Robert Holte

IJCAI Conference 2017 Conference Paper

Additive Merge-and-Shrink Heuristics for Diverse Action Costs

• Gaojian Fan
• Martin Müller
• Robert Holte

In many planning applications, actions can have highly diverse costs. Recent studies focus on the effects of diverse action costs on search algorithms, but not on their effects on domain-independent heuristics. In this paper, we demonstrate there are negative impacts of action cost diversity on merge-and-shrink (M&S), a successful abstraction method for producing high-quality heuristics for planning problems. We propose a new cost partitioning method for M&S to address the negative effects of diverse action costs. We investigate non-unit cost IPC domains, especially those for which diverse action costs have severe negative effects on the quality of the M&S heuristic. Our experiments demonstrate that in these domains, an additive set of M&S heuristics using the new cost partitioning method produces much more informative and effective heuristics than creating a single M&S heuristic which directly encodes diverse costs.

AAAI Conference 2016 Conference Paper

Bidirectional Search That Is Guaranteed to Meet in the Middle

• Robert Holte
• Ariel Felner
• Guni Sharon
• Nathan Sturtevant

We present MM, the first bidirectional heuristic search algorithm whose forward and backward searches are guaranteed to “meet in the middle”, i. e. never expand a node beyond the solution midpoint. We also present a novel framework for comparing MM, A*, and brute-force search, and identify conditions favoring each algorithm. Finally, we present experimental results that support our theoretical analysis.

IJCAI Conference 2016 Conference Paper

Improved Heuristic and Tie-Breaking for Optimally Solving Sokoban

• Andr
• eacute; G. Pereira
• Robert Holte
• Jonathan Schaeffer
• Luciana S. Buriol
• Marcus Ritt

We present a novel admissible pattern database heuristic (D) and tie-breaking rule (L) for Sokoban, allowing us to increase the number of optimally solved standard Sokoban instances from 20 to 28 and the number of proved optimal solutions from 25 to 32 compared to previous methods. The previously best heuristic for Sokoban (I) used the idea of an intermediate goal state to enable the effective use of pattern database heuristics in transportation domains, where the mapping of movable objects to goal locations is not fixed beforehand. We extend this idea to allow the use of multiple intermediate goal states and show that heuristic I is no longer effective. We solve this problem and show that our heuristic D is effective in this situation. Sokoban is a well-known single-agent search domain characterized by a large branching factor, long solution lengths, and the presence of unsolvable states. Given the exponential growth in the complexity of standard Sokoban instances, the increase in the number of optimally solved instances represents a major advance in our understanding of how to search in extremely large search spaces.

AAAI Conference 2014 Conference Paper

Adding Local Exploration to Greedy Best-First Search in Satisficing Planning

• Fan Xie
• Martin Müller
• Robert Holte

Greedy Best-First Search (GBFS) is a powerful algorithm at the heart of many state of the art satisficing planners. One major weakness of GBFS is its behavior in so-called uninformative heuristic regions (UHRs) - parts of the search space in which no heuristic provides guidance towards states with improved heuristic values. This work analyzes the problem of UHRs in planning in detail, and proposes a two level search framework as a solution. In Greedy Best-First Search with Local Exploration (GBFS- LE), a local exploration is started from within a global GBFS whenever the search seems stuck in UHRs. Two different local exploration strategies are developed and evaluated experimentally: Local GBFS (LS) and Local Random Walk Search (LRW). The two new planners LAMA-LS and LAMA-LRW integrate these strategies into the GBFS component of LAMA-2011. Both are shown to yield clear improvements in terms of both coverage and search time on standard International Planning Competition benchmarks, especially for domains that are proven to have large or unbounded UHRs.

AAAI Conference 2014 Conference Paper

Type-Based Exploration with Multiple Search Queues for Satisficing Planning

• Fan Xie
• Martin Müller
• Robert Holte
• Tatsuya Imai

Utilizing multiple queues in Greedy Best-First Search (GBFS) has been proven to be a very effective approach to satisficing planning. Successful techniques include extra queues based on Helpful Actions (or Preferred Operators), as well as using Multiple Heuristics. One weakness of all standard GBFS algorithms is their lack of exploration. All queues used in these methods work as priority queues sorted by heuristic values. Therefore, misleading heuristics, especially early in the search process, can cause the search to become ineffective. Type systems, as introduced for heuristic search by Lelis et al, are a development of ideas for exploration related to the classic stratified sampling approach. The current work introduces a search algorithm that utilizes type systems in a new way – for exploration within a GBFS multiqueue framework in satisficing planning. A careful case study shows the benefits of such exploration for overcoming deficiencies of the heuristic. The proposed new baseline algorithm Type-GBFS solves almost 200 more problems than baseline GBFS over all International Planning Competition problems. Type-LAMA, a new planner which integrates Type-GBFS into LAMA-2011, solves 36. 8 more problems than LAMA-2011.

AAAI Conference 2012 Conference Paper

Fast and Accurate Predictions of IDA*’s Performance

• Levi Lelis
• Sandra Zilles
• Robert Holte

Korf, Reid and Edelkamp initiated a line of research for developing methods (KRE and later CDP) that predict the number of nodes expanded by IDA* for a given start state and cost bound. Independent of that, Chen developed a method (SS) that can also be used to predict the number of nodes expanded by IDA*. In this paper we advance these prediction methods. First, we develop a variant of CDP that can be orders of magnitude faster than CDP while producing exactly the same predictions. Second, we show how ideas developed in the KRE line of research can be used to substantially improve the predictions produced by SS. Third, we make an empirical comparison between our new enhanced versions of CDP and SS. Our experimental results point out that CDP is suitable for applications that require less accurate but very fast predictions, while SS is suitable for applications that require more accurate predictions but allow more computation time.

AAAI Conference 2012 Conference Paper

Partial-Expansion A* with Selective Node Generation

• Ariel Felner
• Meir Goldenberg
• Guni Sharon
• Roni Stern
• Tal Beja
• Nathan Sturtevant
• Jonathan Schaeffer
• Robert Holte

A* is often described as being ‘optimal’, in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* (PEA*) (Yoshizumi, Miura, and Ishida 2000) addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. n is re-inserted into the OPEN list, but with the f-cost of the next best child. This paper introduces an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* generates only the children with the same f-cost as the parent. EPEA* is generalized to its iterative-deepening variant, EPE-IDA*. For some domains, these algorithms yield substantial performance improvements. State-of-the-art results were obtained for the pancake puzzle and for some multi-agent pathfinding instances. Drawbacks of EPEA* are also discussed.

AAAI Conference 2012 Conference Paper

Using Sliding Windows to Generate Action Abstractions in Extensive-Form Games

• John Hawkin
• Robert Holte
• Duane Szafron

In extensive-form games with a large number of actions, careful abstraction of the action space is critically important to performance. In this paper we extend previous work on action abstraction using no-limit poker games as our test domains. We show that in such games it is no longer necessary to choose, a priori, one specific range of possible bet sizes. We introduce an algorithm that adjusts the range of bet sizes considered for each bet individually in an iterative fashion. This flexibility results in a substantially improved game value in no-limit Leduc poker. When applied to no-limit Texas Hold’em our algorithm produces an action abstraction that is about one third the size of a state of the art hand-crafted action abstraction, yet has a better overall game value.

AAAI Conference 2011 Conference Paper

Automated Action Abstraction of Imperfect Information Extensive-Form Games

• John Hawkin
• Robert Holte
• Duane Szafron

Multi-agent decision problems can often be formulated as extensive-form games. We focus on imperfect information extensive-form games in which one or more actions at many decision points have an associated continuous or manyvalued parameter. A stock trading agent, in addition to deciding whether to buy or not, must decide how much to buy. In no-limit poker, in addition to selecting a probability for each action, the agent must decide how much to bet for each betting action. Selecting values for these parameters makes these games extremely large. Two-player no-limit Texas Hold’em poker with stacks of 500 big blinds has approximately 1071 states, which is more than 1050 times more states than twoplayer limit Texas Hold’em. The main contribution of this paper is a technique that abstracts a game’s action space by selecting one, or a small number, of the many values for each parameter. We show that strategies computed using this new algorithm for no-limit Leduc poker exhibit significant utility gains over -Nash equilibrium strategies computed with standard, hand-crafted parameter value abstractions.

AAAI Conference 2011 Conference Paper

Block A*: Database-Driven Search with Applications in Any-Angle Path-Planning

• Peter Yap
• Neil Burch
• Robert Holte
• Jonathan Schaeffer

We present three new ideas for grid-based path-planning algorithms that improve the search speed and quality of the paths found. First, we introduce a new type of database, the Local Distance Database (LDDB), that contains distances between boundary points of a local neighborhood. Second, an LDDB-based algorithm is introduced, called Block A*, that calculates the optimal path between start and goal locations given the local distances stored in the LDDB. Third, our experimental results for any-angle path planning in a wide variety of test domains, including real game maps, show that Block A* is faster than both A* and the previously best gridbased any-angle search algorithm, Theta*.

AIJ Journal 2011 Journal Article

Inconsistent heuristics in theory and practice

• Ariel Felner
• Uzi Zahavi
• Robert Holte
• Jonathan Schaeffer
• Nathan Sturtevant
• Zhifu Zhang

JMLR Journal 2011 Journal Article

Models of Cooperative Teaching and Learning

• Sandra Zilles
• Steffen Lange
• Robert Holte
• Martin Zinkevich

While most supervised machine learning models assume that training examples are sampled at random or adversarially, this article is concerned with models of learning from a cooperative teacher that selects "helpful" training examples. The number of training examples a learner needs for identifying a concept in a given class C of possible target concepts (sample complexity of C ) is lower in models assuming such teachers, that is, "helpful" examples can speed up the learning process. The problem of how a teacher and a learner can cooperate in order to reduce the sample complexity, yet without using "coding tricks", has been widely addressed. Nevertheless, the resulting teaching and learning protocols do not seem to make the teacher select intuitively "helpful" examples. The two models introduced in this paper are built on what we call subset teaching sets and recursive teaching sets. They extend previous models of teaching by letting both the teacher and the learner exploit knowing that the partner is cooperative. For this purpose, we introduce a new notion of "coding trick"/"collusion". We show how both resulting sample complexity measures (the subset teaching dimension and the recursive teaching dimension ) can be arbitrarily lower than the classic teaching dimension and known variants thereof, without using coding tricks. For instance, monomials can be taught with only two examples independent of the number of variables. The subset teaching dimension turns out to be nonmonotonic with respect to subclasses of concept classes. We discuss why this nonmonotonicity might be inherent in many interesting cooperative teaching and learning scenarios. [abs] [ pdf ][ bib ] &copy JMLR 2011. ( edit, beta )

AAAI Conference 2011 Conference Paper

Time Complexity of Iterative-Deepening A*: The Informativeness Pathology (Abstract)

• Levi Lelis
• Sandra Zilles
• Robert Holte

AAAI Conference 2010 Conference Paper

Searching Without a Heuristic: Efficient Use of Abstraction

• Bradford Larsen
• Ethan Burns
• Wheeler Ruml
• Robert Holte

In problem domains where an informative heuristic evaluation function is not known or not easily computed, abstraction can be used to derive admissible heuristic values. Optimal path lengths in the abstracted problem are consistent heuristic estimates for the original problem. Pattern databases are the traditional method of creating such heuristics, but they exhaustively compute costs for all abstract states and are thus usually appropriate only when all instances share the same single goal state. Hierarchical heuristic search algorithms address these shortcomings by searching for paths in the abstract space on an as-needed basis. However, existing hierarchical algorithms search less efficiently than pattern database constructors: abstract nodes may be expanded many times during the course of a base-level search. We present a novel hierarchical heuristic search algorithm, called Switchback, that uses an alternating direction of search to avoid abstract node re-expansions. This algorithm is simple to implement and demonstrates superior performance to existing hierarchical heuristic search algorithms on several standard benchmarks.

AAAI Conference 2010 Conference Paper

Using Lookaheads with Optimal Best-First Search

• Roni Stern
• Tamar Kulberis
• Ariel Felner
• Robert Holte

We present an algorithm that exploits the complimentary benefits of best-first search (BFS) and depth-first search (DFS) by performing limited DFS lookaheads from the frontier of BFS. We show that this continuum requires significantly less memory than BFS. In addition, a time speedup is also achieved when choosing the lookahead depth correctly. We demonstrate this idea for breadth-first search and for A*. Additionally, we show that when using inconsistent heuristics, Bidirectional Pathmax (BPMX), can be implemented very easily on top of the lookahead phase. Experimental results on several domains demonstrate the benefits of all our ideas.

IJCAI Conference 2009 Conference Paper

• Zhifu Zhang
• Nathan R. Sturtevant
• Robert Holte
• Jonathan Schaeffer
• Ariel Felner

Early research in heuristic search discovered that using inconsistent heuristics with A* could result in an exponential increase in the number of node expansions. As a result, the use of inconsistent heuristics has largely disappeared from practice. Recently, inconsistent heuristics have been shown to be effective in IDA*, especially when applying the bidirectional pathmax (BPMX) enhancement. This paper presents new worst-case complexity analysis of A*’s behavior with inconsistent heuristics, discusses how BPMX can be used with A*, and gives experimental results justifying the use of inconsistent heuristics in A* searches.

AAAI Conference 2006 Conference Paper

Dual Search in Permutation State Spaces

• Uzi Zahavi
• Robert Holte

Geometrical symmetries are commonly exploited to improve the efficiency of search algorithms. We introduce a new logical symmetry in permutation state spaces which we call duality. We show that each state has a dual state. Both states share important attributes and these properties can be used to improve search efficiency. We also present a new search algorithm, dual search, which switches between the original state and the dual state when it seems likely that the switch will improve the chances of a cutoff. The decision of when to switch is very important and several policies for doing this are investigated. Experimental results show significant improvements for a number of applications.

IJCAI Conference 2003 Conference Paper

Comparison of Different Grid Abstractions for Pathfinding on Maps

• Yngvi Bjornsson
• Markus Enzenberger
• Robert Holte
• Jonathan Schaejfer
• Peter Yap

Pathfinding on a map is a fundamental problem in many applications, including robotics and computer games. Typically a grid is superimposed over the map where each cell in the grid forms a unique state. A state-space-based search algorithm, such as A* or IDA*, is then used for finding the optimal (shortest) path. In this paper we analyze the search behavior of both A* and IDA* using different grid representations, providing various new insights via analytical and empirical results.

TCS Journal 1992 Journal Article

Pinwheel scheduling with two distinct numbers

• Robert Holte
• Louis Rosier
• Igor Tulchinsky
• Donald Varvel