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Learning hierarchical task networks by observation

Learning hierarchical task networks by observation
Learning hierarchical task networks by observation

Learning Hierarchical Task Networks by Observation

Negin Nejati negin@https://www.wendangku.net/doc/6a84256.html, Pat Langley langley@https://www.wendangku.net/doc/6a84256.html, Tolga Konik konik@https://www.wendangku.net/doc/6a84256.html, Computational Learning Laboratory,Center for the Study of Language and Information,Stanford University, Stanford,CA94305USA

Abstract

Knowledge-based planning methods o?er

bene?ts over classical techniques,but they

are time consuming and costly to construct.

There has been research on learning plan

knowledge from search,but this can take sub-

stantial computer time and may even fail

to?nd solutions on complex tasks.Here

we describe another approach that observes

sequences of operators taken from expert

solutions to problems and learns hierarchi-

cal task networks from them.The method

has similarities to previous algorithms for

explanation-based learning,but di?ers in its

ability to acquire hierarchical structures and

in the generality of learned conditions.These

increase the method’s capability to trans-

fer learned knowledge to other problems and

supports the acquisition of recursive proce-

dures.After presenting the learning algo-

rithm,we report experiments that compare

its abilities to other techniques on two plan-

ning domains.In closing,we review related

work and directions for future research.

1.Introduction

In recent years,hierarchical task networks have emerged as a powerful framework for representing and organizing knowledge about action(Ilghami et al., 2002;Wilkins&desJardins,2001).With access to such content,an agent can generate or execute plans far more e?ectively than it can from domain operators alone,because the knowledge speci?es how to decom-pose complex tasks into simpler ones.Such approaches have been applied successfully to a variety of challeng-Appearing in Proceedings of the23rd International Con-ference on Machine Learning,Pittsburgh,PA,2006.Copy-right2006by the authors.ing domains,and they scale to complexity much better than classical planning methods.

Despite their clear advantages,hierarchical task net-works can be di?cult and time consuming to construct manually.This suggests the use of machine learning to acquire the knowledge base from experience,but,de-spite a substantial literature on learning for planning (Zimmerman&Kambhampati,2003),there have been remarkably few e?orts toward acquiring hierarchical plan structures.Moreover,most work in this area has focused on learning from the results of search,which can produce poor solutions and may even fail entirely on some tasks.

An alternative approach is to learn from traces of an expert’s behavior.Research on behavioral cloning (e.g.,Sammut,1996)incorporates this idea,but typ-ically learns?at rules for reactive control.Two other paradigms–learning apprentices(e.g.,Mitchell et al.,1985)and programming by demonstration(e.g., Cypher,1993)–emphasize di?erent induction meth-ods and problems but also focus on nonhierarchical structures.In this paper,we adapt the general idea of learning from expert traces to acquire a class of hi-erarchical task networks–teleoreactive logic programs –that are distinctive because they index methods by the goals they achieve.We can state the learning task more precisely in terms of its inputs and outputs:?Given:a set of operators that produce predictable e?ects under known conditions;

?Given:a set of training problems,each of which speci?es an initial state and a goal;

?Given:for each training problem,a sequence of operator instances that achieves the goal from the initial state;

?Find:a teleoreactive logic program that repro-duces the solutions to the training problems and generalizes well to new ones.

We will see that,unlike research on behavioral cloning, our approach chains backward from the goal achieved by each sample trace to analyze the reasons for each action.In this sense,it bears similarity to early work on explanation-based learning,which also relied on goal regression.However,these methods jettisoned the explanation structure after learning,whereas our approach retains it to determine the hierarchical orga-nization of learned knowledge.

In the next section,we describe the knowledge struc-tures given to and acquired by our method,along with the performance mechanisms that operate over that knowledge.After this,we describe the learning algo-rithm in detail and illustrate its operation on a simple example.Next we report experiments with the tech-nique on two planning domains,including comparisons with more traditional learning methods.Finally,we examine at more length how our approach relates to earlier work on learning plan knowledge and discuss some directions for additional research.

2.Knowledge Representation

Before we can explain our performance and learning methods,we must?rst describe the representation we use to encode the knowledge they use and acquire. This formalism supports a specialized class of hier-archical task networks that we call teleoreactive logic programs,which Langley and Choi(2006)report in more detail.Such programs consist of two distinct but interconnected knowledge bases that describe di?erent aspects of a domain.

The?rst knowledge base includes a set of concept def-initions that recognize classes of situations in the do-main and describe them at di?erent levels of abstrac-tion.Concepts are encoded in a hierarchical language and shape the system’s beliefs about the domain.Each concept includes a head,which is stated as a predicate with zero or more arguments,and a body,which in-cludes one or more arithmetic tests or relations that must hold.The lowest-level concepts only refer to the perceptual inputs from the domain,while the higher level ones can refer to other concepts as well.Table1 shows examples of two primitive concept de?nitions, on and hand-empty,and two nonprimitive concepts, clear and unstackable,for the Blocks World.

The second knowledge base contains the de?nitions of primitive and high-level skills that can be executed to change the environment.Primitive skills are de?ned in terms of the actions the agent can perform with each clause having a head that speci?es its name and argu-ments,a set of typed variables,a single start condition, a set of e?ects,and a set of executable actions.The Table1.Examples of concepts from the Blocks World. (on(?blk1?blk2)

:percepts((block?blk1x?x1y?y1)

(block?blk2x?x2y?y2h?h))

:tests((equal?x1?x2)

(>=?y1?y2)

(<=?y1(+?y2?h))))

(clear(?block)

:percepts((block?block))

:negatives((on?other?block)))

(unstackable(?block?from)

:percepts((block?block)(block?from))

:positives((on?block?from)

(clear?block)(hand-empty))) (hand-empty()

:percepts((hand?hand status?status))

:tests((eq?status’empty)))

e?ects of each primitive skill are known to the system and are speci?ed in terms of known concepts.These correspond to primitive tasks or operators in hierarchi-cal task networks.

Higher level skills,which are the result of the learn-ing,specify ways to decompose complex activities into simple ones.They correspond to methods in hierarchi-cal task networks but di?er in that the head of each skill clause is the goal concept it achieves if executed to completion.This introduces a connection between concepts and skills that is essential for our learning method,as we describe in Section4.The body of a high-level skill includes the necessary perceptual in-puts,the start conditions,and the relevant subskills. Table2and Figure1show examples of primitive and high-level skills from the Blocks World.

Both concept and skill knowledge bases are stored in long-term memories,while the speci?c instances of them are stored in short-term memories that change as the environment evolves.

3.Inference and Execution Mechanisms The performance mechanisms of a teleoreactive logic program re?ect the fact that it operates in a physi-cal setting that changes over time.As Langley and Choi(2006)report,the basic architecture functions in discrete cycles.On each cycle it deposits,in a per-ceptual bu?er,low-level sensory information about ob-jects within the agent’s?eld of view.The system then calls an inference module that operates in a bottom-up,data-driven manner to infer relational beliefs from these perceptions and concept de?nitions.The in-ference procedure?rst produces instances of primi-

Table2.Two primitive skills for the Blocks World domain. (unstack(?block?from)

:percepts((block?block ypos?ypos)

(block?from))

:start((unstackable?block?from))

:effects((clear?from)

(holding?block))

:actions((*grasp?block)

(*v-move?block(+?ypos10)))) (stack(?block?to)

:percepts((block?block)

(block?to x?x y?y h?h))

:start((stackable?block?to))

:effects((on?block?to)

(hand-empty))

:actions((*h-move?block?x)

(*v-move?block(+?y?h))

(*ungrasp?block)))

tive concepts,which depend only on perceived objects, then asserts beliefs based on higher-level concepts. After this,the architecture invokes an execution mod-ule that,in contrast with inference,operates in a top-down manner to achieve high-level goals.On each cy-cle,using the beliefs produced during inference,the system?nds all applicable paths through the skill hi-erarchy that start from the agent’s goal.Since goals are stated as concept instances and the heads of non-primitive skills refer to the concept they achieve,the agent can easily pick executable paths that are rele-vant to its current goal.The applicability of a skill path depends on the applicability of every skill clause on that path.An individual skill instance is appli-cable when in the current state its preconditions are satis?ed but its head is not satis?ed.Note that a skill path is not about a course of action over time;it de-scribes the hierarchical context from the highest-level skill down to a primitive skill.When the agent carries out the actions associated with the selected skill path, the environment changes and the architecture repeats the same procedure until it achieves the goal.

To assure reactivity,on the cycle the system also con-siders the previously executed subskills.This enables it to invoke those subskills again if their objectives are no longer satis?ed due to unexpected events.On the other hand,to prevent the agent from switching among multiple intentions instead of persistently working on one and moving to the next,the architecture prefers skill paths that are more similar to the path that it chose on the previous cycle.

Our approach to skill utilization bears many similari-ties to those for hierarchical task networks(Wilkins&Table3.A training example for learning by observation from the Blocks World.

Goal:(clear A)

Primitive skill sequence:

((unstack C B)(putdown C T1)(unstack B A)) Initial state:

((unstackable C B)(hand-empty)(clear C)

(ontable A T1)(on C B)(on B A)) desJardins,2001),which have often emphasized plan execution over plan generation.However,most work in this tradition has relied on sophisticated notations for describing complex activities that make them dif-?cult to learn.Our formalism for teleoreactive logic programs is closer to the one assumed by Ilghami et al.’s(2002)SHOP2,which focuses on plan gener-ation rather than execution.As we will see shortly, this representation supports the incremental learning of hierarchical skills from traces of expert behavior.

4.Learning Mechanism

Now that we have described the processes that inter-pret a teleoreactive logic program to achieve an agent’s goals,we can turn to methods for learning these struc-tures by observation.As mentioned earlier,our ap-proach builds on knowledge about a domain and ex-pands upon it to incorporate skills that can achieve complicated tasks.This background knowledge in-cludes the de?nitions for concepts and primitive skills. Our system learns from problem-solution pairs pro-vided by the expert.Each problem is de?ned by a goal instance and a speci?c initial state of the envi-ronment.The solution is a sequence of primitive skill instances provided by the expert that achieves the goal starting from the initial state.Table3shows a train-ing example for a simple problem in the Blocks World domain.The initial state for this problem has a three-block tower with C on B and B on A,and the goal is to get block A clear.

Given these inputs,the algorithm proceeds to parse and explain the solution steps using a strategy similar to that in explanation-based learning(Ellman,1989). It starts by chaining backward from the goal by focus-ing on the?nal primitive skill provided by the expert, such as(unstack B A)in our example from Table3. At each step,it selects between two alternative ac-counts of the expert trace.

If the primitive skill contains the goal as one of its ef-fects,the algorithm explains the goal using skill chain-ing.If this skill is applicable in the initial state of

the problem,one can directly execute it to achieve the goal.However,if its precondition is not satis?ed,extra work is needed to make it applicable.In this case,the algorithm tags the single precondition of this skill as its new goal and tries to justify the previous solution steps with respect to it.Figure1illustrates the parsing procedure on the Blocks World example from Table3. In this example,the last primitive skill,(unstack B A),achieves the goal(clear A)directly,but its pre-condition,(unstackable B A),is not satis?ed in the initial state.This unsatis?ed precondition is consid-ered as the goal the expert was pursuing before the?-nal move.Therefore,the algorithm proceeds to justify the primitive skill sequence(unstack C B)(putdown C T1)for achieving(unstackable B A).

When the goal is not one of the e?ects of the prim-itive skill in the sequence,the algorithm explains it using concept chaining.In this case,the skill either achieves one of the goal’s subconcepts or it is an un-necessary step that presumably achieves some other purpose.The system determines the possible subgoals from the de?nition of the goal concept,and then looks back through the state sequence to?nd the order in which the expert achieved them.All primitive skills executed before achieving a subgoal are treated as po-tential contributors.This can lead to considering a skill for more than one subgoal,which is reasonable since skills can have multiple e?ects that contribute to di?erent aims.In addition,this lets the system handle interleaved subtraces when the expert alternates be-tween pursuing di?erent subgoals.When a subtrace includes a skill that is irrelevant to achieving a goal, the system simply ignores it.Each subgoal with its as-sociated sequence of primitive skills poses a new prob-lem is handled by calling the main routine recursively. Continuing with our Blocks World example,the sequence(unstack C B)(putdown C)in Table3 makes B and A unstackable,but none of these prim-itive skills include(unstackable B A)as their ef-fects.This results in concept chaining and break-ing down(unstackable B A)into its subgoals–(hand-empty),(on B A),and(clear B)–as de-?ned in Table1.By tracking the order of subgoal achievements through the state sequence,(unstack C B)is assigned to(clear B),while both(unstack C B)and(putdown C)are considered as contributors to achieving(hand-empty).The method will detect the literal(unstack C B)as an irrelevant step for this goal later in its processing.

After the algorithm has?nished parsing the expert’s solution trace,it uses the explanation structure to learn new skill clauses for future use.For skill chain-ing,if the precondition P of the current primitive

skill Figure1.Illustration of the learning algorithm on a simple problem from the Blocks World and the acquired skills.

S is satis?ed in the initial state and the expert did nothing to achieve that,the system learns a new skill clause with the achieved goal G as its head,P as its start condition,and a single subskill S.1If the ex-pert has done work to achieve P,the system learns a skill clause that achieves G by composing the skill that achieves P(which has the same head as P and has already been learned in the shallower recursion calls) with S.The start conditions of the learned skill are the same as the start conditions of the skill P.In Fig-ure1,(clear?B)and(clear?A)are examples of skill clauses learned through skill chaining.

For concept chaining,if the goal G has n subgoals, g1,...,g n,and m of them are satis?ed in the initial state,the lower level skills that are learned for achiev-ing g m+1,...,g n comprise the subskills?eld of the new skill,but the g1,...,g m concepts determine the start condition of this new skill.The nonprimitive skill (unstackable?B?A)in Figure1is an example of a skill clause learned by this procedure.As we discuss shortly,the acquired precondition does not guarantee successful execution,but it still often serves as a use-ful heuristic.The learning mechanism can produce disjunctive skills,since di?erent methods of achieving a goal have the same head.This convention leads to ?exible skills,since each clause can be expanded with all combinations of its subskills’di?erent clauses.

As demonstrated elsewhere(Langley&Choi,2006), one can use traces generated by a problem solver to learn analogous skills.The method introduced here replaces the problem-solving traces with ones from an expert performing the task.Although we use a simi-lar subroutine for creating skill clauses,the resulting hierarchy can di?er because the expert may provide di?erent solution traces than the problem solver.We 1For the distinction between this learned clause and the primitive skill it incorporates,see Langley and Choi(2006).

expect that learning by observation will be more prac-tical in complex domains because of the heavy search they impose on problem solvers.

5.Experimental Evaluation

To evaluate the behavior of our approach to learning teleoreactive logic programs by observation,we de-signed and carried out experiments in two planning domains.Below we describe our experimental design, after which we report the results of these studies.

5.1.Experimental Design

Since our method operates in an incremental man-ner,we chose to employ an online training regimen in which we presented randomly sampled problems one at a time.If the system fails to achieve the goal using its current knowledge,it retrieves an expert trace stored with the problem.After learning a set of skill clauses from this trace,the system turns to the next problem. This lets us measure performance as a function of the number of problems encountered.We selected the cu-mulative number of tasks solved successfully as our performance metric,primarily because di?erent prob-lems involved distinct levels of di?culty,and thus were not directly comparable.We also averaged the results across di?erent sequences of problems to guard against order e?ects.Other metrics such as CPU time are not relevant here,as the performance system does not in-clude a problem solver and simply fails to solve a task if it does not have all the necessary skills.

Because our approach to learning by observation con-structs an explanation of the expert trace,it seems appropriate that we compare its behavior to tradi-tional methods for explanation-based learning.We considered two variations on this idea,each tied to one of our theoretical claims.First,we maintain that our method should acquire more?exible knowledge than explanation-based techniques because it retains the explanation structure in its skill hierarchy.Thus, we implemented a standard algorithm for learning a ?at macro-operator(Mooney,1990)from each expert trace that collects a set of su?cient conditions,with constants replaced by variables,to achieve that prob-lem’s top-level goal.This macro-operator can solve the training problem on which it is based,but the method ?nds very speci?c conditions,and preliminary experi-ments suggested it generalized so poorly to new tasks that we did not pursue it further.

A second claim revolves around our method for select-ing conditions on learned skills,which does not rely on goal regression and only uses information about component skills and concepts.For comparison pur-poses,we developed an alternative technique that still learns hierarchical skills by analyzing expert traces, but that invokes the same condition-?nding scheme for each clause as for macro-operator formation.This produces conditions that are su?cient to achieve the goal in each clause’s head,making them more speci?c than those our method generates,but also less likely to initiate chains of action that the agent cannot com-plete.Initial studies suggested that this alternative generalized reasonably well,so we included it in our formal experiments.

We settled on two domains for our studies:the Blocks World and Depots,which we describe more fully later. The former is not especially di?cult,but it is well understood,and we had a handcrafted task network that we could compare with learned skills.Depots is a more challenging domain that involves a much larger search space,which we predicted would help distinguish our approach from the explanation-based alternative.However,because we had no handcrafted program against which to compare learned skills,we could only evaluate the methods on this domain in terms of their behavior.

5.2.Experiments with the Blocks World

The Blocks World consists of a table,a gripper,and several cubical blocks that are distributed in one or multiple columns on the table.The system distin-guishes di?erent situations in the environment using nine de?ned concepts,including the ones in Table1. It can also change its environment using four primi-tive skills:stack,unstack(see Table2),pickup,and putdown.The goals refer to con?gurations of blocks that are de?ned via existing concepts.This knowledge is su?cient,in principle,to solve all the problems in the domain by employing extensive search.However, when there are more than a few blocks in the environ-ment,search is slow and impractical.

Our experiment used240random problems with three distinct goals:clear,holding,and on.The environ-ment included up to seven blocks with random initial con?gurations and the di?culty level of the problems ranged from one to16-step solutions.Inspection re-vealed the system learned skills that are equivalent to the handcrafted ones.Figure1shows the skills acquired from the sample input in Table3.These high-level skills equip the system to achieve goals like clearing a block on many new problems.One reason is their potential for being applied recursively.For example,the learned skills in the?gure can clear a block regardless of the number of blocks on top of

Table4.Some examples of skills acquired in the Blocks World using explanation-based learning.

(clear(?A)

:percepts((block?A)(block?B)

(block?C))

:start((hand-empty)(on?B?A)

(on?C?B)(clear?C)

:ordered((unstackable?B?A)

(unstack?B?A)))

(unstackable(?B?A)

:percepts((block?A)(block?B)

(block?C))

:start((hand-empty)(on?B?A)

(on?C?B)(clear?C))

:ordered((clear?B)(hand-empty)))

it.Table4shows the analogous skills learned by the explanation-based method,which have very speci?c start conditions.This results in learning distinct ver-sions of(clear?A)for problems with di?erent num-ber of blocks stacked on block A.

The left hand graph in Figure2shows the superior performance of our system compared to explanation-based learning.The plots show the cumulative num-ber of successful examples averaged over20di?erent selections and orderings of100input problems in the Blocks World domain for each algorithm.On average, our system learns14new skills from a few problems and solves100percent of the test problems,while the explanation-based method learns119skills and solves fewer than50percent of the novel problems.The dot-ted line shows the behavior of an expert who can solve all problems from the outset.Our method’s behaviour follows this line very closely,with a small lag caused by a few failures at the early stages of learning.The small error bars show that the behaviors are similar across di?erent problem orderings.

5.3.Experiments with Depots

Depots is a more complicated domain that was intro-duced in the Third International Planning Competi-tion(Bacchus,2000).With crates that can be loaded into trucks and driven to di?erent locations where they are unloaded and stacked onto pallets,it combines at-tributes of Blocks World with logistics planning.Since a typical problem involves many objects and each state has many possible actions,search can be very expen-sive in this domain and manually coding the knowledge base is challenging.We gave the system23concepts and eight primitive skills,and we used two di?erent goals that refer to con?gurations of one or two crates.For this study,we generated96random problems for use in the experiment.These problems include up to ?ve crates,with di?culty levels ranging from one to 13-step solution paths depending on the initial con-?guration.The right-hand graph in Figure2shows the cumulative number of successes averaged over20 di?erent problem orderings for our algorithm.

The number of skills our system learns through this experiment is42on average,which is not su?cient to solve all the problems,but which does solve70per-cent of them.For this domain,although the hierarchi-cal explanation-based algorithm generated some cor-rect skills,it was very slow and could solve very few of the problems.As anticipated,because the learned skills are overspeci?c,it creates many skills(e.g.,some 100skills resulted from only four problems).However, we may be able to improve these results by generat-ing multiple traces from a single problem.For ex-ample,if a goal G is associated with a skill sequence S1,S2,S3,...,S n,the current technique learns one skill that achieves G using these subskills,but the subse-quences(S2,S3,...,S n),(S3,S4,...,S n),...,(S n)are also valid sequences for achieving G and can be used for training purposes.On the other hand,this would produce a more complex collection of skills that could slow response time further.

6.Related Research

Developing agents that can learn complex skills from experience has been a recurring goal in arti?cial in-telligence.A common approach to this problem has focused on learning from delayed external rewards. Some methods(e.g.,Moriarty et al.,1999)search through the space of the policies directly,whereas others(e.g.,Kaelbling et al.,1996)estimate value functions for state-action pairs.In contrast,our ap-proach di?ers by learning from traces of expert behav-ior rather than from exploration and by constructing hierarchical structures rather than?at policies. There has been some work on learning control poli-cies from expert traces.One of the main paradigms, known as behavioral cloning,transforms the observed traces into supervised training cases and induces re-active controllers that reproduce the behavior in sim-ilar situations.This approach typically casts learned knowledge as decision trees that determine which ac-tions to take based on sensor input(e.g.,Urbancic& Bratko,1994).More recently,some e?orts(e.g.,Isaac &Sammut,2003)have used goal information,stated as desired values for state variables,to improve the robustness of the learned controllers.In contrast,our approach infers intermediate structural goals by ex-

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C u m u l a t i v e p r o b l e m s s o l v e d Expert behavior

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80100Number of problems encountered

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Hier. task network learning Figure 2.Cumulative number of solved problems in the Blocks World and Depots domains,with 95percent con?dence intervals.The diagonal lines depict the behavior of an expert who solves all the problems.

plaining the expert behavior in terms of the top-level goal and background knowledge.Moreover,our frame-work di?ers from most work on behavioral cloning by incorporating a hierarchical and relational representa-tion for states and activities.

K¨o nik and Laird (2004)report an approach to behav-ioral cloning that uses a relational representation and learns hierarchical controllers,but it requires the ex-pert to annotate the trace with information about the start and end of activities at each level.A few other systems also learn hierarchical structures from expert behavior.Ilghami et al.(2005)describe a method for constructing hierarchical task networks,but they assume the hierarchical structure is given and use a version-space algorithm to determine conditions on methods.Tecuci’s (1998)Disciple acquires hierarchi-cal rules,but it requires user information about how to decompose problems and the reasons for decisions.Other research on learning skills by observing others’behavior has,like our own,utilized domain knowledge to interpret traces.Some work on explanation-based learning (e.g.,Segre,1987;Mooney 1990)took this approach,as did the paradigms of learning appren-tices (e.g.,Mitchell et al.,1985)and programming by demonstration (e.g.,Cypher,1993;Lau et al.,2003).Both often used analytic methods to generate candi-date procedures,but neither focused on the acquisi-tion of hierarchical skills,and programming by demon-stration typically requires user feedback about candi-date hypotheses.As noted earlier,our approach dif-fers from explanation-based learning in that it retains the explanation structure and does not use deductive analysis to determine start conditions on new skills.

7.Concluding Remarks

In this paper,we have presented a new approach to learning hierarchical task networks from observation.We explained our reliance on expert traces to avoid the need for extensive search during problem solving.We also reviewed the notion of teleoreactive logic pro-grams,a special class of task networks that are indexed by the goals they achieve,along with mechanisms for executing them to reach these objectives.After this,we described the details of our method for learning skill clauses from solution traces,which alternates between chaining o?skills and concept de?nitions to generate an explanation of the expert’s behavior.The system then creates one skill clause for each node in the expla-nation structure,using a simple technique for ?nding conditions on clauses that uses only local information.Our approach incorporates ideas from a number of dis-tinct traditions,including behavioral cloning,learn-ing apprentices,and programming by demonstration,but it goes beyond these movements to construct hi-erarchical structures that generalize well to new prob-lems.Moreover,experiments in two domains demon-strated that our method learns much more rapidly than explanation-based techniques,whether they con-struct ?at macro-operators or take advantage of the learned skill hierarchy.This suggests that our ap-proach to constructing hierarchical task networks of-fers advantages over more traditional techniques for learning plan knowledge.

Despite these encouraging results,our work on learn-ing by observation remains in its early stages,and our current implementation makes some simplifying as-

sumptions that we should remedy in future work.One assumption is that the expert trace includes all rele-vant steps,whereas a more robust agent might infer oc-casional steps that it does not observe.Another is that learner knows the agent’s goals,whereas an improved system would infer them from the trace and back-ground knowledge.Our current method also assumes that the environment changes only when the agent takes some action,whereas future versions should han-dle settings in which some events are due to indepen-dent physical causes or other agents’behaviors.

In addition,our approach relies heavily on accurate knowledge about each skill’s e?ects,whereas a more ?exible learner would also include some ability to re-vise its action models based on observed results.Fi-nally,the current system assumes that the expert has carried out the best sequence to achieve the goal, whereas a more sophisticated approach would analyze the trace for loops or other ine?ciencies and remove them before learning.We hope to address each of these issues in future learning systems that combine domain knowledge with traces of expert behavior to acquire complex hierarchical task networks. Acknowledgements

This paper reports research sponsored by DARPA un-der agreement FA8750-05-2-0283.The https://www.wendangku.net/doc/6a84256.html,ern-ment may reproduce and distribute reprints for Gov-ernmental purposes notwithstanding any copyrights. The authors’views and conclusions should not be in-terpreted as representing o?cial policies or endorse-ments,expressed on implied,of DARPA or the Gov-ernment.We thank Dongkyu Choi for discussions that contributed to the ideas presented in this paper. References

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