[Paper Review] Rational Deployment of Multiple Heuristics in IDA*

David Tolpin, Oded Betzalel+2 more|arXiv (Cornell University)|Nov 24, 2014

Robotic Path Planning Algorithms11 references4 citations

TL;DR

This paper introduces Rational Lazy IDA* (RLIDA*), a meta-reasoning approach that dynamically decides whether to compute expensive heuristics during IDA* search based on a myopic expected regret criterion. By lazily evaluating heuristics and rationally skipping costly evaluations when beneficial, RLIDA* achieves faster search times than both standard IDA* and Lazy IDA*, outperforming them in sliding tile puzzles and container relocation problems.

ABSTRACT

Recent advances in metareasoning for search has shown its usefulness in improving numerous search algorithms. This paper applies rational metareasoning to IDA* when several admissible heuristics are available. The obvious basic approach of taking the maximum of the heuristics is improved upon by lazy evaluation of the heuristics, resulting in a variant known as Lazy IDA*. We introduce a rational version of lazy IDA* that decides whether to compute the more expensive heuristics or to bypass it, based on a myopic expected regret estimate. Empirical evaluation in several domains supports the theoretical results, and shows that rational lazy IDA* is a state-of-the-art heuristic combination method.

Motivation & Objective

• To improve the efficiency of IDA* when multiple admissible heuristics are available, especially when some are computationally expensive.
• To address the high overhead of computing all heuristics for every node in standard IDA*, which can slow down search despite improved guidance.
• To develop a rational meta-reasoning framework that decides at runtime whether to compute a secondary heuristic or skip it based on expected regret.
• To outperform existing methods like standard IDA* and Lazy IDA* in terms of total search time while preserving optimality.
• To evaluate the method empirically in challenging domains such as sliding tile puzzles and container relocation problems.

Proposed method

• Proposes Lazy IDA*, a variant of IDA* that evaluates heuristics one at a time, only computing h₂(n) if h₁(n) does not cause a cutoff.
• Introduces Rational Lazy IDA* (RLIDA*), which uses a myopic expected regret criterion to decide whether to compute h₂(n) or expand the node immediately.
• Employs a decision rule based on the expected regret of skipping h₂(n), balancing the cost of computation against the benefit of improved f-value estimation.
• Uses a probabilistic estimate p_h of the likelihood that h₂(n) will cause a cutoff to guide the rational decision to compute or skip h₂.
• Applies the method in a depth-first, iterative-deepening framework, maintaining linear space and optimal solution guarantees.
• Extends the framework to handle cases where the assumption that h₁ does not prune any children is violated, though this is treated as a secondary concern.

Experimental results

Research questions

• RQ1 Can rational meta-reasoning reduce the time spent on heuristic computation in IDA* without sacrificing solution quality?
• RQ2 How effective is lazy evaluation of heuristics in reducing overhead when multiple admissible heuristics are available?
• RQ3 To what extent can a myopic expected regret criterion improve search efficiency by selectively skipping expensive heuristic evaluations?
• RQ4 How does RLIDA* compare to standard IDA* and Lazy IDA* in terms of runtime and node expansion count across different problem domains?
• RQ5 What is the impact of violating the assumption that h₁ does not prune any children on the performance of RLIDA*?

Key findings

• RLIDA* achieves the best overall performance among IDA*, Lazy IDA*, and standard IDA* in both sliding tile puzzles and the container relocation problem.
• Empirical results show that RLIDA* significantly reduces total search time by avoiding unnecessary computation of expensive heuristics.
• The method reduces the number of h₂ evaluations by up to 40% in some domains, with minimal increase in node expansions.
• Despite violating the assumption that h₁ does not prune any children in about 40% of nodes in tile puzzles, RLIDA* still achieves most of the potential speedup.
• In the container relocation problem, where the assumption was violated in 60% of nodes, a gap remains between RLIDA* and the clairvoyant ideal, suggesting room for improvement.
• The non-realizable clairvoyant scheme serves as an upper bound on performance gain, and RLIDA* achieves a substantial fraction of this theoretical maximum.