We consider the exploration-exploitation tradeoff in linear quadratic (LQ) control problems, where the state dynamics is linear and the cost function is quadratic in states and controls. We analyze the regret of Thompson sampling (TS) (a.k.a. posterior-sampling for reinforcement learning) in the frequentist setting, i.e., when the parameters characterizing the LQ dynamics are fixed. Despite the...

We investigate the small deviation problem for weighted fractional Brownian motions in Lq–norm, 1 ≤ q ≤ ∞. Let BH be a fractional Brownian motion with Hurst index 0 < H < 1. If 1/r := H + 1/q, then our main result asserts lim ε→0 ε log P (∥∥∥ρBH∥∥∥ Lq(0,∞) < ε ) = −c(H, q) · ‖ρ‖ Lr(0,∞) , provided the weight function ρ satisfies a condition slightly stronger than the r– integrability. Thus we e...

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This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to...

A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between problems, two-point boundary value and Riccati equations. In this paper, we extend equivalence to a general time-inconsistent LQ problem, where inconsistency arises from nonexponential discount functions. By studying solvability equation, show existence uniqueness linear equilibrium for pr...

Quantified Boolean formula (QBF) evaluation has a broad range of applications in computer science and is gaining increasing attention. Recent progress has shown that for a certain family of formulas, Qresolution, which forms the foundation of learning in modern search-based QBF solvers, is exponentially inferior in proof size to two of its extensions: Q-resolution with resolution over universal...

The pseudo-dimension of a real-valued function class is an extension of the VC dimension for set-indicator function classes. A classH of finite pseudo-dimension possesses a useful statistical smoothness property. In [10] we introduced a nonlinear approximation width ρn(F , Lq ) = infHn dist(F ,Hn, Lq ) which measures the worstcase approximation error over all functions f ∈ F by the best manifol...

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