Case-Based Plan Recognition with Incomplete Plan Libraries

ion and Indexing Although the intermediate states are very helpful when recognizing plans with incomplete plan libraries, the statespace for a given planning domain may be quite large (Kerkez and Cox, 2001). A large number of possible situations negatively affect the retrieval efficiency of the recognizer. We developed an indexing and retrieval scheme based on the concept of state abstraction that allows the recognizer to reduce its search space by focusing only on relevant subsets of the state-space where potential similar past situations may be found. The abstraction scheme, as well as the whole recognition process, requires that the states in the planner’s environment are represented as collection of ground literals, a trademark of state-space planners (Carbonell et. al., 1992). Another requirement is that the objects, which are the arguments of literals, have an associated abstraction hierarchy that allows efficient root type determinations. Figure 2 shows an example of a state from the blocksworld domain and its abstract representation. The abstracted states are non-negative integer vectors, whose dimension values indicate the count of occurrences of literals of a particular root type. Figure 2. An example of representational scheme from the blocksworld planning domain. Figure 3. Indexing and storage structures. Abstract states (asi) point to bins (bold lines), containing world states (sj). World states in turn point (dashed lines) to past plans (Pj) in which they are contained. The main indexing structures in the context of the casebased plan recognition are shown in Figure 3. Abstract states point to structures called bins, which contain the concrete world states. Each state in a single bin has an identical abstract representation, which allows for the efficient retrieval of past situations that are similar at the abstract level to the currently observed situation. Once the correct bin is located, the plans containing concrete states within the bin are retrieved and used to guide the current predictions of the planner’s intent. Because the state-space size can be large for complex planning domains, our system constructs the plan library incrementally from the observations of the planner’s behavior. Such incremental construction also minimizes the occurrence of extraneous plans, because only the plans pursued by the planner are actually stored in the library. An issue that arises with abstract indexing is the potential saturation of bins. That is, some bins may contain a large number of concrete states, which in turn may point to a large number of past plans, and may influence the recognizer’s efficiency. Given an equivalence relation on the set of the concrete world states, the bins may be further divided into disjoint subsets that further narrow the search space. To achieve this, we utilize a representation changing technique that transforms the world states into corresponding state graphs (Kerkez, 2002). An equivalence relation based on the isomorphism mapping among the state graphs provides a means to further divide the states in a single bin so that the states that are structurally identical are in the same equivalence class. However, graph isomorphism is computationally intractable for all but the simplest planning domains. We developed a sub-optimal pseudo-isomorphism equivalence relation whose equality comparison time is linear in the number of state literals (Kerkez and Cox, 2002). We have also shown that the accuracy of the local action prediction increases significantly with the pseudo-isomorphism equivalence relations. Figure 4. Percentages of correctly predicted next actions, abstract (suffix “_A”) and concrete, with (suffix “W_S”) and without argument substitutions, for the 3-city logistics domain. Current implementation of our system works with the PRODIGY state-space planner, whose execution cycle has been amended to include the intermediate state information. We experimentally evaluated the recognition performance for predictions that are local to the currently observed planning state, consisting of recognizing the next planning action. Figure 4 shows the percentages of correctly predicted next actions for eight different action selection strategies in the 3-city logistics planning domain while observing about 60,000 planning steps. The recognizer first predicts the next action type without predicting the action arguments. Such predictions are called abstract level predictions and are indicated in the figure by the suffix “A”. After choosing the action prediction at the abstract level, the recognizer may reuse the arguments from the chosen past action, or it may attempt to substitute the past action arguments with their counterparts with respect to the current situation in hand. Strategies involving the argument substitutions are indicated by the suffix “W_S” in Figure 4. Baseline (B) tests consist of choosing an action at random from a pool of all previously observed actions. Random elimination (RE) strategy chooses an action at random from an equivalence class in a single bin that matches the abstract representation of the currently observed situation, while the most frequent (F) strategies choose the action pursued with the highest frequency among the potential candidates. We can see from Figure 4 that RE strategies significantly outperform the baseline strategies, while F strategies perform slightly better than RE strategies. Concrete action predictions with argument substitutions perform significantly better than their counterparts without the argument substitutions. Further research efforts will concentrate on improving the local prediction accuracy with the help of various heuristics, as well as making the global predictions concerning the goals and the plans of the planning agent. Conclusion Given the low-level knowledge intensity, the data-driven recognition approach, and the ability to reason in light of novel plans, the recognition system presented here is applicable to a wide variety of planning domains. Whenever the planner’s environment can be amended to display the plans as sequences of action-state pairs, and whenever state abstraction is possible, the system may benefit from the recognition techniques described in here. One potential future application of the recognizer is in the domain of computer-aided tutoring, where the planner is a human being trained to operate a computer system. In performing the actions on the screen by clicking the input devices, a human user changes the state of the environment in which he or she is currently working. Because human trainees have goals associated with the tasks they are performing, they are effectively performing sequences of state-changing actions that (hopefully) lead to the satisfaction of their goals. A plan recognition system may be utilized to recognize potential faulty user plans and subsequently tutor the user towards the correct solution. For this scenario to be feasible, the recognizer would have to possess the ability to monitor the actions performed by human users in terms of (typically) keyboard and mouse clicks. Our future research efforts will focus on establishing techniques to monitor computer user’s actions and applying the plan recognition techniques to the user interface planning domains.