Blai Bonet

Planning as heuristic search

In the AIPS98 Planning Contest, the HSP planner showed that heuristic search planners can be competitive with state-of-the-art Graphplan and SAT planners. Heuristic search planners like HSP transform planning problems into problems of heuristic search by automatically extracting heuristics from Strips encodings. They differ from specialized problem solvers such as those developed for the 24-Puzzle and Rubik’s Cube in that they use a general declarative language for stating problems and a general mechanism for extracting heuristics from these representations. In this paper, we study a family of heuristic search planners that are based on a simple and general heuristic that assumes that action preconditions are independent. The heuristic is then used in the context of best-first and hill-climbing search algorithms, and is tested over a large collection of domains. We then consider variations and extensions such as reversing the direction of the search for speeding node evaluation, and extracting information about propositional invariants for avoiding dead-ends. We analyze the resulting planners, evaluate their performance, and explain when they do best. We also compare the performance of these planners with two state-of-the-art planners, and show that the simplest planner based on a pure best-first search yields the most solid performance over a large set of problems. We also discuss the strengths and limitations of this approach, establish a correspondence between heuristic search planning and Graphplan, and briefly survey recent ideas that can reduce the current gap in performance between general heuristic search planners and specialized solvers.  2001 Elsevier Science B.V. All rights reserved.

Planning as Heuristic Search: New Results

In the recent AIPS98 Planning Competition, the hsp planner, based on a forward state search and a domain-independent heuristic, showed that heuristic search planners can be competitive with state of the art Graphplan and Satisfiability planners. hsp solved more problems than the other planners but it often took more time or produced longer plans. The main bottleneck in hsp is the computation of the heuristic for every new state. This computation may take up to 85% of the processing time. In this paper, we present a solution to this problem that uses a simple change in the direction of the search. The new planner, that we call hspr, is based on the same ideas and heuristic as hsp , but searches backward from the goal rather than forward from the initial state. This allows hspr to compute the heuristic estimates only once. As a result, hspr can produce better plans, often in less time. For example, hspr solves each of the 30 logistics problems from Kautz and Selman in less than 3 seconds. This is two orders of magnitude faster than blackbox. At the same time, in almost all cases, the plans are substantially smaller. hspr is also more robust than hsp as it visits a larger number of states, makes deterministic decisions, and relies on a single adjustable parameter than can be fixed for most domains. hspr, however, is not better than hsp accross all domains and in particular, in the blocks world, hspr fails on some large instances that hsp can solve. We discuss also the relation between hspr and Graphplan, and argue that Graphplan can also be understood as a heuristic search planner with a precise heuristic function and search algorithm.

mGPT: a probabilistic planner based on heuristic search

We describe the version of the GPT planner used in the probabilistic track of the 4th International Planning Competition (IPC-4). This version, called mGPT, solves Markov Decision Processes specified in the PPDDL language by extracting and using different classes of lower bounds along with various heuristic-search algorithms. The lower bounds are extracted from deterministic relaxations where the alternative probabilistic effects of an action are mapped into different, independent, deterministic actions. The heuristic-search algorithms use these lower bounds for focusing the updates and delivering a consistent value function over all states reachable from the initial state and the greedy policy.

The AIPS-98 Planning Competition

In 1998, the international planning community was invited to take part in the first planning competition, hosted by the Artificial Intelligence Planning Systems Conference, to provide a new impetus for empirical evaluation and direct comparison of automatic domain-independent planning systems. This article describes the systems that competed in the event, examines the results, and considers some of the implications for the future of the field.

Planning under partial observability by classical replanning: theory and experiments

Planning with partial observability can be formulated as a non-deterministic search problem in belief space. The problem is harder than classical planning as keeping track of beliefs is harder than keeping track of states, and searching for action policies is harder than searching for action sequences. In this work, we develop a framework for partial observability that avoids these limitations and leads to a planner that scales up to larger problems. For this, the class of problems is restricted to those in which 1) the non-unary clauses representing the uncertainty about the initial situation are invariant, and 2) variables that are hidden in the initial situation do not appear in the body of conditional effects, which are all assumed to be deterministic. We show that such problems can be translated in linear time into equivalent fully observable non-deterministic planning problems, and that an slight extension of this translation renders the problem solvable by means of classical planners. The whole approach is sound and complete provided that in addition, the state-space is connected. Experiments are also reported.

Planning and Control in Artificial Intelligence: A Unifying Perspective

The problem of selecting actions in environments that are dynamic and not completely predictable or observable is a central problem in intelligent behavior. In AI, this translates into the problem of designing controllers that can map sequences of observations into actions so that certain goals are achieved. Three main approaches have been used in AI for designing such controllers: the programming approach, where the controller is programmed by hand in a suitable high-level procedural language, the planning approach, where the control is automatically derived from a suitable description of actions and goals, and the learning approach, where the control is derived from a collection of experiences. The three approaches exhibit successes and limitations. The focus of this paper is on the planning approach. More specifically, we present an approach to planning based on various state models that handle various types of action dynamics (deterministic and probabilistic) and sensor feedback (null, partial, and complete). The approach combines high-level representations languages for describing actions, sensors, and goals, mathematical models of sequential decisions for making precise the various planning tasks and their solutions, and heuristic search algorithms for computing those solutions. The approach is supported by a computational tool we have developed that accepts high-level descriptions of actions, sensors, and goals and produces suitable controllers. We also present empirical results and discuss open challenges.

Directed Unfolding of Petri Nets

The key to efficient on-the-fly reachability analysis based on unfolding is to focus the expansion of the finite prefix towards the desired marking. However, current unfolding strategies typically equate to blind (breadth-first) search. They do not exploit the knowledge of the marking that is sought, merely entertaining the hope that the road to it will be short. This paper investigates directed unfolding , which exploits problem-specific information in the form of a heuristic function to guide the unfolding towards the desired marking. In the unfolding context, heuristic values are estimates of the distance between configurations. We show that suitable heuristics can be automatically extracted from the original net. We prove that unfolding can rely on heuristic search strategies while preserving the finiteness and completeness of the generated prefix, and in some cases, the optimality of the firing sequence produced. We also establish that the size of the prefix obtained with a useful class of heuristics is never worse than that obtained by blind unfolding. Experimental results demonstrate that directed unfolding scales up to problems that were previously out of reach of the unfolding technique.

Belief tracking for planning with sensing: width, complexity and approximations

We consider the problem of belief tracking in a planning setting where states are valuations over a set of variables that are partially observable, and beliefs stand for the sets of states that are possible. While the problem is intractable in the worst case, it has been recently shown that in deterministic conformant and contingent problems, belief tracking is exponential in a width parameter that is often bounded and small. In this work, we extend these results in two ways. First, we introduce a width notion that applies to non-deterministic problems as well, develop a factored belief tracking algorithm that is exponential in the problem width, and show how it applies to existing benchmarks. Second, we introduce a meaningful, powerful, and sound approximation scheme, beam tracking, that is exponential in a smaller parameter, the problem causal width, and has much broader applicability. We illustrate the value of this algorithm over large instances of problems such as Battleship, Minesweeper, and Wumpus, where it yields state-of-the-art performance in real-time.

On the Speed of Convergence of Value Iteration on Stochastic Shortest-Path Problems

We establish a bound on the convergence time of the value iteration algorithm on stochastic shortest-path problems. The bound, which applies for admissible initial vectors as, for example, J\equiv 0 , implies a polynomial-time convergence of value iteration for all problems with polynomially bounded \Vert{J^*}\Vert/\underline{g} . This result gives a partial answer to the open problem of bounding the convergence time of value iteration on arbitrary initial vectors. The proof is obtained by analyzing a stochastic process associated with the shortest-path problem.

Recent advances in unfolding technique

We propose a new, and to date the most general, framework for Petri net unfolding, which broadens its applicability, makes it easier to use, and increases its efficiency. In particular: (i) we propose a user-oriented view of the unfolding technique, which simply tells which information will be preserved in the final prefix and how to declare an event a cut-off in the algorithm, while hiding the technical parameters like the adequate order; (ii) the notion of the adequate order is generalised to a well-founded relation, and the requirement that it must refine ? is replaced by a weaker one; and (iii) the order in which the unfolding algorithm selects the possible extensions of the prefix is entirely disentangled from the cut-off condition. We demonstrate the usefulness of the developed theory on some case studies.