit rigorous proofs.

Let $(\tilde{X}(t),\tilde{Y}(t),\tilde{Z}(t))$ solve the transformed fully coupled forward-backward stochastic Hamiltonian system displayed above, with…

Natural-gradient complexity conjecture. This bound should be improvable at least to

Error-tolerance sharpness conjecture. The convergence bounds of these corollaries are sharp in their dependence on $\epsilon$.

Let $X_\varepsilon(\cdot)$ solve the regularized closed-loop state equation associated with the feedback operator $\Theta_\varepsilon(\cdot)$ for Problem $\text{(SLQ)}^0$ at…

Solvability characterization conjecture. In the stochastic case, the equation subject to the constraint $\varDelta(P)\gg 0$ should be solvable if and only if it has a subsolution s…

Converse solvability conjecture. If the singular LQ problem admits a regular solution for every initial state $x_0\in\mathbb{R}^n$, then the generalized continuous algebraic Riccat…