Beyond Distance Estimates: A New Theory of Heuristics for State-Space Search

Project Information

BDE

Grant agreement ID: 817639

DOI

10.3030/817639

Project closed

EC signature date 18 December 2018

Start date 1 February 2019

End date 31 January 2024

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 997 510,00

EU contribution

€ 1 997 510,00

Coordinated by

UNIVERSITAT BASEL
Switzerland

Periodic Reporting for period 4 - BDE (Beyond Distance Estimates: A New Theory of Heuristics for State-Space Search)

Reporting period: 2023-08-01 to 2024-01-31

Summary of the context and overall objectives of the project

Many problems in computer science can be cast as state-space search, where the objective is to find a path from an initial state to a goal state in a directed graph called a state space. State-space search is challenging due to the state explosion problem a.k.a. curse of dimensionality: interesting state spaces are often astronomically large, defying brute-force exploration.

State-space search has been a core research problem in Artificial Intelligence since its early days and is alive as ever. Every year, a substantial fraction of research published at the ICAPS and SoCS conferences is concerned with state-space search, and the topic is very active at general AI conferences such as IJCAI and AAAI.

Algorithms in the A* family, dating back to 1968, are still the go-to approach for state-space search. A* is a graph search algorithm whose only "intelligence" stems from a so-called heuristic function, which estimates the distance from a state to the nearest goal state. The efficiency of A* depends on the accuracy of this estimate, and decades of research have pushed the envelope in devising increasingly accurate estimates.

In this project, we question the "A* + distance estimator" paradigm and explore three new directions that go beyond the classical approach:

1. We propose a new paradigm of declarative heuristics, where heuristic information is not represented as distance estimates, but as properties of solutions amenable to introspection and general reasoning.

2. We suggest moving the burden of creativity away from the human expert by casting heuristic design as a meta-optimization problem that can be solved automatically.

3. We propose abandoning the idea of exploring sequential paths in state spaces, instead transforming state-space search into combinatorial optimization problems with no explicit sequencing aspect. We argue that the curse of sequentiality is as bad as the curse of dimensionality and must be addressed head-on.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

We published 41 papers on the topics of the project, of which 32 appeared in flagship venues for research in this area (ICAPS, IJCAI, AAAI, JAIR).

Highlights include the following papers:

1. "Merge-and-Shrink: A Compositional Theory of Transformations of Factored Transition Systems" (JAIR 2021)

This paper is the crowning piece of 14 years of working on merge-and-shrink abstractions. This 103-page journal paper recasts the existing work on merge-and shrink abstractions in a unifying theory of factored representations and greatly extends it. It focuses on transformations of such representations and their properties. In doing so, it closes several major open questions regarding the properties of the four previously suggested transformations in this framework: merging, shrinking, label reduction and pruning. For the pruning transformation, it is the first time that it is described in detail, and for label reduction, we develop a new theory that is much cleaner and at the same time much more powerful than the earlier theory that formed the core of a paper in the Journal of the ACM that we published in 2014. The new theory of merge-and-shrink replaces the previous patchwork with clean mathematical abstractions that can easily be extended to new transformations and new properties.

2. "Lagrangian Decomposition for Optimal Cost Partitioning" (ICAPS 2019)

The paper received the ICAPS 2019 Best Paper Award. It explains optimal cost partitioning, perhaps the most influential idea in optimal AI planning since the 2000s, as a form of Lagrangian decomposition, a mathematical optimization method that rose to prominence in the 1950s. Even though both techniques have been intensively studied, the close formal connection between the two has not previously been observed. Finding this connection allowed us to significantly improve cost partitioning algorithms and open the door to adapting the rich array of tools from Lagrangian decomposition to factored state-space search.

3. "An Atom-Centric Perspective on Stubborn Sets" (SoCS 2020)

The paper received the SoCS 2020 best paper award. It deals with partial-order reduction, i.e. methods that avoid exploring permutations of candidate solution paths needlessly. Our new method achieves the same pruning as earlier methods while being several orders of magnitude faster. This makes partial-order reduction algorithmically viable in many cases where it was previously too expensive and changes it from a technique that is worth using in niche cases to one that is always worth considering.

4. "Exploiting Cyclic Dependencies in Landmark Heuristics" and "Landmark Progression in Heuristic Search" (ICAPS 2021/2023)

The first paper was runner-up for ICAPS 2021 Best Student Paper Award; the second received the ICAPS 2023 Best Paper Award. Landmark heuristics have been studied since 2004 and shot to the forefront of AI planning with Richter's work on the LAMA planning system in 2008.
Landmark heuristics have been studied since 2004 and shot to the forefront of AI planning with Silvia Richter's work on the LAMA planning system in 2008. We extended this line of research with domain-independent ways of reasoning about landmarks and their orderings that allows determining that certain landmarks have cyclic dependencies and must therefore be achieved multiple times.
This allows us to connect to highly successful domain-specific search approaches based on such cyclic dependencies, pioneered by Richard Karp and collaborators working on "implicit hitting set" problems and by John Slaney working on "set-theoretic duality" in optimization.
The second paper proves the landmark reasoning in LAMA to be theoretically flawed, which was overlooked since 2008. We present a new, theoretically sound approach that also leads to improved performance. Our work puts the highly influential landmark approach on solid theoretical foundations.

5. "Saturated Cost Partitioning for Optimal Classical Planning" (JAIR 2020)

This paper reports on one of the two main contributions of Jendrik Seipp's PhD thesis, which was recognized with the ICAPS 2020 Best Dissertation Award as one of two awarded theses. It also covers additional work conducted after the PhD. It introduces the idea of saturated cost partitioning, an almost-linear-time (O(n log n)) cost partitioning method that has opened new avenues for combining different heuristics for optimal state space-search and led to dramatic improvements in scalability for AI planning algorithms based on optimal heuristic search.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Many of the results of the project constitute significant progress beyond the state of the art, both in terms of theory and in terms of algorithms and implemented systems. On the theory side, the papers "Merge-and-Shrink: A Compositional Theory of Transformations of Factored Transition Systems" and "Lagrangian Decomposition for Optimal Cost Partitioning" are the most important achievements. In terms of practical algorithms, optimal planning algorithms based on saturated cost partitioning as described in the paper "Saturated Cost Partitioning for Optimal Classical Planning" are the most important result.

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