Thomas Keller Publikationen
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2020
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Florian Geißer, David Speck und Thomas Keller.
Trial-based Heuristic Tree Search for MDPs with Factored Action Spaces.
In
Proceedings of the 13th Annual Symposium on Combinatorial Search (SoCS 2020), S. 38-47.
2020.
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MDPs with factored action spaces, i.e. where actions are described as assignments to a set of action variables, allow reasoning over action variables instead of action states, yet most algorithms only consider a grounded action representation. This includes algorithms that are instantiations of the trial-based heuristic tree search (THTS) framework, such as AO* or UCT.
To be able to reason over factored action spaces, we propose a generalisation of THTS where nodes that branch over all applicable actions are replaced with subtrees that consist of nodes that represent the decision for a single action variable. We show that many THTS algorithms retain their theoretical properties under the generalised framework, and show how to approximate any state-action heuristic to a heuristic for partial action assignments. This allows to guide a UCT variant that is able to create exponentially fewer nodes than the same algorithm that considers ground actions. An empirical evaluation on the benchmark set of the probabilistic track of the latest International Planning Competition validates the benefits of the approach.
2019
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Florian Geißer, David Speck und Thomas Keller.
An Analysis of the Probabilistic Track of the IPC 2018.
In
Proceedings of the ICAPS-2019 Workshop on the International Planning Competition (WIPC 2019), S. 27-35.
2019.
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The International Planning Competition 2018 consisted of several tracks on classical, temporal and probabilistic planning. In this paper, we focus on the discrete MDP track of the probabilistic portion of the competition.
We discuss the changes to the input language RDDL, which give rise to new challenges for planning systems, and analyze each of the eight competition domains separately and highlight unique properties. We demonstrate flaws of the used evaluation criterion, the IPC score, and discuss the need for optimal upper bounds. An evaluation of the three top-performers, including their post-competition versions, and a brief analysis of their performance highlights the strengths and weaknesses of the individual approaches.
2016
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Thomas Keller, Florian Pommerening, Jendrik Seipp, Florian Geißer und Robert Mattmüller.
State-dependent Cost Partitionings for Cartesian Abstractions in Classical Planning (Extended Abstract).
In
Proceedings of the 39th German Conference on Artificial Intelligence (KI 2016).
2016.
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Abstraction heuristics are a popular method to guide optimal search algorithms in classical planning. Cost partitionings allow to sum heuristic estimates admissibly by partitioning action costs among the abstractions. We introduce state-dependent cost partitionings which take context information of actions into account, and show that an optimal state-dependent cost partitioning dominates its state-independent counterpart. We demonstrate the potential of state-dependent cost partitionings with a state-dependent variant of the recently proposed saturated cost partitioning, and show that it can sometimes improve not only over its state-independent counterpart, but even over the optimal state-independent cost partitioning.
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Thomas Keller, Florian Pommerening, Jendrik Seipp, Florian Geißer und Robert Mattmüller.
State-dependent Cost Partitionings for Cartesian Abstractions in Classical Planning:Full Proofs.
Technischer Bericht CS-2016-002,
University of Basel, 2016.
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Abstraction heuristics are a popular method to guide optimal search algorithms in classical planning. Cost partitionings allow to sum heuristic estimates admissibly by distributing action costs among the heuristics. We introduce state-dependent cost partitionings which take context information of actions into account, and show that an optimal state-dependent cost partitioning dominates its state-independent counterpart. We demonstrate the potential of our idea with a state-dependent variant of the recently proposed saturated cost partitioning, and show that it has the potential to improve not only over its state-independent counterpart, but even over the optimal state-independent cost partitioning. Our empirical results give evidence that ignoring the context of actions in the computation of a cost partitioning leads to a significant loss of information. This technical report contains the full proofs for Theorem 1, Theorem 3 and Lemma 1.
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Thomas Keller, Florian Pommerening, Jendrik Seipp, Florian Geißer und Robert Mattmüller.
State-dependent Cost Partitionings for Cartesian Abstractions in Classical Planning.
In
Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI 2016).
2016.
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Abstraction heuristics are a popular method to guide optimal search algorithms in classical planning. Cost partitionings allow to sum heuristic estimates admissibly by distributing action costs among the heuristics. We introduce state-dependent cost partitionings which take context information of actions into account, and show that an optimal state-dependent cost partitioning dominates its state-independent counterpart. We demonstrate the potential of our idea with a state-dependent variant of the recently proposed saturated cost partitioning, and show that it has the potential to improve not only over its state-independent counterpart, but even over the optimal state-independent cost partitioning. Our empirical results give evidence that ignoring the context of actions in the computation of a cost partitioning leads to a significant loss of information.
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Florian Geißer, Thomas Keller und Robert Mattmüller.
Abstractions for Planning with State-Dependent Action Costs.
In
Proceedings of the 26th International Conference on Automated Planning and Scheduling (ICAPS 2016).
2016.
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Extending the classical planning formalism with state-dependent action
costs (SDAC) allows an up to exponentially more compact task encoding.
Recent work proposed to use edge-valued multi-valued decision diagrams
(EVMDDs) to represent cost functions, which allows to automatically detect
and exhibit structure in cost functions and to make heuristic estimators
accurately reflect SDAC. However, so far only the inadmissible additive
heuristic has been considered in this context. In this paper, we define
informative admissible abstraction heuristics which enable optimal
planning with SDAC. We discuss how abstract cost values can be extracted
from EVMDDs that represent concrete cost functions without adjusting them
to the selected abstraction. Our theoretical analysis shows that this is
efficiently possible for abstractions that are Cartesian or coarser. We
adapt the counterexample-guided abstraction refinement approach to derive
such abstractions. An empirical evaluation of the resulting heuristic
shows that highly accurate values can be computed quickly.
2015
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Florian Geißer, Thomas Keller und Robert Mattmüller.
Delete Relaxations for Planning with State-Dependent Action Costs.
In
Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015).
2015.
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Most work in planning focuses on tasks with state-independent or
even uniform action costs. However, supporting state-dependent
action costs admits a more compact representation of many
tasks. We investigate how to solve such tasks using heuristic
search, with a focus on delete-relaxation heuristics. We first
define a generalization of the additive heuristic to such tasks
and then discuss different ways of computing it via compilations
to tasks with state-independent action costs and more directly
by modifying the relaxed planning graph. We evaluate these
approaches theoretically and present an implementation of the
generalized additive heuristic for planning with state-dependent
action costs. To our knowledge, this gives rise to the first
approach able to handle even the hardest instances of the
combinatorial Academic Advising domain from the International
Probabilistic Planning Competition (IPPC) 2014.
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Florian Geißer, Thomas Keller und Robert Mattmüller.
Delete Relaxations for Planning with State-Dependent Action Costs.
In
Proceedings of the 8th Annual Symposium on Combinatorial Search (SoCS 2015).
2015.
Extended abstract of the IJCAI 2015 paper by the same name.
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Supporting state-dependent action costs in planning admits a
more compact representation of many tasks. We generalize the
additive heuristic and compute it by embedding decision-diagram
representations of action cost functions into the RPG. We give a
theoretical evaluation and present an implementation of the
generalized additive heuristic. This allows us to handle even
the hardest instances of the combinatorial Academic Advising
domain from the IPPC 2014.
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Thomas Keller und Florian Geißer.
Better Be Lucky Than Good: Exceeding Expectations in MDP Evaluation.
In
Proceedings of the 29th AAAI Conference on Artificial
Intelligence (AAAI
2015).
AAAI Press 2015.
Erratum: On page 7, we mention that the results at IPPC
would have differed by "-0.09", "+0.04" and "+0.05", which should
read "-0.009", "+0.004" and "+0.005" instead.
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We introduce the MDP-Evaluation Stopping Problem, the
optimization problem faced by participants of the International
Probabilistic Planning Competition 2014 that focus on their own
performance. It can be constructed as a meta-MDP where actions
correspond to the application of a policy on a base-MDP, which
is intractable in practice. Our theoretical analysis reveals
that there are tractable special cases where the problem can be
reduced to an optimal stopping problem. We derive approximate
strategies of high quality by relaxing the general problem to an
optimal stopping problem, and show both theoretically and
experimentally that it not only pays off to pursue luck in the
execution of the optimal policy, but that there are even cases
where it is better to be lucky than good as the execution of a
suboptimal base policy is part of an optimal strategy in the
meta-MDP.
2014
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Tim Schulte und Thomas Keller.
Balancing Exploration and Exploitation in Classical Planning.
In
Proceedings of the Seventh Annual Symposium on Combinatorial Search (SoCS 2014)
(SoCS 2014).
2014.
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Successful heuristic search planners for satisficing planning like FF or LAMA
are usually based on one or more best first search techniques. Recent research
has led to planners like Arvand, Roamer or Probe, where novel techniques like
Monte-Carlo Random Walks extend the traditional exploitation-focused best first
search by an exploration component. The UCT algorithm balances these
contradictory incentives and has shown tremendous success in related areas of
sequential decision making but has never been applied to classical planning
yet. We make up for this shortcoming by applying the Trial-based Heuristic Tree
Search framework to classical planning. We show how to model the best first
search techniques Weighted A* and Greedy Best First Search with only three
ingredients: action selection, initialization and backup function. Then we use
THTS to derive four versions of the UCT algorithm that differ in the used
backup functions. The experimental evaluation shows that our main algorithm,
GreedyUCT*, outperforms all other algorithms presented in this paper,
both in terms of coverage and quality.
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Andreas Hertle, Christian Dornhege, Thomas Keller, Robert Mattmüller, Manuela Ortlieb und Bernhard Nebel.
An Experimental Comparison of Classical, FOND and Probabilistic Planning.
In
Proceedings of the 37th German Conference on Artificial Intelligence (KI 2014), S. 297-308.
Springer 2014.
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Domain-independent planning in general is broadly applicable to a wide range of tasks.
Many formalisms exist that allow to describe different aspects of realistic problems.
Which one is best is not clear as usually more expressiveness comes with a cost in
planning time. Under the assumption that hard guarantees are not required, users are
faced with a decision between multiple approaches. In this work we study the effect of
nondeterministic action outcomes. As a generic model we use a probabilistic description
in the form of Markov Decision Processes (MDPs). We define abstracting translations
into a classical planning formalism and fully observable nondeterministic (FOND)
planning. Our goal is to give insight into how state-of-the-art systems perform on
different MDP planning domains. We evaluate those MDPs by running state-of-the-art
planning systems on the abstracted formalisms.
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Florian Geißer, Thomas Keller und Robert Mattmüller.
Past, Present, and Future: An Optimal Online Algorithm for Single-Player GDL-II Games.
In
Proceedings of the 21st European Conference on Artificial Intelligence (ECAI 2014), S. 357-362.
2014.
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In General Game Playing, a player receives the rules of an unknown game and
attempts to maximize his expected reward. Since 2011, the GDL-II rule language
extension allows the formulation of nondeterministic and partially observable
games. In this paper, we present an algorithm for such games, with a focus on
the single-player case. Conceptually, at each stage, the proposed Norns algorithm
distinguishes between the past, present and future steps of the game. More
specifically, a belief state tree is used to simulate a potential past that
leads to a present that is consistent with received observations. Unlike other
related methods, our method is asymptotically optimal. Moreover, augmenting the
belief state tree with iteratively improved probabilities speeds up the
process over time significantly.
As this allows a true picture of the present, we additionally present an
optimal version of the well-known UCT algorithm for partially observable
single-player games. Instead of performing hindsight optimization on a
simplified, fully observable tree, the true future is simulated on an
action-observation tree that takes partial observability into account. The
expected reward estimates of applicable actions converge towards the true
expected rewards even for moves that are only used to gather information. We
prove that our algorithm is asymptotically optimal for single-player games and
POMDPs and support our claim with an empirical evaluation.
2013
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Thomas Keller und Malte Helmert.
Trial-based Heuristic Tree Search for Finite Horizon MDPs.
In
Proceedings of the 1st Multidisciplinary Conference on Reinforcement Learning and Decision Making
(RLDM 2013), S. 101-105.
2013.
Extended abstract of the ICAPS 2013 paper by the same name.
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Dynamic programming is a well-known approach for solving MDPs. In
large state spaces, asynchronous versions like Real-Time Dynamic
Programming (RTDP) have been applied successfully. If unfolded
into equivalent trees, Monte-Carlo Tree Search algorithms are a
valid alternative. UCT, the most popular representative, obtains
good anytime behavior by guiding the search towards promising
areas of the search tree and supporting non-admissible
heuristics. The global Heuristic Search algorithm AO* finds
optimal solutions for MDPs that can be represented as acyclic
AND/OR graphs.
Despite the differences, these approaches actually have much in
common. We present the Trial-based Heuristic Tree Search (THTS)
framework that subsumes these approaches and distinguishes them
based on only five ingredients: heuristic function, backup
function, action selection, outcome selection, and trial
length. We describe the ingredients that model RTDP, AO* and UCT
within this framework, and use THTS to combine attributes of these
algorithms step by step in order to derive novel algorithms with
superior theoretical properties. We merge Full Bellman and
Monte-Carlo backup functions to Partial Bellman backups, and gain
a function that both allows partial updates and a procedure that
labels states when they are solved. DP-UCT combines attributes and
theoretical properties from RTDP and UCT even though it differs
from the latter only in the used Partial Bellman backups. Our main
algorithm, UCT* adds a limited trial length to DP-UCT to inherit
the global search behavior of AO*, which ensures that parts of the
state space that are closer to the root are investigated more
thoroughly. The experimental evaluation shows that both DP-UCT and
UCT* are not only superior to UCT, but also outperform P ROST, the
winner of the International Probabilistic Planning Competition
(IPPC) 2011 on the benchmarks of IPPC 2011.
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Thomas Keller und Malte Helmert.
Trial-based Heuristic Tree Search for Finite Horizon MDPs.
In
Proceedings of the 23rd International Conference on
Automated Planning and Scheduling (ICAPS 2013), S. 135-143.
2013.
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Dynamic programming is a well-known approach for solving
MDPs. In large state spaces, asynchronous versions like
Real-Time Dynamic Programming have been applied successfully. If
unfolded into equivalent trees, Monte-Carlo Tree Search
algorithms are a valid alternative. UCT, the most popular
representative, obtains good anytime behavior by guiding the
search towards promising areas of the search tree. The Heuristic
Search algorithm AO∗ finds optimal solutions for MDPs that can
be represented as acyclic AND/OR graphs.
We introduce a common framework, Trial-based Heuristic Tree
Search, that subsumes these approaches and distinguishes them
based on five ingredients: heuristic function, backup function,
action selection, outcome selection, and trial length. Using
this framework, we describe three new algorithms which mix these
ingredients in novel ways in an attempt to combine their
different strengths. Our evaluation shows that two of our
algorithms not only provide superior theoretical properties to
UCT, but also outperform state-of-the-art approaches
experimentally.
2012
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Thomas Keller und Patrick Eyerich.
PROST: Probabilistic Planning Based on UCT.
In
Proceedings of the 22nd International Conference on
Automated Planning and Scheduling (ICAPS 2012), S. 119-127.
2012.
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We present PROST, a probabilistic planning system that is based
on the UCT algorithm by Kocsis and Szepesvari (2006), which has
been applied successfully to many areas of planning and acting
under uncertainty. The objective of this paper is to show the
application of UCT to domain-independent probabilistic planning,
an area it had not been applied to before. We furthermore
present several enhancements to the algorithm, including a
method that is able to drastically reduce the branching factor
by identifying superfluous actions. We show how search depth
limitation leads to a more thoroughly investigated search space
in parts that are influential on the quality of a policy, and
present a sound and polynomially computable detection of reward
locks, states that correspond to, e.g., dead ends or goals. We
describe a general Q-value initialization for unvisited nodes in
the search tree that circumvents the initial random walks
inherent to UCT, and leads to a faster convergence on
average. We demonstrate the significant influence of the
enhancements by providing a comparison on the IPPC benchmark
domains.
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Johannes Löhr, Patrick Eyerich, Thomas Keller und Bernhard Nebel.
A Planning Based Framework for Controlling Hybrid Systems.
In
Proceedings of the 22nd International Conference on
Automated Planning and Scheduling (ICAPS
2012).
2012.
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The control of dynamic systems, which aims to minimize the
deviation of state variables from reference values in a contin-
uous state space, is a central domain of cybernetics and con-
trol theory. The objective of action planning is to find
feasible state trajectories in a discrete state space from an
initial state to a state satisfying the goal conditions, which
in principle ad- dresses the same issue on a more abstract
level. We combine these approaches to switch between dynamic
system charac- teristics on the fly, and to generate control
input sequences that affect both discrete and continuous state
variables. Our approach (called Domain Predictive Control) is
applicable to hybrid systems with linear dynamics and
discretizable inputs.
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Andreas Hertle, Christian Dornhege, Thomas Keller und Bernhard Nebel.
Planning with Semantic Attachments: An Object-Oriented View.
In
Proceedings of the European Conference on Artificial Intelligence (ECAI).
2012.
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In recent years, domain-independent planning has been applied to
a rising number of real-world applications. Usually, the
description language of choice is PDDL. However, PDDL is not
suited to model all challenges imposed by real-world
applications. Dornhege et al. proposed semantic attachments to
allow the computation of Boolean fluents by external processes
called modules during planning. To acquire state information
from the planning system a module developer must perform manual
requests through a callback interface which is both
inefficient and error-prone.
In this paper, we present the Object-oriented Planning Language
OPL, which incorporates the structure and advantages of modern
object-oriented programming languages. We demonstrate how a
domain-specific module interface that allows to directly access
the planner state using object member functions is automatically
gen- erated from an OPL planning task. The generated
domain-specific interface allows for a safe and less error-prone
implementation of modules. We show experimentally that this
interface is more efficient than the PDDL-based module interface
of TFD/M.
2011
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Danijel Skocaj, Matej Kristan, Alen Vrecko, Marko Mahnic, Miroslav Janicek, Geert-Jan M. Kruijff, Marc Hanheide, Nick Hawes, Thomas Keller, Michael Zillich und Kai Zhou.
A system for interactive learning in dialogue with a tutor.
In
Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011).
2011.
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In this paper we present representations and mechanisms that
facilitate continuous learning of visual concepts in dialogue
with a tutor and show the implemented robot system. We present
how beliefs about the world are created by processing visual
and linguistic information and show how they are used for
planning system behaviour with the aim at satisfying its
internal drive -- to extend its knowledge. The system
facilitates different kinds of learning initiated by the human
tutor or by the system itself. We demonstrate these principles
in the case of learning about object colours and basic shapes.
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Thomas Keller und Patrick Eyerich.
A Polynomial All Outcome Determinization for Probabilistic
Planning.
In
Fahiem Bacchus, Carmel Domshlak, Stefan Edelkamp und Malte Helmert (Hrsg.),
Proceedings of the 21th International Conference on Automated
Planning and Scheduling (ICAPS 2011), S. 331-334.
AAAI Press 2011.
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Most predominant approaches in probabilistic planning utilize
techniques from the more thoroughly investigated field of
classical planning by determinizing the problem at hand. In
this paper, we present a method to map probabilistic operators
to an equivalent set of probabilistic operators in a novel
normal form, requiring polynomial time and space. From this,
we directly derive a determinization which can be used for,
\eg, replanning strategies incorporating a classical planning
system. Unlike previously described all outcome
determinizations, the number of deterministic operators is not
exponentially but polynomially bounded in the number of
parallel probabilistic effects, enabling the use of more
sophisticated determinization-based techniques in the future.
2010
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Thomas Keller, Patrick Eyerich und Bernhard Nebel.
Task Planning for an Autonomous Service Robot.
In
Rüdiger Dillmann, Jürgen Beyerer, Uwe Hanebeck und Tanja Schultz (Hrsg.),
Proceedings on the 33rd Annual German Conference on Artificial Intelligence (KI 2010), S. 358-365.
Springer-Verlag 2010.
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In the DESIRE project an autonomous robot capable of performing service tasks in a typical kitchen environment has been developed. The overall system consists of various loosely coupled subcomponents providing particular features like manipulating objects or recognizing and interacting with humans. To bring all these subcomponents together to act as monolithic system, a high-performance planning system has been implemented. In this paper, we present this system’s basic architecture and some advanced extensions necessary to cope with the various challenges arising in dynamic and uncertain environments like those a real world service robot is usually faced with.
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Patrick Eyerich, Thomas Keller und Malte Helmert.
High-Quality Policies for the Canadian Traveler's Problem.
In
Maria Fox und David Poole (Hrsg.),
Proceedings of the Twenty-Fourth AAAI Conference on Artificial
Intelligence (AAAI
2010), S. 51-58.
AAAI Press 2010.
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We consider the stochastic variant of the Canadian
Traveler's Problem, a path planning problem where adverse
weather can cause some roads to be untraversable. The agent
does not initially know which roads can be used. However, it
knows a probability distribution for the weather, and it can
observe the status of roads incident to its location. The
objective is to find a policy with low expected travel cost.
We introduce and compare several algorithms for the
stochastic CTP. Unlike the optimistic approach most
commonly considered in the literature, the new approaches we
propose take uncertainty into account explicitly. We show
that this property enables them to generate policies of much
higher quality than the optimistic one, both theoretically
and experimentally.
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Patrick Eyerich, Thomas Keller und Malte Helmert.
High-Quality Policies for the Canadian Traveler's Problem
(Extended Abstract).
In
Ariel Felner und Nathan Sturtevant (Hrsg.),
Proceedings of the Third Annual Symposium on Combinatorial
Search (SoCS 2010), S. 147-148.
AAAI Press 2010.
Extended abstract of the AAAI paper by the same name.
(PDF)
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Moritz Göbelbecker, Thomas Keller, Patrick Eyerich, Michael Brenner und Bernhard Nebel.
Coming Up with Good Excuses: What To Do When No Plan Can be Found.
In
Ronen Brafman, Héctor Geffner, Jörg Hoffmann und Henry Kautz (Hrsg.),
Proceedings of the 20th International Conference on Automated Planning and Scheduling
(ICAPS 2010), S. 81-88.
AAAI Press 2010.
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When using a planner-based agent architecture, many things can
go wrong. First and foremost, an agent might fail to execute
one of the planned actions for some reasons. Even more
annoying, however, is a situation where the agent is
incompetent, i.e., unable to come up with a plan. This
might be due to the fact that there are principal reasons that
prohibit a successful plan or simply because the task's
description is incomplete or incorrect. In either case, an
explanation for such a failure would be very helpful. We will
address this problem and provide a formalization of coming
up with excuses for not being able to find a plan. Based
on that, we will present an algorithm that is able to find
excuses and demonstrate that such excuses can be found in
practical settings in reasonable time.
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Patrick Eyerich, Thomas Keller und Malte Helmert.
High-Quality Policies for the Canadian Traveler's Problem.
In
Proceedings of the
ICAPS-2010
Workshop on Planning and Scheduling Under Uncertainty.
2010.
Superseded by the AAAI 2010 paper by the same name.
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We consider the stochastic variant of the Canadian
Traveler's Problem, a path planning problem where adverse
weather can cause some roads to be untraversable. The agent
does not initially know which roads can be used. However, it
knows a probability distribution for the weather, and it can
observe the status of roads incident to its location. The
objective is to find a policy with low expected travel cost.
We introduce and compare several algorithms for the
stochastic CTP. Unlike the optimistic approach most
commonly considered in the literature, the new approaches we
propose take uncertainty into account explicitly. We show
that this property enables them to generate policies of much
higher quality than the optimistic one, both theoretically
and experimentally.
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Patrick Eyerich, Thomas Keller und Bernhard Nebel.
Combining Action and Motion Planning via Semantic Attachments.
In
Proceedings of the Workshop on Combining Action and Motion Planning at ICAPS 2010
(CAMP 2010), S. 19.
2010.
Extended Abstract.
(PDF)
(BIB)
2009
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Christian Dornhege, Patrick Eyerich, Thomas Keller, Sebastian Trüg, Michael Brenner und Bernhard Nebel.
Semantic Attachments for Domain-Independent Planning Systems.
In
Proceedings of the 19th International Conference on Automated
Planning and Scheduling (ICAPS 2009), S. 114-121.
AAAI Press 2009.
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Solving real-world problems using symbolic planning often
requires a simplified formulation of the original problem,
since certain subproblems cannot be represented at all or only
in a way leading to inefficiency. For example, manipulation
planning may appear as a subproblem in a robotic planning
context or a packing problem can be part of a logistics
task. In this paper we propose an extension of PDDL for
specifying semantic attachments. This allows the evaluation of
grounded predicates as well as the change of fluents by
externally specified functions. Furthermore, we describe a
general schema of integrating semantic attachments into a
forward-chaining planner and report on our experience of
adding this extension to the planners FF and Temporal Fast
Downward. Finally, we present some preliminary experiments
using semantic attachments.
2008
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Thomas Keller.
Optimales domänenspezifisches Planen in der Transport- und Routenplanungsfamilie.
Diplomarbeit,
Albert-Ludwigs-Universität,
Freiburg, Germany 2008.
In German.
(PDF)
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Thomas Keller und Sebastian Kupferschmid.
Automatic Bidding for the Game of Skat.
In
Andreas R. Dengel, Karsten Berns, Thomas M. Breuel, Frank
Bomarius und Thomas R. Roth-Berghofer (Hrsg.),
Proceedings of the 31st Annual German Conference on Artificial Intelligence (KI 2008), S. 95-102.
Springer-Verlag 2008.
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In recent years, researchers started to study the game of Skat.
The strength of existing Skat playing programs is definitely the
card play phase. The bidding phase, however, was treated quite
poorly so far. This is a severe drawback since bidding abilities
influence the overall playing performance drastically. In this
paper we present a powerful bidding engine which is based on a
k-nearest neighbor algorithm.