Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation, which employs global optimization. The formulation provides strong a priori guarantees on both robust and expected policy loss by minimizing specific norms ...

We construct a fuzzy varying coefficient bilinear regression model to deal with the interval financial data and then adopt the least-squares method based on symmetric fuzzy number space. Firstly, we propose a varying coefficient model on the basis of the fuzzy bilinear regression model. Secondly, we develop the least-squares method according to the complete distance between fuzzy numbers to est...

We discuss the relation of a certain type of generalized Lyapunov equations to Gramians of stochastic and bilinear systems together with the corresponding energy functionals. While Gramians and energy functionals of stochastic linear systems show a strong correspondence to the analogous objects for deterministic linear systems, the relation of Gramians and energy functionals for bilinear system...

By access structure and attribute set, attribute-based encryption realizes fine-grained access control and one to many encryption. The expression of access structure directly decides the application range of one scheme and the general circuit reaches the best form. Since the safety of multilinear maps is suffered question, using relatively efficient and safe bilinear maps to construct circuit a...

Definition 1.1. Suppose that R is a commutative ring (possibly a field) and that A, B and C are R-modules. A function f : A× B → C is bilinear if • f (a1 + a2, b) = f (a1, b) + f (a1, b), • f (a, b1 + b2) = f (a, b1) + f (a, b2), and • f (ra, b) = f (a, rb) = r f (a.b). 1.2. The most basic examples of bilinear functions are the functions R×R→ R given by homogeneous quadratic polynomials of degr...

Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation, which employs global optimization. The formulation provides strong a priori guarantees on both robust and expected policy loss by minimizing specific norms ...

This paper proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilber...

This paper presents a comprehensive picture of the mapping of structural properties associated with general linear multivariable systems under bilinear transformation. While the mapping of poles of linear multivariable systems under such a transformation is well known, the question of how the structural invariant properties of a given system are mapped remains unanswered. This paper addresses t...

This paper presents a unified approach to solve different bilinear factorization problems in Computer Vision in the presence of missing data in the measurements. The problem is formulated as a constrained optimization problem where one of the factors is constrained to lie on a specific manifold. To achieve this, we introduce an equivalent reformulation of the bilinear factorization problem. Thi...

Up to now, several non-delegatable identity-based (strong) designated verifier signature schemes using bilinear pairings are proposed. In these identity-based (strong) designated verifier signature schemes, bilinear pairings are employed either in signing and verifying steps or only in the verifying step. However, the computation cost of pairings at a security level equivalent to a 128-bit symm...