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EASe : integrating search with learned episodes
Weak methods are insufficient to solve complex problems. Constrained weak methods, like hill-climbing, search too little of the problem space. Unconstrained weak methods, like breadth-first search, are intractable. Fortunately, through the integration of multiple weak methods more powerful problem solvers can be created. We demonstrate that augmenting a weak constrained search method with episodes provides a tractable method for solving a large class of problems. We demonstrate that these episodes can be generated using an unconstrained weak method while solving simple problems from a domain. We provide an analytical model of our approach and empirical results from the logic synthesis domain of VLSI design as well as the classic tile-sliding domain
Structure and Complexity in Planning with Unary Operators
Unary operator domains -- i.e., domains in which operators have a single
effect -- arise naturally in many control problems. In its most general form,
the problem of STRIPS planning in unary operator domains is known to be as hard
as the general STRIPS planning problem -- both are PSPACE-complete. However,
unary operator domains induce a natural structure, called the domain's causal
graph. This graph relates between the preconditions and effect of each domain
operator. Causal graphs were exploited by Williams and Nayak in order to
analyze plan generation for one of the controllers in NASA's Deep-Space One
spacecraft. There, they utilized the fact that when this graph is acyclic, a
serialization ordering over any subgoal can be obtained quickly. In this paper
we conduct a comprehensive study of the relationship between the structure of a
domain's causal graph and the complexity of planning in this domain. On the
positive side, we show that a non-trivial polynomial time plan generation
algorithm exists for domains whose causal graph induces a polytree with a
constant bound on its node indegree. On the negative side, we show that even
plan existence is hard when the graph is a directed-path singly connected DAG.
More generally, we show that the number of paths in the causal graph is closely
related to the complexity of planning in the associated domain. Finally we
relate our results to the question of complexity of planning with serializable
subgoals
The GRT Planning System: Backward Heuristic Construction in Forward State-Space Planning
This paper presents GRT, a domain-independent heuristic planning system for
STRIPS worlds. GRT solves problems in two phases. In the pre-processing phase,
it estimates the distance between each fact and the goals of the problem, in a
backward direction. Then, in the search phase, these estimates are used in
order to further estimate the distance between each intermediate state and the
goals, guiding so the search process in a forward direction and on a best-first
basis. The paper presents the benefits from the adoption of opposite directions
between the preprocessing and the search phases, discusses some difficulties
that arise in the pre-processing phase and introduces techniques to cope with
them. Moreover, it presents several methods of improving the efficiency of the
heuristic, by enriching the representation and by reducing the size of the
problem. Finally, a method of overcoming local optimal states, based on domain
axioms, is proposed. According to it, difficult problems are decomposed into
easier sub-problems that have to be solved sequentially. The performance
results from various domains, including those of the recent planning
competitions, show that GRT is among the fastest planners
FLECS: Planning with a Flexible Commitment Strategy
There has been evidence that least-commitment planners can efficiently handle
planning problems that involve difficult goal interactions. This evidence has
led to the common belief that delayed-commitment is the "best" possible
planning strategy. However, we recently found evidence that eager-commitment
planners can handle a variety of planning problems more efficiently, in
particular those with difficult operator choices. Resigned to the futility of
trying to find a universally successful planning strategy, we devised a planner
that can be used to study which domains and problems are best for which
planning strategies. In this article we introduce this new planning algorithm,
FLECS, which uses a FLExible Commitment Strategy with respect to plan-step
orderings. It is able to use any strategy from delayed-commitment to
eager-commitment. The combination of delayed and eager operator-ordering
commitments allows FLECS to take advantage of the benefits of explicitly using
a simulated execution state and reasoning about planning constraints. FLECS can
vary its commitment strategy across different problems and domains, and also
during the course of a single planning problem. FLECS represents a novel
contribution to planning in that it explicitly provides the choice of which
commitment strategy to use while planning. FLECS provides a framework to
investigate the mapping from planning domains and problems to efficient
planning strategies.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
Enumerating Subgraph Instances Using Map-Reduce
The theme of this paper is how to find all instances of a given "sample"
graph in a larger "data graph," using a single round of map-reduce. For the
simplest sample graph, the triangle, we improve upon the best known such
algorithm. We then examine the general case, considering both the communication
cost between mappers and reducers and the total computation cost at the
reducers. To minimize communication cost, we exploit the techniques of (Afrati
and Ullman, TKDE 2011)for computing multiway joins (evaluating conjunctive
queries) in a single map-reduce round. Several methods are shown for
translating sample graphs into a union of conjunctive queries with as few
queries as possible. We also address the matter of optimizing computation cost.
Many serial algorithms are shown to be "convertible," in the sense that it is
possible to partition the data graph, explore each partition in a separate
reducer, and have the total computation cost at the reducers be of the same
order as the computation cost of the serial algorithm.Comment: 37 page
Cooperation between Top-Down and Bottom-Up Theorem Provers
Top-down and bottom-up theorem proving approaches each have specific
advantages and disadvantages. Bottom-up provers profit from strong redundancy
control but suffer from the lack of goal-orientation, whereas top-down provers
are goal-oriented but often have weak calculi when their proof lengths are
considered. In order to integrate both approaches, we try to achieve
cooperation between a top-down and a bottom-up prover in two different ways:
The first technique aims at supporting a bottom-up with a top-down prover. A
top-down prover generates subgoal clauses, they are then processed by a
bottom-up prover. The second technique deals with the use of bottom-up
generated lemmas in a top-down prover. We apply our concept to the areas of
model elimination and superposition. We discuss the ability of our techniques
to shorten proofs as well as to reorder the search space in an appropriate
manner. Furthermore, in order to identify subgoal clauses and lemmas which are
actually relevant for the proof task, we develop methods for a relevancy-based
filtering. Experiments with the provers SETHEO and SPASS performed in the
problem library TPTP reveal the high potential of our cooperation approaches
A Formal Framework for Speedup Learning from Problems and Solutions
Speedup learning seeks to improve the computational efficiency of problem
solving with experience. In this paper, we develop a formal framework for
learning efficient problem solving from random problems and their solutions. We
apply this framework to two different representations of learned knowledge,
namely control rules and macro-operators, and prove theorems that identify
sufficient conditions for learning in each representation. Our proofs are
constructive in that they are accompanied with learning algorithms. Our
framework captures both empirical and explanation-based speedup learning in a
unified fashion. We illustrate our framework with implementations in two
domains: symbolic integration and Eight Puzzle. This work integrates many
strands of experimental and theoretical work in machine learning, including
empirical learning of control rules, macro-operator learning, Explanation-Based
Learning (EBL), and Probably Approximately Correct (PAC) Learning.Comment: See http://www.jair.org/ for any accompanying file
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