Local Minima, Heavy Tails, and Search Effort for GBFS

Abstract

Problem difficulty for greedy best first search (GBFS) is not entirely understood, though existing work points to deep local minima and poor correlation between the h-values and the distance to goal as factors that have significant negative effect on the search effort. In this work, we show that there is a very strong exponential correlation between the depth of the single deepest local minima encountered in a search and the overall search effort. Furthermore, we find that the distribution of local minima depth changes dramatically based on the constrainedness of problems, suggesting an explanation for the previously observed heavy-tailed behavior in GBFS. In combinatorial search, a similar result led to the use of randomized restarts to escape deep subtrees with no solution and corresponding significant speed-ups. We adapt this method and propose a randomized restarting GBFS variant that improves GBFS performance by escaping deep local minima, and does so even in the presence of other, randomization-based, search enhancements.

The Bench Transition System and Stochastic Exploration

“…It will then have to expand every state in that crater before it can move on to the next bench (Heusner, Keller, and Helmert 2017). Craters/local minima are important state space features since the total search effort of GBFS strongly correlates with the size and depth of the largest local minima encountered during the search (Cohen and Beck 2018).…”

Biased Exploration for Satisficing Heuristic Search

“…As we mentioned above, the notion of bench-exit states in their work is similar to closest nodes but limited to GBFS. Cohen and Beck (2018a;2018b) empirically showed that the largest search effort to escape a single local minimum is highly correlated with the overall search effort to solve a problem and that the existence of a deep local minimum is related to the heavy-tailed distribution of search effort. None of the previous work defined a good node independently from particular heuristic search algorithms.…”

“…Although DBFS is a complicated algorithm, it is similar to our biased exploration mechanisms in that it selects a node, from which local search is performed, according to the probability biased by its heuristic value. RR-GBFS (Cohen and Beck 2018b) uses randomized restarts to avoid getting stuck in a large local minimum. Asai and Fukunaga (2017) proposed a randomized tie-breaking strategy for GBFS to explore diverse nodes.…”