Bounded-cost Search Using Estimates of Uncertainty

Abstract

Many planning problems are too hard to solve optimally. In bounded-cost search, one attempts to find, as quickly as possible, a plan that costs no more than a user-provided absolute cost bound. Several algorithms have been previously proposed for this setting, including Potential Search (PTS) and Bounded-cost Explicit Estimation Search (BEES). BEES attempts to improve on PTS by predicting whether nodes will lead to plans within the cost bound or not. This paper introduces a relatively simple algorithm, Expected Effort Search (XES), which uses not just point estimates but belief distributions in order to estimate the probability that a node will lead to a plan within the bound. XES's expansion order minimizes expected search time in a simplified formal model. Experimental results on standard planning and search benchmarks show that it consistently exhibits strong performance, outperforming both PTS and BEES. We also derive improved variants of BEES that can exploit belief distributions. These new methods advance the recent trend of taking advantage of uncertainty estimates in deterministic single-agent search.

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“…Expected Effort Search (XES) (Fickert, Gu, and Ruml 2021) is a recent algorithm that orders nodes on an estimate of expected search effort xe(n) = T (n)/p(n), where T (n) is an estimate of the time to find a solution under n and p(n) is the probability that that solution will be within the cost bound. T (n) is instantiated by d(n) and p(n) is derived from a probability distribution centered on f as the probability mass between a lower bound (g, or f if the heuristic is admissible) and the cost bound C.…”

“…Unlike DPS or XES, a node believed to be barely below the bound is treated as equally important as a node that is believed to be far below the bound. Explicitly accounting for uncertainty using belief distributions has yielded promising results recently in realtime search (Mitchell et al 2019;Fickert et al 2020) and bounded-cost search (Fickert, Gu, and Ruml 2021). These belief distributions can be used to explicitly estimate the probability that a node leads to a solution within the suboptimality bound (we give more details in the next subsection).…”

“…In this paper, we consider two additional ideas that have been investigated in other contexts: explicitly estimating the probability that a node will lead to a sufficiently good solution (Fickert, Gu, and Ruml 2021) and using alternating search queues ordered by different criteria (Röger and Helmert 2010). By remixing these ideas with previous work, we develop several new bounded-suboptimal algorithms.…”