Improving multivariate Horner schemes with Monte Carlo tree search

Kuipers, Jan; Plaat, Aske; Vermaseren, J.A.M.; Herik, Jaap van den

doi:10.1016/j.cpc.2013.05.008

Cited by 24 publications

(43 citation statements)

References 22 publications

(43 reference statements)

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“…For each test-polynomial MCTS found better variable orders, typically with half the number of operators than the expressions generated by previous algorithms. The results are reported in detail in [26].…”

Section: Sensitivity To C P and Nmentioning

confidence: 92%

“…5, reproduced from [26]. For small numbers of tree expansions low values for the constant C p should be chosen (less than 0.5).…”

Section: Resultsmentioning

confidence: 99%

“…with Horner schemes. Finding better variable orders for applying the classic Horner's rule algorithm is an exciting first result [26], allowing easy investigation of two search parameters. It will be interesting to find out whether similar results can be found in MCTS as applied in Go programs, and other application domains.…”

Section: Discussionmentioning

confidence: 99%

“…Applying MCTS to this challenge resulted in an unexpected improvement, first reported in [26]. Here we will stress further investigations into parameters that influence the search process.…”

Section: Horner's Rule For Multivariate Polynomialsmentioning

confidence: 99%

“…The performance of MCTS-Horner followed by CSE has been tested by implementing it in FORM [26,27]. MCTS-Horner was tested on a variety of different multivariate polynomials, against the currently best algorithms.…”

Section: Sensitivity To C P and Nmentioning

confidence: 99%

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Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

Herik

Kuipers

Vermaseren

et al. 2014

Communications in Computer and Information Science

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Abstract. After a computer chess program had defeated the human World Champion in 1997, many researchers turned their attention to the oriental game of Go. It turned out that the minimax approach, so successful in chess, did not work in Go. Instead, after some ten years of intensive research, a new method was developed: MCTS (Monte Carlo Tree Search), with promising results. MCTS works by averaging the results of random play-outs. At first glance it is quite surprising that MCTS works so well. However, deeper analysis revealed the reasons.The success of MCTS in Go caused researchers to apply the method to other domains. In this article we report on experiments with MCTS for finding improved orderings for multivariate Horner schemes, a basic method for evaluating polynomials. We report on initial results, and continue with an investigation into two parameters that guide the MCTS search. Horner's rule turns out to be a fruitful testbed for MCTS, allowing easy experimentation with its parameters. The results reported here provide insight into how and why MCTS works. It will be interesting to see if these insights can be transferred to other domains, for example, back to Go.

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Section: Sensitivity To C P and Nmentioning

confidence: 92%

“…5, reproduced from [26]. For small numbers of tree expansions low values for the constant C p should be chosen (less than 0.5).…”

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Horner's Rule For Multivariate Polynomialsmentioning

confidence: 99%

Section: Sensitivity To C P and Nmentioning

confidence: 99%

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Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

Herik

Kuipers

Vermaseren

et al. 2014

Communications in Computer and Information Science

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Two-Agent Self-Play

Plaat

2022

Deep Reinforcement Learning

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Monte Carlo Tree Search: a review of recent modifications and applications

Świechowski¹,

et al. 2022

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Monte Carlo Tree Search (MCTS) is a powerful approach to designing game-playing bots or solving sequential decision problems. The method relies on intelligent tree search that balances exploration and exploitation. MCTS performs random sampling in the form of simulations and stores statistics of actions to make more educated choices in each subsequent iteration. The method has become a state-of-the-art technique for combinatorial games. However, in more complex games (e.g. those with a high branching factor or real-time ones) as well as in various practical domains (e.g. transportation, scheduling or security) an efficient MCTS application often requires its problem-dependent modification or integration with other techniques. Such domain-specific modifications and hybrid approaches are the main focus of this survey. The last major MCTS survey was published in 2012. Contributions that appeared since its release are of particular interest for this review.

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Improving multivariate Horner schemes with Monte Carlo tree search

Cited by 24 publications

References 22 publications

Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

Two-Agent Self-Play

Monte Carlo Tree Search: a review of recent modifications and applications

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