On the Complexity of Learning Lexicographic Strategies

2004

Simple decision heuristics that process cues in a particular order and stop considering cues as soon as a decision can be made have been shown to be both accurate and quick. But one criticism of heuristics such as Take The Best is that these owe much of their simplicity and success to the not inconsiderable computations necessary for setting up the cue search order before the heuristic can be used. The criticism, though, can be countered in two ways: First, there are typically many cue orders possible that will achieve good performance in a given problem domain. And second, as we will show here, there are simple learning rules that can quickly converge on one of these useful cue orders through exposure to just a small number of decisions. We conclude by arguing for the need to take into account the computation necessary for not only the application but also the setup of a heuristic when talking about its simplicity.

Journal of Behavioral …, 2011

The Similarity Heuristic Decision makers are often called on to make snap judgments using fast-and-frugal decision rules called cognitive heuristics. Although early research into cognitive heuristics emphasized their limitations, more recent research has focused on their high level of accuracy. In this paper we investigate the performance a subset of the representativeness heuristic which we call the similarity heuristic. Decision makers who use it judge the likelihood that an instance is a member of one category rather than another by the degree to which it is similar to others in that category. We provide a mathematical model of the heuristic and test it experimentally in a trinomial environment. The similarity heuristic turns out to be a reliable and accurate choice rule and both choice and response time data suggest it is also how choices are made.

European Journal of Operational Research, 2003

In the sequential decision making task known as the best choice problem, n items are presented in a random order one at a time. After each item, the decision maker (DM) can determine only their relative ranks. The DMÕs goal is to select the best of all n items without the possibility of recalling previously observed items. The purpose of this paper is to compare the optimal policy to three classes of heuristic decision rules that were identified and studied in previous research. We also investigate the limiting case as n ! 1.

Games, Norms and Reasons, 2011

Computational Economics, 2004

A consumer entering a new bookstore can face more than 250,000 alternatives. The efficiency of compensatory and noncompensatory decision rules for finding a preferred item depends on the efficiency of their associated information operators. At best, item-by-item information operators lead to linear computational complexity; set information operators, on the other hand, can lead to constant complexity. We perform an experiment demonstrating that subjects are approximately rational in selecting between sublinear and linear rules. Many markets are organized by attributes that enable consumers to employ a set-selection-by-aspect rule using set information operations. In cyberspace decision rules are encoded as decision aids.

Psychological Review, 2010

Heuristics embodying limited information search and noncompensatory processing of information can yield robust performance relative to computationally more complex models. One criticism raised against heuristics is the argument that complexity is hidden in the calculation of the cue order used to make predictions. We discuss ways to order cues that do not entail individual learning. Then we propose and test the thesis that when orders are learned individually, people's necessarily limited knowledge will curtail computational complexity while also achieving robustness. Using computer simulations, we compare the performance of the take-the-best heuristic-with dichotomized or undichotomized cues-to benchmarks such as the naïve Bayes algorithm across 19 environments. Even with minute sizes of training sets, take-the-best using undichotomized cues excels. For 10 environments, we probe people's intuitions about the direction of the correlation between cues and criterion. On the basis of these intuitions, in most of the environments take-the-best achieves the level of performance that would be expected from learning cue orders from 50% of the objects in the environments. Thus, ordinary information about cues-either gleaned from small training sets or intuited-can support robust performance without requiring Herculean computations.

2016

We examined the sequence of decision problems that are encountered in the game of Tetris and found that most of the problems are easy in the following sense: One can choose well among the available actions without knowing an evaluation function that scores well in the game. This is a consequence of three conditions that are prevalent in the game: simple dominance, cumulative dominance, and noncompensation. These conditions can be exploited to develop faster and more effective learning algorithms. In addition, they allow certain types of domain knowledge to be incorporated with ease into a learning algorithm. Among the sequential decision problems we encounter, it is unlikely that Tetris is unique or rare in having these properties.

European Conference on Artificial Intelligence, 2010

We consider the problem of learning a user's ordinal preferences on a multiattribute domain, assuming that her preferences are lexicographic. We introduce a general graphical representation called LP-trees which captures various natural classes of such preference relations, depending on whether the importance order between attributes and/or the local preferences on the domain of each attribute is conditional on the values of other attributes. For each class we determine the Vapnik-Chernovenkis dimension, the communication complexity of preference elicitation, and the complexity of identifying a model in the class consistent with a set of user-provided examples.

Often an agent that has to solve a problem must choose which heuristic or strategy will help it the most in achieving its objectives. Sometimes the agent wishes to obtain additional units of information on the possible heuristics and strategies in order to choose between them, but it may be costly. As a result, the agent's goal is to acquire enough units of information in order to make a decision while incurring minimal cost. We focus on situations where the agent must decide in advance how many units it would like to obtain. We present an algorithm for choosing between two options, and then formulate three methods for the general case where there are k > 2 options to choose from. We investigate the 2-option algorithm and the general k-option methods effectiveness in two domains: the 3-SAT domain, and the CT computer game. In both domains we present the experimental performance of our models. Results will show that applying the 2-option algorithm is beneficial and provides the agent a substantial gain. In addition, applying the k-option method in the domains investigated results in a moderate gain.

Journal of Artificial Intelligence Research, 1997

The easy-hard-easy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of this explanation by examining one of its predictions: if the number of solutions is held fixed by the choice of problems, then increased pruning should lead to a monotonic decrease in search cost. Instead, we find the easy-hard-easy pattern in median search cost even when the number of solutions is held constant, for some search methods. This generalizes previous observations of this pattern and shows that the existing theory does not explain the full range of the peak in search cost. In these cases the pattern appears to be due to changes in the size of the minimal unsolvable subproblems, rather than changing numbers of solutions.