Lookahead Pathology in Monte-Carlo Tree Search

Monte-Carlo Tree Search (MCTS) is an adversarial search paradigm that first found prominence with its success in the domain of computer Go. Early theoretical work established the game-theoretic soundness and convergence bounds for Upper Confidence bounds applied to Trees (UCT), the most popular instantiation of MCTS; however, there remain notable gaps in our understanding of how UCT behaves in practice. In this work, we address one such gap by considering the question of whether UCT can exhibit lookahead pathology -- a paradoxical phenomenon first observed in Minimax search where greater search effort leads to worse decision-making. We introduce a novel family of synthetic games that offer rich modeling possibilities while remaining amenable to mathematical analysis. Our theoretical and experimental results suggest that UCT is indeed susceptible to pathological behavior in a range of games drawn from this family

Rolling Lookahead Learning for Optimal Classification Trees

Classification trees continue to be widely adopted in machine learning applications due to their inherently interpretable nature and scalability. We propose a rolling subtree lookahead algorithm that combines the relative scalability of the myopic approaches with the foresight of the optimal approaches in constructing trees. The limited foresight embedded in our algorithm mitigates the learning pathology observed in optimal approaches. At the heart of our algorithm lies a novel two-depth optimal binary classification tree formulation flexible to handle any loss function. We show that the feasible region of this formulation is an integral polyhedron, yielding the LP relaxation solution optimal. Through extensive computational analyses, we demonstrate that our approach outperforms optimal and myopic approaches in 808 out of 1330 problem instances, improving the out-of-sample accuracy by up to 23.6% and 14.4%, respectively.Comment: 41 pages, 19 tables, 10 figure

A survey of cost-sensitive decision tree induction algorithms

The past decade has seen a significant interest on the problem of inducing decision trees that take account of costs of misclassification and costs of acquiring the features used for decision making. This survey identifies over 50 algorithms including approaches that are direct adaptations of accuracy based methods, use genetic algorithms, use anytime methods and utilize boosting and bagging. The survey brings together these different studies and novel approaches to cost-sensitive decision tree learning, provides a useful taxonomy, a historical timeline of how the field has developed and should provide a useful reference point for future research in this field

A Theoretical Examination of Practical Game Playing: Lookahead Search

Abstract. Lookahead search is perhaps the most natural and widely used game playing strategy. Given the practical importance of the method, the aim of this paper is to provide a theoretical performance examination of lookahead search in a wide variety of applications. To determine a strategy play using lookahead search, each agent predicts multiple levels of possible re-actions to her move (via the use of a search tree), and then chooses the play that optimizes her future payoff accounting for these re-actions. There are several choices of optimization function the agents can choose, where the most appropriate choice of function will depend on the specifics of the actual game- we illustrate this in our examples. Furthermore, the type of search tree chosen by computationally-constrained agent can vary. We focus on the case where agents can evaluate only a bounded number, k, of moves into the future. That is, we use depth k search trees and call this approach k-lookahead search. We apply our method in five well-known settings: industrial organization (Cournot’s model); AdWord auctions; congestion games; valid-utility games and basic-utility games; cost-sharing network design games. We consider two questions. First, what i

A Survey of Parallel Data Mining

With the fast, continuous increase in the number and size of databases, parallel data mining is a natural and cost-effective approach to tackle the problem of scalability in data mining. Recently there has been a considerable research on parallel data mining. However, most projects focus on the parallelization of a single kind of data mining algorithm/paradigm. This paper surveys parallel data mining with a broader perspective. More precisely, we discuss the parallelization of data mining algorithms of four knowledge discovery paradigms, namely rule induction, instance-based learning, genetic algorithms and neural networks. Using the lessons learned from this discussion, we also derive a set of heuristic principles for designing efficient parallel data mining algorithms

Regression tree construction by bootstrap: Model search for DRG-systems applied to Austrian health-data

Background. DRG-systems are used to allocate resources fairly to hospitals based on their performance. Statistically, this allocation is based on simple rules that can be modeled with regression trees. However, the resulting models often have to be adjusted manually to be medically reasonable and ethical. Methods. Despite the possibility of manual, performance degenerating adaptations of the original model, alternative trees are systematically searched. The bootstrap-based method bumping is used to build diverse and accurate regression tree models for DRG-systems. A two-step model selection approach is proposed. First, a reasonable model complexity is chosen, based on statistical, medical and economical considerations. Second, a medically meaningful and accurate model is selected. An analysis of 8 data-sets from Austrian DRG-data is conducted and evaluated based on the possibility to produce diverse and accurate models for predefined tree complexities. Results. The best bootstrap-based trees offer increased predictive accuracy compared to the trees built by the CART algorithm. The analysis demonstrates that even for very small tree sizes, diverse models can be constructed being equally or even more accurate than the single model built by the standard CART algorithm. Conclusions. Bumping is a powerful tool to construct diverse and accurate regression trees, to be used as candidate models for DRG-systems. Furthermore, Bumping and the proposed model selection approach are also applicable to other medical decision and prognosis tasks. 2010 Grubinger et al; licensee BioMed Central Ltd