A Polynomial Planning Algorithm That Beats LAMA and FF

Abstract

It has been shown recently that heuristic and width-based search can be combined to produce planning algorithms with a performance that goes beyond the state-of-the-art. Such algorithms are based on best-first width search (BFWS), a plain best-first search set with evaluations functions combined lexicographically to break ties, some of which express novelty based preferences. In BFWS(f5), for example, the evaluation function f5 weights nodes by a novelty measure, breaking ties by the number of non-achieved goals. BFWS(f5) is a best-first algorithm, and hence, it is complete but not polynomial, and its performance doesn’t match the state of the art. In this work we show, however, that incomplete versions of BFWS(f5) where nodes with novelty greater than k are pruned, are not only polynomial but have an empirical performance that is better than both BFWS(f5) and state-of-the-art planners. This is shown by considering all the international planning competition instances. This is the first time where polynomial algorithms with meaningful bounds are shown to achieve state-of-the-art performance in planning. Practical and theoretical implications of this empirical finding are briefly sketched.

Approximate Novelty Search

“…Whereas, Definition 2 has linear complexity allowing us to compute ŵ(s) for any value of i ∈ [1, |F |]. In the following section, we describe the impact of increasing W ∈ [1, i + 1] in the polynomial planners: BFWS(f 5 ) with novelty pruning (Lipovetzky and Geffner 2017b). From Theorem 1, we note that the bound on number of nodes with w(s) = ω + 1 increases by O(|F |) in comparison to those with w(s) = ω , which makes nodes with large value of ŵ(s) unlikely candidates for expansion.…”

“…In order to evaluate the impact novelty approximation and open list control has on width-based planners, we implemented different instantiations of BFWS(f 5 ): complete as described in the Section 2, or incomplete if nodes with novelty greater than a given bound are pruned (Lipovetzky and Geffner 2017b). We used the Downward Lab's experiment module (Seipp et al 2017) on a server with Intel Xeon Processors (2 GHz) with a 1800 sec and 8 GB time and memory limit, respectively.…”

“…multiple IPCs, we used the problem set from the most recent IPC. We compare our new planners against notable polynomial planners: BFWS(f 5 ) with novelty pruning and 1, 2-C-M , a sequential polynomial planner (Lipovetzky and Geffner 2017b), as well as two state-of-the-art planners DUAL-BFWS (Lipovetzky and Geffner 2017a) and LAMAfirst (Richter and Westphal 2010). We show that the introduction of these methods has a significant impact on the performance of the BFWS algorithms.…”

General Policies, Representations, and Planning Width

“…Other types of novelty measures have been used in reinforcement learning for dealing with sparse rewards and in genetic algorithms for dealing with local minima (Tang, Houthooft, Foote, Stooke, Chen, Duan, Schulman, DeTurck, & Abbeel, 2017;Pathak, Agrawal, Efros, & Darrell, 2017;Ostrovski, Bellemare, Oord, & Munos, 2017), but the results are mostly empirical. In classical planning, where novelty measures are part of state-of-the-art search algorithms (Lipovetzky & Geffner, 2017b, 2017a, there is a solid body of theory that relates a specific type of novelty measures with a notion of problem width that bounds the complexity of planning problems (Lipovetzky & Geffner, 2012).…”

Making Hill-Climbing Great Again through Online Relaxation Refinement and Novelty Pruning

“…Despite its simplicity, novelty pruning performs very well on many standard planning benchmarks (e.g. (Lipovetzky and Geffner 2017a;Katz et al 2017;Lipovetzky and Geffner 2017b)).…”