We consider sparse signals embedded in additive white noise. We study parametrically optimal as well as **tree**-**search** sub-optimal signal detection policies. As a special case, we consider a constant signal and Gaussian noise, with and without data outliers present. In the presence of outliers, we study outlier resistant robust detection techniques. We compare the studied policies in terms of error performance, complexity and resistance to outliers.

over the alternative ‘naive’ approach. A more recent work (Lai 2015) introduced a deep learning implementation of TDLeaf(λ) called Giraffe. Testing it on the game of Chess, the authors claim (during publication) it is “the most success- ful attempt thus far at using end-to-end machine learning to play chess”. In light of our theoretical results and empirical success described above, we argue that backing up the opti- mal value from a **tree** **search** should be considered as a ‘best practice’ among RL practitioners.

Monte Carlo **Tree** **Search** (MCTS) is a directed **search** technique that has gained prominence in recent years and has been used with success for several types of games such as Go (Silver et al. 2016) and Kriegspiel (Ciancarini and Favini 2009). The basic algorithm involves an iterative construction of a **search** **tree** until some computational limit is achieved. (Browne et al. 2012). There are four steps per- formed during each iteration of MCTS: selection, expan- sion, simulation, and backpropagation. Figure 2 shows the structure of each MCTS phase and the **search** **tree** associat- ed.

Show more
Ensemble in RL Wiering and Van Hasselt (2008) de- signed four ensemble methods combining five RL algo- rithms with a voting scheme based on value functions of different RL algorithms. Hans and Udluft (2010) used a net- work ensemble to improve the performance of Fitted Q- Iteration. Osband et al. (2016) used a Q ensemble to ap- proximate Thomas’ sampling, resulting in improved explo- ration and performance boost in challenging video games. Huang et al. (2017) used both an actor ensemble and a critic ensemble in continuous control problems. However, to our best knowledge, the present work is the first to relate ensem- ble with options and to use an ensemble for a look-ahead **tree** **search** in continuous control problems.

Show more
Abstract— We are addressing the course timetabling problem in this work. In a university, students can select their favorite courses each semester. Thus, the general requirement is to allow them to attend lectures without clashing with other lectures. A feasible solution is a solution where this and other conditions are satisfied. Constructing reasonable solutions for course timetabling problem is a hard task. Most of the existing methods failed to generate reasonable solutions for all cases. This is since the problem is heavily constrained and an e ﬀ ective method is required to explore and exploit the **search** space. We utilize Monte Carlo **Tree** **Search** (MCTS) in finding feasible solutions for the first time. In MCTS, we build a **tree** incrementally in an asymmetric manner by sampling the decision space. It is traversed in the best-first manner. We propose several enhancements to MCTS like simulation and **tree** pruning based on a heuristic. The performance of MCTS is compared with the methods based on graph coloring heuristics and Tabu **search**. We test the solution methodologies on the three most studied publicly available datasets. Overall, MCTS performs better than the method based on graph coloring heuristic; however, it is inferior compared to the Tabu based method. Experimental results are discussed.

Show more
Syntactic **search** is one of the basic tools necessary to work with syntactically annotated corpora, both manually annotated treebanks of modest size and massive automatically analyzed parsebanks, which may go into hundreds of millions of sentences and billions of words. Traditionally, tools such as TGrep2 (Rohde, 2004) and TRegex (Levy and An- drew, 2006) have been used for **tree** **search**. How- ever, these tools are focused on constituency trees annotated with simple part-of-speech tags, and have not been designed to deal with dependency graphs and rich morphologies. Existing **search** systems are traditionally designed for searching from treebanks rarely going beyond million tokens. However, **tree**- bank sized corpora may not be sufficient enough for searching rare linguistic phenomena, and therefore ability to cover billion-word parsebanks is essen- tial. Addressing these limitations in existing tools, we present SETS, a toolkit for **search** in dependency treebanks and parsebanks that specifically empha- sizes expressive **search** of dependency graphs in- cluding detailed morphological analyses, simplicity of querying, speed, and scalability.

Show more
Thanks to Chapel’s global view of the control flow and data structures, it is possible to conceive a distributed **tree** **search** starting from its multicore counterpart by incrementally adding few lines of code. The distributed implementation performs load balancing among different processes and also uses all CPU cores that a computer node has. Despite the high level of its features, the distributed **tree** **search** in Chapel is on average 16% slower and reaches up to reaches 80% of the scalability reached by its C-MPI+OpenMP counterpart. Finally, the distributed load balancing strategies provided are effective: the dynamic load balancing version is up to 1.5× faster than its static counterpart.

Show more
The reconfigurable trellis (**tree**) **search** algorithm has been employed in channel decoders [14, 15]. It achieves near-ML performance with low complexity. The key idea is to arrange symbol positions according to di ﬀ erent reliabilities of sym- bols. During the **search** process in the previously mentioned ITS algorithm, the number of branches is decreased by ex- ploring paths that are most likely to be part of the maximum- likelihood path (MLP), while discarding those paths that are unlikely to belong to the MLP as early in the **search** as pos- sible. Few branches are needed to be explored and a reduced **search** algorithm can stop any further exploration of a path relatively early in the **search** without losing the MLP, if the influence of unexplored branch metrics on the rank order of the path metrics are insignificant. The order is only deter- mined at the first iteration and a reconfigurable **tree** structure is constructed according to the order; during the following it- erations, the detection process is based on the reconfigurable **tree** structure.

Show more
ABSTRACT: Game **tree** **Search** algorithm is used to **search** the best move in game **tree**. GTS is a combinatorial problem in which it is hard to find optimal solution from huge possible solutions. Focus of the system is to take advantage of GPU’s massive parallelism capability to accelerate the speed of game **tree** algorithm and propose a concise and general parallel game **tree** algorithm on GPUs. GPU computing is getting popular among scientific community because of cheap and high performance computational power. Proposed system is implemented for Connect4 and Connect6 game using CUDA and MPI programming environment. It is found that parallelization tasks on SIMD processors of graphics cards perform better during searching and evaluating a GTS. In this CPU is responsible for maintain **tree** structure of game **tree** and GPU is responsible for evaluating node simultaneously. Thus choice is to use combination of CPU-GPU solution with DFS-BFS **search** respectively. Comparison is done with serial implementation for Connect4 and Connect 6 games.

Show more
Teaching computer programs to play games through machine learning has been an important way to achieve better artificial intelligence (AI) in a variety of real-world applications. Monte Carlo **Tree** **Search** (MCTS) is one of the key AI techniques developed recently that enabled AlphaGo to defeat a legendary professional Go player. What makes MCTS particularly attractive is that it only understands the basic rules of the game and does not rely on expert-level knowledge. Researchers thus expect that MCTS can be applied to other com- plex AI problems where domain-specific expert-level knowledge is not yet available. So far there are very few analytic studies in the literature. In this pa- per, our goal is to develop analytic studies of MCTS to build a more funda- mental understanding of the algorithms and their applicability in complex AI problems. We start with a simple version of MCTS, called random playout **search** (RPS), to play Tic-Tac-Toe, and find that RPS may fail to discover the correct moves even in a very simple game position of Tic-Tac-Toe. Both the probability analysis and simulation have confirmed our discovery. We con- tinue our studies with the full version of MCTS to play Gomoku and find that while MCTS has shown great success in playing more sophisticated games like Go, it is not effective to address the problem of sudden death/win. The main reason that MCTS often fails to detect sudden death/win lies in the random playout **search** nature of MCTS, which leads to prediction distortion. There- fore, although MCTS in theory converges to the optimal minimax **search**, with real world computational resource constraints, MCTS has to rely on RPS as an important step in its **search** process, therefore suffering from the same fun- damental prediction distortion problem as RPS does. By examining the de- tailed statistics of the scores in MCTS, we investigate a variety of scenarios where MCTS fails to detect sudden death/win. Finally, we propose an im- proved MCTS algorithm by incorporating minimax **search** to overcome pre- diction distortion. Our simulation has confirmed the effectiveness of the pro- posed algorithm. We provide an estimate of the additional computational How to cite this paper: Li, W. (2018)

Show more
34 Read more

In order to address problems with larger **search** spaces, we must turn to alternative methods. Monte Carlo **tree** **search** (MCTS) has had a lot of success in Go and in other appli- cations [2] [1]. MCTS eschews the typical brute force **tree** searching methods, and utilizes statistical sampling instead. This makes MCTS a probabilistic algorithm. As such, it will not always choose the best action, but it still performs rea- sonably well given sufficient time and memory. MCTS per- forms lightweight simulations that randomly select actions. These simulations are used to selectively grow a game **tree** over a large number of iterations. Since these simulations do not take long to perform, it allows MCTS to explore **search** spaces quickly. This is what gives MCTS the advantage over deterministic methods in large **search** spaces.

Show more
Game **tree** **search** is digraph, nodes in digraph indicate position and lines or edges denote moves in a game as it mentioned in a game theory. From game of point view, the complete game **tree** is the hierarchical game **tree** structure begins at the initial position as a node and containing all possible moves from each position. It is very hard to find optimal solution for taking best move for many computer games as it contains exponential time complexity, games like Connect4/Connect6 [6], Sim, Chess[7],Havannah etc. The focus on GTS algorithm to obtain near-optimal solutions using node based approach. It is used to speed up or accelerating the GTS algorithms for the computer.

Show more
However, this problem is intrinsically difficult be- cause it is hard to encode what to say into a sentence while ensuring its syntactic correctness. We propose to use Monte Carlo **tree** **search** (MCTS) (Kocsis and Szepesvari, 2006; Browne et al., 2012), a stochastic **search** algorithm for decision processes, to find an optimal solution in the decision space. We build a **search** **tree** of possible syntactic trees to generate a sentence, by selecting proper rules through numer- ous random simulations of possible yields.

In recent years there has been much interest in the Monte Carlo **Tree** **Search** (MCTS) algorithm. In 2006 it was a new, adaptive, randomized optimization algo- rithm [Cou06, KS06]. In fields as diverse as Artificial Intelligence, Operations Re- **search**, and High Energy Physics, research has established that MCTS can find valu- able approximate answers without domain-dependent heuristics [KPVvdH13]. The strength of the MCTS algorithm is that it provides answers with a random amount of error for any fixed computational budget [GBC16]. Much effort has been put into the development of parallel algorithms for MCTS to reduce the running time. The ef- forts are applied to a broad spectrum of parallel systems; ranging from small shared- memory multi-core machines to large distributed-memory clusters. In the last years, parallel MCTS played a major role in the success of AI by defeating humans in the game of Go [SHM + 16, HS17].

Show more
196 Read more

Adaptive Slots Collision Tracking **Tree** Algorithm (ASCTTA) uses the idea of multi-slot response, while using the collision tracking **tree** to determine the specific collision, to determine the prefix of the next reader query; and introduce the collision factor, according to the collision factor to dynamically change the tag response time slot. The algorithm reduces the probability of collision by automatically adjusting the time slot to achieve better recognition efficiency.

These measurements, averaged across all 5000 deals, are pre- sented in Table II. It should be noted that these measurements are a function of the deal; the Þ rst measurement is exact for each deal, while the second depends on the sampled deter- minizations. These measurements were made only for the non-Landlord players since the playing strength experiments in Section VII-B were conducted from the point of view of the Landlord player. This means the algorithms tested always had the same number of branches at nodes where the Land- lord makes a move, since the Landlord can see his cards in hand. The Þ rst measurement is an indicator for the number of branches that may be expected at opponent nodes for the cheating UCT player as the Landlord. Similarly, the second measurement indicates the number of branches for opponent nodes with determinized UCT as the Landlord. Both of these measurements are upper bounds, since if an opponent has played any cards at all then the number of leading plays will be smaller. The third, fourth, and Þ fth measurements indicate how many expansions ISMCTS will be making at opponent nodes after a certain number of visits, since a new determinization is used on each iteration. Again this measurement is an upper bound since only one move is actually added per iteration and if there were moves unique to a determinization which were never seen again, only one of them would be added to the **tree**.

Show more
25 Read more

● Interesting under strong time constraints ● Result: 60-40%.. Pondering[r]

103 Read more

any choice of the depth l, we present the first approximation guarantee for this **search** process. Defeatist BSP-**tree** **search** has been explored with the spill **tree** [11], a binary **tree** with overlapping sibling nodes unlike the disjoint nodes in the usual BSP-**tree**. The **search** involves selecting the can- didates in (all) the leaf node(s) which contain the query. The level of overlap guarantees the **search** approximation, but this **search** method lacks any rigorous runtime guarantee; it is hard to bound the number of leaf nodes that might contain any given query. Dasgupta & Sinha (2013) [12] show that the probability of finding the exact nearest neighbor with defeatist **search** on certain randomized partition trees (randomized spill trees and RP-trees being among them) is directly proportional to the relative contrast of the **search** task [13], a recently proposed quantity which characterizes the difficulty of a **search** problem (lower relative contrast makes exact **search** harder).

Show more
11 Read more

The methods we have reviewed so far tackle the prob- lem of offline sampling. While these methods can to some degree be extended to the online case (see e.g. (Belov et al. 2017)), some information is lost in the process. For in- stance, one way to adapt offline sampling to online **tree**-size prediction is to treat the leaves obtained by the **tree** **search** procedure as if they had been obtained randomly. However, while in offline sampling, samples are drawn independently, this does not hold when obtaining leaves online. This phe- nomenon clearly materializes in the difference between of- fline and online results of (Belov et al. 2017). Indeed, at any given point in the **search**, supposing that samples are inde- pendent equates to supposing that the first or latest samples observed are equally good predictors of the next samples to be observed. In other words, any such method would ignore possible trends in the series of samples. However, we ar- gue that there are multiple types of trends affecting the sam- ples obtained in the B&B. First, since the depth of the **tree** grows as the **search** progresses, increasingly deeper leaves are found, although this is not a monotonic process. Sec- ond, and conversely, after a primal solution is found which improves the primal bound, nodes can be pruned at shal- lower depths than previously. A similar phenomenon oc- curs with strong conflicts (Achterberg 2007a). Other factors such as “smart” node selection strategies (Berthold, Hendel, and Koch 2017) contribute to creating varying trends in the amount of resources required to reach a leaf. Hence, in an online setting, while we cannot suppose that samples are in- dependent, capturing trends may mitigate this loss.

Show more
After developing a spell-checker using radix **search** **tree** technique. It is trained using training dataset and the accuracy is calculated for the developed spell-checker accordingly. Thus, the overall accuracy almost reached to 100% ; it provides a high accuracy. The above evidences are sufficient to make sure that the radix **search** **tree** could be used efficiently to build a spell-checker for Arabic language. The future scope will convey to find new techniques that can keep spell-checker as highly efficient and accurate as possible.

Show more