Refining complexity analyses in planning by exploiting the exponential time hypothesis

The use of computational complexity in planning, and in AI in general, has always been a disputed topic. A major problem with ordinary worst-case analyses is that they do not provide any quantitative information: they do not tell us much about the running time of concrete algorithms, nor do they tell us much about the running time of optimal algorithms. We address problems like this by presenting results based on the exponential time hypothesis (ETH), which is a widely accepted hypothesis concerning the time complexity of 3-SAT. By using this approach, we provide, for instance, almost matching upper and lower bounds onthe time complexity of propositional planning.Funding Agencies|National Graduate School in Computer Science (CUGS), Sweden; Swedish Research Council (VR) [621-2014-4086]</p

Implementation och utökning av en typhärledningsalgoritm för Common Lisp

Programmeringsspråk har oftast ett typsystem och kan välja att använda olika statiska verktyg att analysera koden. Statiska språk utför typkontroller innan körtillfället och kan då ge garantier att typfel inte kan förekomma, dynamiska språk gör däremot dessa kontroller under körtillfället och om ett dåligt beteende upptäcks avbryts programmet. Eftersom kontrollerna görs under körtillfället skrivs inte typsignaturer ut i dynamiska språk. Ett dynamiskt språk kan vara mer flexibelt än ett statiskt språk eftersom inga garantier ges. Eftersom inga typsignaturer skrivs ut går det att skriva program på ett mer koncist sätt. I statiska språk tvingas oftast användaren att skriva ut typerna explicit för variabler och funktioner. Typhärledning är processen att härleda typer för uttryck. En typhärledningalgoritm kommer att undersökas, hur kraftfull algoritmen är samt hur algoritmen kan utökas för att klara av flera konstruktioner och ett kraftfullare språk. Typhärledningsalgoritmen kommer att implementeras för Common Lisp. Common Lisp ger inga typgarantier och inga typsignaturer skrivs ut. Alla typer kommer att härledas vilket innebär att vi gör om en delmängd av Common Lisp till ett statiskt språk. Algoritmen kommer att utökas för att klara av polymorfism, closures, listor och par. Rapporten undersöker vilka ändringar som behöver göras för att stödja konstruktionerna, hur vi kan göra ändringarna hur de kan implementeras. Fördelar med att ha typhärledning är att användaren slipper skriva ut typsignaturer och kan få ökad produktivitet. Den mest generella typsignaturen kommer alltid att härledas och funktioner som är polymorfa kommer att upptäckas automatiskt. Typhärledningsalgoritmen kommer att även typkontrollera programmet, och kan ge garantier att inga problem kommer att uppstå. Verktyget kommer även att skapa ett nytt program med typsignaturer utskrivna som kompilatorn kan använda för att generera effektivare kod

Tailoring Pattern Databases for Unsolvable Planning Instances

There has been an astounding improvement in domain-independent planning for solvable instances over the last decades and planners have become increasingly efficient at constructing plans. However, this advancement has not been matched by a similar improvement for identifying unsolvable instances. In this paper, we specialise pattern databases for dead-end detection and, thus, for detecting unsolvable instances. We propose two methods of constructing pattern collections and show that spending any more time constructing the pattern collection is likely to be unproductive. In other words, very few other pattern collections within the given space bounds are able to detect more dead-ends. We show this by carrying out a novel statistical analysis: a large computer cluster has been used to approximate the limit of pattern collections with respect to dead-end detection for many unsolvable instances, and this information is used in the analysis of the proposed methods. Consequently, further improvement must come from combining pattern databases with other techniques, such as mutexes. Furthermore, we explain why one of the proposed methods tends to find significantly more unsolvable variable projections, which is desirable since they imply that the instance is unsolvable. Finally, we compare the best proposed method with the winner and the runner up of the first unsolvability international planning competition, and show that the method is competitive

Implementation och utökning av en typhärledningsalgoritm för Common Lisp

Programmeringsspråk har oftast ett typsystem och kan välja att använda olika statiska verktyg att analysera koden. Statiska språk utför typkontroller innan körtillfället och kan då ge garantier att typfel inte kan förekomma, dynamiska språk gör däremot dessa kontroller under körtillfället och om ett dåligt beteende upptäcks avbryts programmet. Eftersom kontrollerna görs under körtillfället skrivs inte typsignaturer ut i dynamiska språk. Ett dynamiskt språk kan vara mer flexibelt än ett statiskt språk eftersom inga garantier ges. Eftersom inga typsignaturer skrivs ut går det att skriva program på ett mer koncist sätt. I statiska språk tvingas oftast användaren att skriva ut typerna explicit för variabler och funktioner. Typhärledning är processen att härleda typer för uttryck. En typhärledningalgoritm kommer att undersökas, hur kraftfull algoritmen är samt hur algoritmen kan utökas för att klara av flera konstruktioner och ett kraftfullare språk. Typhärledningsalgoritmen kommer att implementeras för Common Lisp. Common Lisp ger inga typgarantier och inga typsignaturer skrivs ut. Alla typer kommer att härledas vilket innebär att vi gör om en delmängd av Common Lisp till ett statiskt språk. Algoritmen kommer att utökas för att klara av polymorfism, closures, listor och par. Rapporten undersöker vilka ändringar som behöver göras för att stödja konstruktionerna, hur vi kan göra ändringarna hur de kan implementeras. Fördelar med att ha typhärledning är att användaren slipper skriva ut typsignaturer och kan få ökad produktivitet. Den mest generella typsignaturen kommer alltid att härledas och funktioner som är polymorfa kommer att upptäckas automatiskt. Typhärledningsalgoritmen kommer att även typkontrollera programmet, och kan ge garantier att inga problem kommer att uppstå. Verktyget kommer även att skapa ett nytt program med typsignaturer utskrivna som kompilatorn kan använda för att generera effektivare kod

Methods for Detecting Unsolvable Planning Instances using Variable Projection

In this thesis we study automated planning, a branch of artificialintelligence, which deals with construction of plans. A plan is typically an action sequence that achieves some specific goal. In particular, we study unsolvable planning instances, i.e. there is no plan. Historically, this topic has been neglected by the planning community, and up to recently the International Planning Competition has only evaluated planners on solvable planning instances. For many applications we can know, e.g. by design, that there is a solution, but this cannot be a general assumption. One example is penetration testing in computer security, where a system inconsidered safe if there is no plan for intrusion. Other examples are resource bound planning instances that have insufficient resources to achieve the goal. The main theme of this thesis is to use variable projection to prove unsolvability of planning instances. We implement and evaluate two planners: the first checks variable projections with the goal of finding an unsolvable projection, and the second builds a pattern collection to provide dead-end detection. In addition to comparing the planners to existing planners, we also utilise a large computer cluser to statistically assess whether they can be optimised further. On the benchmarks of planning instances that we used, it turns out that further improvement is likely to come from supplementary techniques rather than optimisation. We pursued this and enhanced variable projections with mutexes, which yielded a very competitive planner. We also inspect whether unsolvable variable projections tend to be composed of variables that play different roles, i.e. they are not 'similar'. We devise a variable similarity measure to rate how similar two variables are on a scale, and statistically analyse it. The measure can differentiate between unsolvable and solvable planning instances quite well, and is integrated into our planners. We also define a binary version of the measure, namely, that two variables are isomorphic if they behave exactly the same in some optimal solution (extremely similar). With the help of isomorphic variables we identified a computationally tractable class of planning instances that meet certain restrictions. There are several special cases of this class that are of practical interest, and this result encompass them

Identifying Unsolvable Instances, Forbidden States and Irrelevant Information in Planning

Planning is a central research area in artificial intelligence, and a lot of effort has gone into constructing more and more efficient planning algorithms. In real-world examples, many problem instances do not have a solution. Hence, there is an obvious need for methods that are capable of identifying unsolvable instances efficiently. It is not possible to efficiently identify all unsolvable instances due to the inherent high complexity of planning, but many unsolvable instances can be identified in polynomial time. We present a number of novel methods for doing this. We adapt the notion of k-consistency (a well-studied concept from constraint satisfaction) for testing unsolvability of planning instances. The idea is to decompose a given problem instance into a number of smaller instances which can be solved in polynomial time. If any of the smaller instances are unsolvable, then the original instance is unsolvable. If all the smaller instances are solvable, then it is possible to extract information which can be used to guide the search. For instance, we introduce the notion of forbidden state patterns that are partial states that must be avoided by any solution to the problem instance. This can be viewed as the opposite of pattern databases which give information about states which can lead to a solution.  We also introduce the notion of critical sets and show how to identify them. Critical sets describe operators or values which must be used or achieved in any solution. It is a variation on the landmark concept, i.e., operators or values which must be used in every solution. With the help of critical sets we can identify superfluous operators and values. These operators and values can be removed by preprocessing the problem instance to decrease planning time

Learning Generalized Unsolvability Heuristics for Classical Planning

Recent work in classical planning has introduced dedicated techniques for detecting unsolvable states, i.e., states from which no goal state can be reached. We approach the problem from a generalized planning perspective and learn first-order-like formulas that characterize unsolvability for entire planning domains. We show how to cast the problem as a self-supervised classification task. Our training data is automatically generated and labeled by exhaustive exploration of small instances of each domain, and candidate features are automatically computed from the predicates used to define the domain. We investigate three learning algorithms with different properties and compare them to heuristics from the literature. Our empirical results show that our approach often captures important classes of unsolvable states with high classification accuracy. Additionally, the logical form of our heuristics makes them easy to interpret and reason about, and can be used to show that the characterizations learned in some domains capture exactly all unsolvable states of the domain.

Tractable Cost-Optimal Planning over Restricted Polytree Causal Graphs

Causal graphs are widely used to analyze the complexity of planning problems. Many tractable classes have been identified with their aid and state-of-the-art heuristics have been derived by exploiting such classes. In particular, Katz and Keyder have studied causal graphs that are hourglasses (which is a generalization of forks and inverted-forks) and shown that the corresponding cost-optimal planning problem is tractable under certain restrictions. We continue this work by studying polytrees (which is a generalization of hourglasses) under similar restrictions. We prove tractability of cost-optimal planning by providing an algorithm based on a novel notion of variable isomorphism. Our algorithm also sheds light on the k-consistency procedure for identifying unsolvable planning instances. We speculate that this may, at least partially, explain why merge-and-shrink heuristics have been successful for recognizing unsolvable instances

Fast Detection of Unsolvable Planning Instances Using Local Consistency

There has been a tremendous advance in domain-independent planning over the past decades, and planners have become increasingly efficient at finding plans. However, this has not been paired by any corresponding improvement in detecting unsolvable instances. Such instances are obviously important but largely neglected in planning. In other areas, such as constraint solving and model checking, much effort has been spent on devising methods for detecting unsolvability. We introduce a method for detecting unsolvable planning instances that is loosely based on consistency checking in constraint programming. Our method balances completeness against efficiency through a parameter k: the algorithm identifies more unsolvable instances but takes more time for increasing values of k. We present empirical data for our algorithm and some standard planners on a number of unsolvable instances, demonstrating that our method can be very efficient where the planners fail to detect unsolvability within reasonable resource bounds. We observe that planners based on the h^m heuristic or pattern databases are better than other planners for detecting unsolvability. This is not a coincidence since there are similarities (but also significant differences) between our algorithm and these two heuristic methods

Learning General Optimal Policies with Graph Neural Networks: Expressive Power, Transparency, and Limits

It has been recently shown that general policies for many classical planning domains can be expressed and learned in terms of a pool of features defined from the domain predicates using a description logic grammar. At the same time, most description logics correspond to a fragment of $k$-variable counting logic ($C_k$) for $k=2$, that has been shown to provide a tight characterization of the expressive power of graph neural networks. In this work, we make use of these results to understand the power and limits of using graph neural networks (GNNs) for learning optimal general policies over a number of tractable planning domains where such policies are known to exist. For this, we train a simple GNN in a supervised manner to approximate the optimal value function $V^{*}(s)$ of a number of sample states $s$. As predicted by the theory, it is observed that general optimal policies are obtained in domains where general optimal value functions can be defined with $C_2$ features but not in those requiring more expressive $C_3$ features. In addition, it is observed that the features learned are in close correspondence with the features needed to express $V^{*}$ in closed form. The theory and the analysis of the domains let us understand the features that are actually learned as well as those that cannot be learned in this way, and let us move in a principled manner from a combinatorial optimization approach to learning general policies to a potentially, more robust and scalable approach based on deep learning.Comment: Proceedings of the 32nd International Conference on Automated Planning and Scheduling (ICAPS-22