Monte Carlo Tree Search with Heuristic Evaluations using Implicit Minimax Backups

Monte Carlo Tree Search (MCTS) has improved the performance of game engines in domains such as Go, Hex, and general game playing. MCTS has been shown to outperform classic alpha-beta search in games where good heuristic evaluations are difficult to obtain. In recent years, combining ideas from traditional minimax search in MCTS has been shown to be advantageous in some domains, such as Lines of Action, Amazons, and Breakthrough. In this paper, we propose a new way to use heuristic evaluations to guide the MCTS search by storing the two sources of information, estimated win rates and heuristic evaluations, separately. Rather than using the heuristic evaluations to replace the playouts, our technique backs them up implicitly during the MCTS simulations. These minimax values are then used to guide future simulations. We show that using implicit minimax backups leads to stronger play performance in Kalah, Breakthrough, and Lines of Action.Comment: 24 pages, 7 figures, 9 tables, expanded version of paper presented at IEEE Conference on Computational Intelligence and Games (CIG) 2014 conferenc

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

An Efficient Interpolation Technique for Jump Proposals in Reversible-Jump Markov Chain Monte Carlo Calculations

Selection among alternative theoretical models given an observed data set is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty: it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the MCMC algorithm and convergence is correspondingly slow. Here we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose inter-model jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient "global" proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher-dimensional spaces efficiently.Comment: Minor revision to match published versio

CP-violating top quark couplings at future linear e+e−e^+e^- colliders

We study the potential of future lepton colliders to probe violation of the CP symmetry in the top quark sector. In certain extensions of the Standard Model, such as the two-Higgs-doublet model (2HDM), sizeable anomalous top quark dipole moments can arise, that may be revealed by a precise measurement of top quark pair production. We present results from detailed Monte Carlo studies for the ILC at 500~\GeV{} and CLIC at 380~\gev{} and use parton-level simulations to explore the potential of high-energy operation. We find that precise measurements in $e^+e^- \rightarrow t\bar{t}$ production with subsequent decay to lepton plus jets final states can provide sufficient sensitivity to detect Higgs-boson-induced CP violation in a viable two-Higgs-doublet model. The potential of a linear $e^+e^-$ collider to detect CP-violating electric and weak dipole form factors of the top quark exceeds the prospects of the HL-LHC by over an order of magnitude

Monte-Carlo tree search with heuristic knowledge: A novel way in solving capturing and life and death problems in Go

Monte-Carlo (MC) tree search is a new research field. Its effectiveness in searching large state spaces, such as the Go game tree, is well recognized in the computer Go community. Go domain- specific heuristics and techniques as well as domain-independent heuristics and techniques are sys- tematically investigated in the context of the MC tree search in this dissertation. The search extensions based on these heuristics and techniques can significantly improve the effectiveness and efficiency of the MC tree search. Two major areas of investigation are addressed in this dissertation research: I. The identification and use of the effective heuristic knowledge in guiding the MC simulations, II. The extension of the MC tree search algorithm with heuristics. Go, the most challenging board game to the machine, serves as the test bed. The effectiveness of the MC tree search extensions is demonstrated through the performances of Go tactic problem solvers using these techniques. The main contributions of this dissertation include: 1. A heuristics based Monte-Carlo tactic tree search framework is proposed to extend the standard Monte-Carlo tree search. 2. (Go) Knowledge based heuristics are systematically investigated to improve the Monte-Carlo tactic tree search. 3. Pattern learning is demonstrated as effective in improving the Monte-Carlo tactic tree search. 4. Domain knowledge independent tree search enhancements are shown as effective in improving the Monte-Carlo tactic tree search performances. 5. A strong Go Tactic solver based on proposed algorithms outperforms traditional game tree search algorithms. The techniques developed in this dissertation research can benefit other game domains and ap- plication fields