Contingent planning under uncertainty via stochastic satisfiability

We describe a new planning technique that efficiently solves probabilistic propositional contingent planning problems by converting them into instances of stochastic satisfiability (SSAT) and solving these problems instead. We make fundamental contributions in two areas: the solution of SSAT problems and the solution of stochastic planning problems. This is the first work extending the planning-as-satisfiability paradigm to stochastic domains. Our planner, ZANDER, can solve arbitrary, goal-oriented, finite-horizon partially observable Markov decision processes (POMDPs). An empirical study comparing ZANDER to seven other leading planners shows that its performance is competitive on a range of problems. © 2003 Elsevier Science B.V. All rights reserved

Generalized Craig Interpolation for Stochastic Boolean Satisfiability Problems with Applications to Probabilistic State Reachability and Region Stability

The stochastic Boolean satisfiability (SSAT) problem has been introduced by Papadimitriou in 1985 when adding a probabilistic model of uncertainty to propositional satisfiability through randomized quantification. SSAT has many applications, among them probabilistic bounded model checking (PBMC) of symbolically represented Markov decision processes. This article identifies a notion of Craig interpolant for the SSAT framework and develops an algorithm for computing such interpolants based on a resolution calculus for SSAT. As a potential application area of this novel concept of Craig interpolation, we address the symbolic analysis of probabilistic systems. We first investigate the use of interpolation in probabilistic state reachability analysis, turning the falsification procedure employing PBMC into a verification technique for probabilistic safety properties. We furthermore propose an interpolation-based approach to probabilistic region stability, being able to verify that the probability of stabilizing within some region is sufficiently large

MAXPLAN: A New Approach to Probabilistic Planning

Classical arti#cial intelligence planning techniques can operate in large domains but traditionally assume a deterministic universe. Operations research planning techniques can operate in probabilistic domains but break when the domains approach realistic sizes. maxplan is a new probabilistic planning technique that aims at combining the best of these twoworlds. maxplan converts a planning instance into an E-Majsat instance, and then draws on techniques from Boolean satis#ability and dynamic programming to solve the E-Majsat instance. E-Majsat is an NP PP -complete problem that is essentially a probabilistic version of Sat. maxplan performs as much as an order of magnitude better on some standard stochastic test problems than buridan---a state-of-the-art probabilistic planner---and scales better on one test problem than two algorithms based on dynamic programming. INTRODUCTION Classical arti#cial intelligence planning techniques can operate in large domains but, t..

Large-Scale Planning Under Uncertainty: A Survey

Our research area is planning under uncertainty, that is, making sequences of decisions in the face of imperfect information. We are particularly concerned with developing planning algorithms that perform well in large, real-world domains. This paper is a brief introduction to this area of research, which draws upon results from operations research (Markov decision processes), machine learning (reinforcement learning), and artificial intelligence (planning). Although techniques for planning under uncertainty are extremely promising for tackling real-world problems, there is a real need at this stage to look at large-scale applications to provide direction to future development and analysis

Using Caching to Solve . . .

Probabilistic planning algorithms seek effective plans for large, stochastic domains. maxplan is a recently developed algorithm that converts a planning problem into an E-Majsat problem, an NP PP -complete problem that is essentially a probabilistic version of Sat, and draws on techniques from Boolean satisfiability and dynamic programming to solve the E-Majsat problem. This solution method is able to solve planning problems at state-of-the-art speeds, but it depends on the ability to store a value for each CNF subformula encountered in the solution process and is therefore quite memory intensive; searching for moderate-size plans even on simple problems can exhaust memory. This paper presents two techniques, based on caching, that overcome this problem without significant performance degradation. The first technique uses an LRU cache to store a fixed number of subformula values. The second technique uses a heuristic based on a measure of subformula difficulty to se..

Using caching to solve larger probabilistic planning problems

{maj er cik, mlittman} ~cs. duke. edu Probabilistic planning algorithms seek effective plans for large, stochastic domains. MAXPLAN is a recently developed algorithm that converts a planning problem into an E-MAJSAT problem, an NPPP-complete problem that is essentially a probabilistic version of SAT, and draws on techniques from Boolean satisfiability and dynamic programming to solve the E-MAJSAT problem. This solution method is able to solve planning problems at state-of-the-art speeds, but it depends on the ability to store a value for each CNF subformula encountered in the solution process and is therefore quite memory intensive; searching for moderate-size plans even on simple problems can exhaust memory. This paper presents two techniques, based on caching, that overcome this problem without significant performance degradation. The first technique uses an LRU cache to store a fixed number of subformula values. The second technique uses a heuristic based on a measure of subformula difficulty to selectively save the values of only those subformulas whose values are sufficiently difficult to compute and are likely to be reused later in the solution process. We report results for both techniques on a stochastic test problem

Contingent Planning Under Uncertainty via Stochastic Satisfiability

We describe two new probabilistic planning techniques ---c-maxplan and zander---that generate contingent plans in probabilistic propositional domains. Both operate by transforming the planning problem into a stochastic satisfiability problem and solving that problem instead. c-maxplan encodes the problem as an E-Majsat instance, while zander encodes the problem as an S-Sat instance. Although S-Sat problems are in a higher complexity class than E-Majsat problems, the problem encodings produced by zander are substantially more compact and appear to be easier to solve than the corresponding E-Majsat encodings. Preliminary results for zander indicate that it is competitive with existing planners on a variety of problems. Introduction When planning under uncertainty, any information about the state of the world is precious. A contingent plan is one that can make action choices contingent on such information. In this paper, we present an implemented framework for contingent pl..

Approximate Planning in the Probabilistic-Planning-as-Stochastic-Satisfiability Paradigm ∗

zander is a state-of-the-art probabilistic planner that extends the probabilistic-planning-as-stochastic-satisfiability paradigm to support contingent planning in domains where there is uncertainty in the effects of the agent’s actions and where the scope and accuracy of the agent’s observations may be insufficient to establish the agent’s current state with certainty (Majercik & Littman 1999). We describe zander and then discuss an approximation technique we are developing that will help us to scale up our SSat-based technique to large planning problems. We report results using this approximation algorithm on random SSat problems and discuss issues that arise in the application of this algorithm to SSat encodings of planning problems