Goals for reinforcement learning problems are typically defined through handspecified rewards. To design such problems, developers of learning algorithms must inherently be aware of what the task goals are, yet we often require agents to discover them on their own without any supervision beyond these sparse rewards. While much of the power of reinforcement learning derives from the concept that...

Computing the time evolution of quantum systems composed of many coupled degrees of freedom presents serious challenges. Currently, simulations of timedependent properties in polyatomic molecules, clusters, or condensed phases employ a variety of approximations, which are largely built around variational, quantum-classical or semiclassical ideas. While approximate methods have proven extremely ...

We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, a nonsmooth proximable function, and linear composite functions. This is a full splitting approach, in the sense that the gradient and the linear operators involved are applied explici...

Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. The paper investigates the algebraic structure of modal operators. It studies and compares different notions of termination in this class, including an algebraic correspondence proof of Löb’s formula from modal logic. It gives calculational proofs of two fundamental st...

The purpose of this paper is to introduce a viscosity approximation forward-backward splitting method for the implicit midpoint rule of an accretive operators and m-accretive operators in Banach spaces. The strong convergence of this viscosity method is proved under certain assumptions imposed on the sequence of parameters. The results presented in the paper extend and improve some recent resul...

Abstract In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum finitely many monotone operators, which are not based on reduction to two operator inclusion in product space. Each iteration studied requires one resolvent evaluation per set-valued operator, forward cocoercive evaluations operator. Unlike existing methods, structure proposed suitable d...

Modal Kleene algebras are Kleene algebras enriched by forward and backward box and diamond operators. We formalise the symmetries of these operators as Galois connections, complemetarities and dualities. We study their properties in the associated operator algebras and show that the axioms of relation algebra are theorems at the operator level. Modal Kleene algebras provide a unifying semantics...