This paper is concerned with numerical solutions of large scale Sylvester equations AX −XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li andWhite (2002) demonstrated that the so called Cholesky factored ADI method with decent shift parameters can be very effective. In this paper we present a ge...

Propositional STRIPS planning problems can be viewed as finite state automata (FSAs) represented in a factored form. Automaton minimizat ion is a well-known technique for reducing the size of an explicit FSA. Recent work in computer-aided verification on model checking has extended this technique to provide automaton minimizat ion algorithms for factored FSAs. In this paper, we consider the rel...

Hybrid approximate linear programming (HALP) has recently emerged as a promising approach to solving large factored Markov decision processes (MDPs) with discrete and continuous state and action variables. Its central idea is to reformulate initially intractable problem of computing the optimal value function as its linear programming approximation. In this work, we present the HALP framework a...

Most traditional approaches to probabilistic planning in relationally specified MDPs rely on grounding the problem w.r.t. specific domain instantiations, thereby incurring a combinatorial blowup in the representation. An alternative approach is to lift a relational MDP to a firstorder MDP (FOMDP) specification and develop solution approaches that avoid grounding. Unfortunately, state-of-the-art...

The Factored Frontier (FF) algorithm is a simple approximate inference algorithm for Dynamic Bayesian Networks (DBNs). It is very similar to the fully factorized version of the Boyen-Koller (BK) algorithm, but in­ stead of doing an exact update at every step followed by marginalisation (projection), it always works with factored distributions. Hence it can be applied to models for which the exa...

We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network’s Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large block...

Dec-POMDPs are a powerful framework for planning in multiagent systems, but are provably intractable to solve. This paper proposes a factored forward-sweep policy computation method that tackles the stages of the problem one by one, exploiting weakly coupled structure at each of these stages. An empirical evaluation shows that the loss in solution quality due to these approximations is small an...