Towards Model-lite Planning : A Proposal For Learning & Planning with Incomplete Domain Models

Due to the difficulty of defining acompletedomain definition, it is hard to apply planners to real-life application domains. Model-lite planning research has been proposed to address this issue (Kambhampati 2007). While it takes time to develop a complete domain definition, it is rather faster and easier to provide a planner with incomplete but close to complete domain definition. In this paper, we describe our on-going research on a new learning and planning scheme for the model-lite paradigm. In our framework, we use probabilistic logic to leverage the incomplete model and we consider explicit input background knowledge. In the planning side, the core idea is viewing a planning problem as an MPE (most plausible explanation) problem, given incomplete domain definition and the evidence of initial state and goal. We show a reduction procedure from a planning problem to an MPE problem then to a MAXSAT problem, which enables us to use MAXSAT solvers, as deterministic planning uses SAT solvers. In the learning side, we show how we update the domain model, given trajectories using a weighted logic learning package, and how we parsimoniously generate axioms with background knowledge. This is particularly important to leverage the relational structure during planning. Introduction There are many application areas where planning techniques can play an important role. Web service composition, automated computing or dynamic compilation are some of them (Kambhampati 2007). One of the reasons why planning techniques are not being actively used in these areas is the burden of developing domain definition. It is well understood among the planning community that defining a complete domain for the target application is not easy (Bartk & McCluskey 2005; Yang, Wu, & Jiang 2007). Indeed, DARPA has started the Integrated Learning Initiative to address this issue (DARPA 2006). Recently, (Kambhampati 2007) has proposed the model-lite planning paradigm, which motivates the study of planning techniques that do not rely on the complete domain definition. Although it is hard to write a complete domain definition, it may be relatively easy to provide an approximate domain definition which may not be complete. The challenge is to plan with the current-best model and update it Copyright c © 2007, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. as experiences are gathered. In this paper, we describe our on-going research on the learning and planning framework with incomplete domain models. We use probabilistic logic to represent uncertain domain models. We separate precondition and effect of action definitions into two different se t of axioms, precondition and effect axioms, where each of the axiom has an associated probability. This separation helps a straightforward setup of a well known machine learning problem. Then, we show that planning can be viewed as an MPE (most probable explanation) problem, given the initial state, goal and the current domain model. Next, we view MPE problem as weighted MAXSAT problem, as considered by (Park 2002). Thus, the planning problem with an incomplete domain model becomes a weighted MAXSAT problem, which enables us to use publicly available approximate solvers that scales well, e.g., maxwalksat. Note that our proposed approach for planning can also be applied to probabilistic planning. There are two aspects of learning in our framework. • Given a set of weighted precondition and effect axioms, the learning is mainly updating their weight. A weight update on logic formulae can straightforwardly be achieved with MLN (Markov logic network) (Richardson & Domingos 2006) or Problog (De Raedt, Kimmig, & Toivonen 2007) approaches. We show how we construct training data and how the learning updates the domain model. • Given explicit background knowledge, we show how we use the knowledge to reduce the number of potential candidate precondition or effect axioms. This will make later planning easier, as the plangraph construction will be lighter. Explicit consideration of background knowledge is an interesting point of our framework. At first glance, it might be surprising that we assume incomplete domain model but expect background knowledge. However, this is not an unreasonable assumption. In most domain modeling tasks, the problem is not so much that no background knowledge is available, but that it is hard to come up with complete and consistent set of operators that respect all the background knowledge. This is particularly useful when there are obvious domain constraints, e.g. no more than one block on top of a block in Blocksworld, but it is not easy to create a set of actions that maintains the property.