Showing papers on "Admissible heuristic published in 2011"

Bounded suboptimal search: a direct approach using inadmissible estimates

Abstract: 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.

Metareasoning and Bounded Rationality.

Abstract: What role does metareasoning play in models of bounded rationality? We examine the various existing computational approaches to bounded rationality and divide them into three classes. Only one of these classes significantly relies on a metareasoning component. We explore the characteristics of this class of models and argue that it offers desirable properties. In fact, many of the effective approaches to bounded rationality that have been developed since the early 1980’s match this particular paradigm. We conclude with some open research problems and challenges. Computational models of bounded rationality In the pursuit of building decision-making machines, artificial intelligence researchers often turn to theories of “rationality” in decision theory and economics. Rationality is a desired property of intelligent agents since it provides well-defined normative evaluation criteria and since it establishes formal frameworks to analyze agents (Doyle 1990; Russell and Wefald 1991). But in general, rationality requires making optimal choices with respect to one’s desires and goals. As early as 1947, Herbert Simon observed that optimal decision making is impractical in complex domains since it requires one to perform intractable computations within a limited amount of time (Simon 1947; 1982). Moreover, the vast computational resources required to select optimal actions often reduce the utility of the result. Simon suggested that some criterion must be used to determine that an adequate, or satisfactory, decision has been found. He used the Scottish word “satisficing,” which means satisfying, to denote decision making that searches until an alternative is found that is satisfactory by the agent’s aspiration level criterion. Simon’s notion of satisficing has inspired much work within the social sciences and within artificial intelligence in the areas of problem solving, planning and search. In the social sciences, much of the work has focused on developing descriptive theories of human decision making (Gigerenzer 2000). These theories attempt to explain how people make decisions in the real-world, coping with complex situations, uncertainty, and limited amount of time. The answer is often based on a variety of heuristic methods that Copyright c © 2008, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. are used by people to operate effectively in these situations. Work within the AI community–which is the focus of this paper–has produced a variety of computational models that can take into account the computational cost of decision making (Dean and Boddy 1988; Horvitz 1987; Russell et al. 1993; Wellman 1990; Zilberstein 1993). The idea that the cost of decision making must be taken into account was introduced by Simon and later by the statistician Irving Good who used the term Type II Rationality to describe it (Good 1971). Good said that “when the expected time and effort taken to think and do calculations is allowed for in the costs, then one is using the principle of rationality of type II.” But neither Simon nor Good presented any effective computational framework to implement “satisficing” or “type II rationality”. It is by now widely accepted that in most cases the ideal decision-theoretic notion of rationality is beyond our reach. However, the concept of satisficing offers only a vague design principle that needs a good deal of formalization before it can be used in practice. In particular, one must define the required properties of a satisficing criterion and the quality of behavior that is expected when these properties are achieved. AI researchers have introduced over the years a variety of computational models that can be seen as forms of bounded rationality. We start by dividing these models into three broad classes. We are particularly interested in the role that metareasoning plays in these theories. Approximate reasoning One of the early computational approaches to bounded rationality has been based on heuristic search. In fact, Simon has initially identified satisficing with heuristic search. In this context, heuristic search represents a form of approximate reasoning. It uses some domain knowledge to guide the search process, which continues until a satisfactory solution is found. This should be distinguished from admissible heuristic techniques such as A∗ that are designed to always return the optimal answer. Admissible heuristic search is an important part of AI, but it has little to do with bounded rationality. The focus on optimal, rather than satisfying, solutions makes this type of heuristic search simply a more efficient way to find exact answers. Simon refers to another type of heuristic functions in which heuristics are used to select “adequate” solutions. Such heuristic functions are rarely admissible and the corresponding search processes are not optimal in any formal sense. Systems based on non-admissible heuristic functions are often harder to evaluate, especially when optimal decisions are not available. Although it is often assumed that approximate reasoning is aimed at finding approximate answers to a given problem, it can take different forms. For example, the initial problem can be reformulated in such a way that reduces its complexity. The reformulation process could be approximate, yielding a new problem that is easier to solve because it does not retain all the details of the original problem. The resulting problem could then be solved efficiently and perhaps optimally and the obtained solution can then be used as an approximate solution for the original problem. One example of such a process–also referred to as approximate modeling–is when deterministic action models are used in planning, ignoring the uncertainty about action failures. Combined with suitable runtime execution monitoring, such an approach could be beneficial. In fact, the winner of a recent probabilistic planning competition was a planner based on these principles. Regardless of the form of approximation, approximate reasoning techniques can be complemented by some form of explicit or implicit metareasoning. Metareasoning in this context is a mechanism to make certain runtime decisions by reasoning about the problem solving–or object-level–reasoning process. This can be done either explicitly, by introducing another level of reasoning as shown in Figure 1, or implicitly, by pre-compiling metareasoning decisions into the object-level reasoning process at design time. For example, metareasoning has been used to develop search control strategies–both explicitly and implicitly. In some cases, the goal is specifically to optimize the tradeoff between search effort and quality of results (Russell and Wefald 1991). Thus, metareasoning could play a useful role in certain forms of approximate reasoning, but it is not–by definition–a required component. While it is clear that any form of bounded rationality essentially implies that the agent performs approximate reasoning, the opposite is not necessarily true. Generally, frameworks for approximate reasoning do not provide any formal guarantees about the overall performance of the agent. Such guarantees are necessary to offer a satisfactory definition of bounded rationality and thus restore some sort of qualified optimality. So, we do not view a heuristic rule that proves useful in practice to be in itself a framework for bounded rationality if it does not have additional formal properties. The rest of this section describes two additional approaches that offer such precise properties. Optimal metaraesoning Since metareasoning is a component that monitors and controls object-level deliberation, one could pose the question of whether the metareasoning process itself is optimal. Optimality here is with respect to the overall agent performance, given its fixed object-level deliberation capabilities. This is a well-defined question that sometimes has a simple answer. For example, metareasoning may focus on the single question of when to stop deliberation and take action. Depending on how the base-level component is structured, the answer may or may not be straightforward. Optimal metareasoning has been also referred to as rational metareasoning (Horvitz 1989) and metalevel rationality (Russell 1995) to distinguish it from perfect rationality. This offers one precise form of bounded rationality that we will examine in further details in the next section. It should be noted that optimal metareasoning can result in arbitrary poor agent performance. This is true because we do not impose upfront any constraints on the object-level deliberation process, in terms of either efficiency or correctness. Nevertheless, we will see later that this presents an attractive framework for bounded rationality and that performance guarantees can be established once additional constraints are imposed on the overall architecture.

Additive Pattern Database Heuristics

Abstract: We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases, which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving the different subproblems can be added together without overestimating the cost of solving the original problem. Previously, we showed how to statically partition the sliding-tile puzzles into disjoint groups of tiles to compute an admissible heuristic, using the same partition for each state and problem instance. Here we extend the method and show that it applies to other domains as well. We also present another method for additive heuristics which we call dynamically partitioned pattern databases. Here we partition the problem into disjoint subproblems for each state of the search dynamically. We discuss the pros and cons of each of these methods and apply both methods to three different problem domains: the sliding-tile puzzles, the 4-peg Towers of Hanoi problem, and finding an optimal vertex cover of a graph. We find that in some problem domains, static partitioning is most effective, while in others dynamic partitioning is a better choice. In each of these problem domains, either statically partitioned or dynamically partitioned pattern database heuristics are the best known heuristics for the problem.

BJOLP: The Big Joint Optimal Landmarks Planner

Abstract: BJOLP, the Big Joint Optimal Landmarks Planner, uses landmarks to derive an admissible heuristic, which is then used to guide a search for a cost-optimal plan. In this paper we review landmarks and describe how they can be used to derive an admissible heuristic. We conclude with presenting the BJOLP planner.

When optimal is just not good enough: learning fast informative action cost partitionings

Abstract: Several recent heuristics for domain independent planning adopt some action cost partitioning scheme to derive admissible heuristic estimates. Given a state, two methods for obtaining an action cost partitioning have been proposed: optimal cost partitioning, which results in the best possible heuristic estimate for that state, but requires a substantial computational effort, and ad-hoc (uniform) cost partitioning, which is much faster, but is usually less informative. These two methods represent almost opposite points in the tradeoff between heuristic accuracy and heuristic computation time. One compromise that has been proposed between these two is using an optimal cost partitioning for the initial state to evaluate all states. In this paper, we propose a novel method for deriving a fast, informative cost-partitioning scheme, that is based on computing optimal action cost partitionings for a small set of states, and using these to derive heuristic estimates for all states. Our method provides greater control over the accuracy/computation-time tradeoff, which, as our empirical evaluation shows, can result in better performance.

Optimal automatic table layout

Abstract: Automatic layout of tables is useful in word processing applications and is required in on-line applications because of the need to tailor the layout to the viewport width, choice of font and dynamic content. However, if the table contains text, minimizing the height of the table for a fixed maximum width is a difficult combinatorial optimization problem. We present three different approaches to finding the minimum height layout based on standard approaches for combinatorial optimization. All are guaranteed to find the optimal solution. The first is an A*-based approach that uses an admissible heuristic based on the area of the cell content. The second and third are constraint programming (CP) approaches using the same CP model. The second approach uses traditional CP search, while the third approach uses a hybrid CP/SAT approach, lazy clause generation, that uses learning to reduce the search required. We provide a detailed empirical evaluation of the three approaches and also compare them with two mixed integer programming (MIP) encodings due to Bilauca and Healy.

FluCaP: A Heuristic Search Planner for First-Order MDPs

Abstract: We present a heuristic search algorithm for solving first-order Markov Decision Processes (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, in contrast to existing systems, which start with propositionalizing the FOMDP and then perform state abstraction on its propositionalized version we apply state abstraction directly on the FOMDP avoiding propositionalization. This kind of abstraction is referred to as first-order state abstraction. Secondly, guided by an admissible heuristic, the search is restricted to those states that are reachable from the initial state. We demonstrate the usefulness of the above techniques for solving FOMDPs with a system, referred to as FluCaP (formerly, FCPlanner), that entered the probabilistic track of the 2004 International Planning Competition (IPC2004) and demonstrated an advantage over other planners on the problems represented in first-order terms.

Integrating Learning from Examples into the Search for Diagnostic Policies

Abstract: This paper studies the problem of learning diagnostic policies from training examples. A diagnostic policy is a complete description of the decision-making actions of a diagnostician (i.e., tests followed by a diagnostic decision) for all possible combinations of test results. An optimal diagnostic policy is one that minimizes the expected total cost, which is the sum of measurement costs and misdiagnosis costs. In most diagnostic settings, there is a tradeoff between these two kinds of costs. This paper formalizes diagnostic decision making as a Markov Decision Process (MDP). The paper introduces a new family of systematic search algorithms based on the AO* algorithm to solve this MDP. To make AO* efficient, the paper describes an admissible heuristic that enables AO* to prune large parts of the search space. The paper also introduces several greedy algorithms including some improvements over previously-published methods. The paper then addresses the question of learning diagnostic policies from examples. When the probabilities of diseases and test results are computed from training data, there is a great danger of overfitting. To reduce overfitting, regularizers are integrated into the search algorithms. Finally, the paper compares the proposed methods on five benchmark diagnostic data sets. The studies show that in most cases the systematic search methods produce better diagnostic policies than the greedy methods. In addition, the studies show that for training sets of realistic size, the systematic search algorithms are practical on todays desktop computers.

Informed Heuristics for Guiding Stem-and-Cycle Ejection Chains

Abstract: The state of the art in local search for the Traveling Salesman Problem is dominated by ejection chain methods utilising the Stem-and-Cycle reference structure. Though effective such algorithms employ very little information in their successor selection strategy, typically seeking only to minimise the cost of a move. We propose an alternative approach inspired from the AI literature and show how an admissible heuristic can be used to guide successor selection. We undertake an empirical analysis and demonstrate that this technique often produces better results than less informed strategies albeit at the cost of running in higher polynomial time.

Admissible heuristic with multi-landmarks counting

Abstract: Landmarks for a planning task are sub-goals that are necessarily made true at some time steps for any success plan. It is showed that the heuristic search with landmarks guiding has gained great success in 2008 IPC. Present landmark-counting heuristics are competitive until the complete causal landmarks have been extracted. Here, we propose an multi-path dependent heuristic which restricts the fact landmarks to be achieved from the current state during the search with considering the repeatedly appearance of action landmarks. Our cost-sharing heuristic is proved theoretically admissible and empirically efficient.