New Results in Bounded-Suboptimal Search (original) (raw)

Fast and Loose in Bounded Suboptimal Heuristic Search

2008

Applications often demand we tackle problems that are too large to solve optimally. In this paper, our aim is to solve shortest-path problems as quickly as possible while guaranteeing that solution costs are bounded within a specified factor of optimal. We explore two approaches. First, we extend the approach taken by weighted A∗, in which all expanded nodes are guaranteed to remain within the bound. We prove that a looser bound than weighted A∗’s can be used and show how an arbitrary inadmissible heuristic can be employed. As an example, we show how temporal difference learning can learn a heuristic on-line. Second, we show how an optimistic search that expands nodes potentially outside the bound can be modified to ensure bounded solution quality. We test these methods on grid-world path-finding and temporal planning benchmarks, showing that these methods can surpass weighted A∗’s performance.

Faster than weighted A*: An optimistic approach to bounded suboptimal search

2008

Planning, scheduling, and other applications of heuristic search often demand we tackle problems that are too large to solve optimally. In this paper, we address the problem of solving shortest-path problems as quickly as possible while guaranteeing that solution costs are bounded within a specified factor of optimal. 38 years after its publication, weighted A* remains the best-performing algorithm for general-purpose bounded suboptimal search. However, it typically returns solutions that are better than a given bound requires. We show how to take advantage of this behavior to speed up search while retaining bounded suboptimality. We present an optimistic algorithm that uses a weight higher than the user's bound and then attempts to prove that the resulting solution adheres to the bound. While simple, we demonstrate that this algorithm consistently surpasses weighted A* in four different benchmark domains including temporal planning and gridworld pathfinding.

Bounded Suboptimal Search: A Direct Approach Using Inadmissible Estimates

Bounded suboptimal search algorithms offer shorter solving times by sacrificing optimality and instead guaranteeing solution costs within a desired factor of optimal. Typically these algorithms use a single admissible heuristic both for guiding search and bounding solution cost. In this paper, we present a new approach to bounded suboptimal search, Explicit Estimation Search, that separates these roles, consulting potentially inadmissible information to determine search order and using admissible information to guarantee the cost bound. Unlike previous proposals, it successfully combines estimates of solution length and solution cost to predict which node will lead most quickly to a solution within the suboptimality bound. An empirical evaluation across six diverse benchmark domains shows that Explicit Estimation Search is competitive with the previous state of the art in domains with unit-cost actions and substantially outperforms previously proposed techniques for domains in which solution cost and length can differ.

Bounded Suboptimal Heuristic Search in Linear Space

Proceedings of the International Symposium on Combinatorial Search, 2021

It is commonly appreciated that solving search problems optimally can overrun time and memory constraints. Bounded suboptimal search algorithms trade increased solution cost for reduced solving time and memory consumption. However, even suboptimal search can overrun memory on large problems. The conventional approach to this problem is to combine a weighted admissible heuristic with an optimal linear space algorithm, resulting in algorithms such as Weighted IDA* (wIDA*). However, wIDA* does not exploit distanceto-go estimates or inadmissible heuristics, which have recently been shown to be helpful for suboptimal search. In this paper, we present a linear space analogue of Explicit Estimation Search (EES), a recent algorithm specifically designed for bounded suboptimal search. We call our method Iterative Deepening EES (IDEES). In an empirical evaluation, we show that IDEES dramatically outperforms wIDA* on domains with non-uniform edge costs and can scale to problems that are out of reach for the original EES.

Faster bounded-cost search using inadmissible estimates

2012

Many important problems are too difficult to solve optimally. A traditional approach to such problems is bounded suboptimal search, which guarantees solution costs within a userspecified factor of optimal. Recently, a complementary approach has been proposed: bounded-cost search, where solution cost is required to be below a user-specified absolute bound. In this paper, we show how bounded-cost search can incorporate inadmissible estimates of solution cost and solution length. This information has previously been shown to improve bounded suboptimal search and, in an empirical evaluation over five benchmark domains, we find that our new algorithms surpass the state-of-the-art in bounded-cost search as well, particularly for domains where action costs differ.

Potential search: a bounded-cost search algorithm

Proceedings of the Twenty-First International …, 2011

In this paper we address the following search task: find a goal with cost smaller than or equal to a given fixed constant. This task is relevant in scenarios where a fixed budget is available to execute a plan and we would like to find such a plan with minimum search effort. We introduce an algorithm called Potential search (PTS) which is specifically designed to solve this problem. PTS is a best-first search that expands nodes according to the probability that they will be part of a plan whose cost is less than or equal to the given budget. We show that it is possible to implement PTS even without explicitly calculating these probabilities, when a heuristic function and knowledge about the error of this heuristic function are given. In addition, we also show that PTS can be modified to an anytime search algorithm. Experimental results show that PTS outperforms other relevant algorithms in most cases, and is more robust.

A*-Connect: Bounded suboptimal bidirectional heuristic search

2016 IEEE International Conference on Robotics and Automation (ICRA), 2016

The benefits of bidirectional planning over the unidirectional version are well established for motion planning in high-dimensional configuration spaces. While bidirectional approaches have been employed with great success in the context of sampling-based planners such as in RRT-Connect, they have not enjoyed popularity amongst search-based methods such as A*. The systematic nature of search-based algorithms, which often leads to consistent and high-quality paths, also enforces strict conditions for the connection of forward and backward searches. Admissible heuristics for the connection of forward and backward searches have been developed, but their computational complexity is a deterrent. In this work, we leverage recent advances in search with inadmissible heuristics to develop an algorithm called A*-Connect, much in the spirit of RRT-Connect. A*-Connect uses a fast approximation of the classic front-to-front heuristic from literature to lead the forward and backward searches towards each other, while retaining theoretical guarantees on completeness and bounded suboptimality. We validate A*-Connect on manipulation as well as navigation domains, comparing with popular samplingbased methods as well as state-of-the-art bidirectional search algorithms. Our results indicate that A*-Connect can provide several times speedup over unidirectional search while maintaining high solution quality.

Bounded-Cost Bi-Objective Heuristic Search

Proceedings of the International Symposium on Combinatorial Search

There are many settings that extend the basic shortest path search problem. In Bounded-Cost Search, we are given a constant bound and the task is to find a solution within the bound. In Bi-Objective Search, each edge is associated with two costs (objectives) and the task is to minimize both objectives. In this paper, we combine both these settings into a new setting of Bounded-Cost Bi-Objective Search. We are given two bounds, one for each objective and the task is to find a solution within these bounds. We provide a scheme for normalizing the two objectives. We then introduce several algorithms for this new setting and compare them experimentally.

Bounded Suboptimal Search with Learned Heuristics for Multi-Agent Systems

Proceedings of the AAAI Conference on Artificial Intelligence

A wide range of discrete planning problems can be solved optimally using graph search algorithms. However, optimal search quickly becomes infeasible with increased complexity of a problem. In such a case, heuristics that guide the planning process towards the goal state can increase performance considerably. Unfortunately, heuristics are often unavailable or need manual and time-consuming engineering. Building upon recent results on applying deep learning to learn generalized reactive policies, we propose to learn heuristics by imitation learning. After learning heuristics based on optimal examples, they are used to guide a classical search algorithm to solve unseen tasks. However, directly applying learned heuristics in search algorithms such as A∗ breaks optimality guarantees, since learned heuristics are not necessarily admissible. Therefore, we (i) propose a novel method that utilizes learned heuristics to guide Focal Search A∗, a variant of A∗ with guarantees on bounded subopti...

Bounded Suboptimal Search in Linear Space: New Results

Seventh Annual Symposium on Combinatorial Search, 2014

Bounded suboptimal search algorithms are usually faster than optimal ones, but they can still run out of memory on large problems. This paper makes three contributions. First, we show how solution length estimates, used by the current stateof-the-art linear-space bounded suboptimal search algorithm Iterative Deepening EES, can be used to improve unboundedspace suboptimal search. Second, we convert one of these improved algorithms into a linear-space variant called Iterative Deepening A * , resulting in a new state of the art in linear-space bounded suboptimal search. Third, we show how Recursive Best-First Search can be used to create additional linear-space variants that have more stable performance. Taken together, these results significantly expand our armamentarium of bounded suboptimal search algorithms.