scholarly journals Solving Imperfect-Information Games via Discounted Regret Minimization

2019 ◽  
Vol 33 ◽  
pp. 1829-1836 ◽  
Author(s):  
Noam Brown ◽  
Tuomas Sandholm
Keyword(s):  
Imperfect Information ◽  
Large Scale ◽  
State Of The Art ◽  
Iterative Algorithms ◽  
Game Tree ◽  
Regret Minimization ◽  
Imperfect Information Games ◽  
Improved Performance ◽  
Pruning Techniques ◽  
Prior State

Counterfactual regret minimization (CFR) is a family of iterative algorithms that are the most popular and, in practice, fastest approach to approximately solving large imperfectinformation games. In this paper we introduce novel CFR variants that 1) discount regrets from earlier iterations in various ways (in some cases differently for positive and negative regrets), 2) reweight iterations in various ways to obtain the output strategies, 3) use a non-standard regret minimizer and/or 4) leverage “optimistic regret matching”. They lead to dramatically improved performance in many settings. For one, we introduce a variant that outperforms CFR+, the prior state-of-the-art algorithm, in every game tested, including large-scale realistic settings. CFR+ is a formidable benchmark: no other algorithm has been able to outperform it. Finally, we show that, unlike CFR+, many of the important new variants are compatible with modern imperfect-informationgame pruning techniques and one is also compatible with sampling in the game tree.

scholarly journals Smoothing Method for Approximate Extensive-Form Perfect Equilibrium

2017 ◽  
Author(s):  
Christian Kroer ◽  
Gabriele Farina ◽  
Tuomas Sandholm
Keyword(s):  
Nash Equilibrium ◽  
Imperfect Information ◽  
Large Scale ◽  
Nash Equilibria ◽  
Convex Polytope ◽  
Solution Concept ◽  
Extensive Form ◽  
Game Tree ◽  
Equilibrium Refinements ◽  
Perfect Equilibria

Nash equilibrium is a popular solution concept for solving imperfect-information games in practice. However, it has a major drawback: it does not preclude suboptimal play in branches of the game tree that are not reached in equilibrium. Equilibrium refinements can mend this issue, but have experienced little practical adoption. This is largely due to a lack of scalable algorithms.Sparse iterative methods, in particular first-order methods, are known to be among the most effective algorithms for computing Nash equilibria in large-scale two-player zero-sum extensive-form games. In this paper, we provide, to our knowledge, the first extension of these methods to equilibrium refinements. We develop a smoothing approach for behavioral perturbations of the convex polytope that encompasses the strategy spaces of players in an extensive-form game. This enables one to compute an approximate variant of extensive-form perfect equilibria. Experiments show that our smoothing approach leads to solutions with dramatically stronger strategies at information sets that are reached with low probability in approximate Nash equilibria, while retaining the overall convergence rate associated with fast algorithms for Nash equilibrium. This has benefits both in approximate equilibrium finding (such approximation is necessary in practice in large games) where some probabilities are low while possibly heading toward zero in the limit, and exact equilibrium computation where the low probabilities are actually zero.

scholarly journals A View on Deep Reinforcement Learning in Imperfect Information Games

2020 ◽  
Vol 65 (2) ◽  
pp. 31
Author(s):  
T.V. Pricope
Keyword(s):  
Reinforcement Learning ◽  
Imperfect Information ◽  
Large Scale ◽  
Traditional Approach ◽  
Search Space ◽  
Fictitious Play ◽  
Learning Agents ◽  
Real World Applications ◽  
Imperfect Information Games ◽  
Human Player

Many real-world applications can be described as large-scale games of imperfect information. This kind of games is particularly harder than the deterministic one as the search space is even more sizeable. In this paper, I want to explore the power of reinforcement learning in such an environment; that is why I take a look at one of the most popular game of such type, no limit Texas Hold’em Poker, yet unsolved, developing multiple agents with different learning paradigms and techniques and then comparing their respective performances. When applied to no-limit Hold’em Poker, deep reinforcement learning agents clearly outperform agents with a more traditional approach. Moreover, if these last agents rival a human beginner level of play, the ones based on reinforcement learning compare to an amateur human player. The main algorithm uses Fictitious Play in combination with ANNs and some handcrafted metrics. We also applied the main algorithm to another game of imperfect information, less complex than Poker, in order to show the scalability of this solution and the increase in performance when put neck in neck with established classical approaches from the reinforcement learning literature.

Game-Tree Search with Adaptation in Stochastic Imperfect-Information Games

2006 ◽  
pp. 21-34 ◽  
Author(s):  
Darse Billings ◽  
Aaron Davidson ◽  
Terence Schauenberg ◽  
Neil Burch ◽  
Michael Bowling ◽  
...  
Keyword(s):  
Imperfect Information ◽  
Tree Search ◽  
Game Tree ◽  
Imperfect Information Games ◽  
Game Tree Search ◽  
Information Games

scholarly journals Efficient Opponent Exploitation in No-Limit Texas Hold’em Poker: A Neuroevolutionary Method Combined with Reinforcement Learning

Electronics ◽  
2021 ◽  
Vol 10 (17) ◽  
pp. 2087
Author(s):  
Jiahui Xu ◽  
Jing Chen ◽  
Shaofei Chen
Keyword(s):  
Reinforcement Learning ◽  
Imperfect Information ◽  
Large Scale ◽  
Higher Learning ◽  
New Approach ◽  
Hybrid Framework ◽  
Gradient Based ◽  
Novel Method ◽  
Imperfect Information Games

In the development of artificial intelligence (AI), games have often served as benchmarks to promote remarkable breakthroughs in models and algorithms. No-limit Texas Hold’em (NLTH) is one of the most popular and challenging poker games. Despite numerous studies having been conducted on this subject, there are still some important problems that remain to be solved, such as opponent exploitation, which means to adaptively and effectively exploit specific opponent strategies; this is acknowledged as a vital issue especially in NLTH and many real-world scenarios. Previous researchers tried to use an off-policy reinforcement learning (RL) method to train agents that directly learn from historical strategy interactions but suffered from challenges of sparse rewards. Other researchers instead adopted neuroevolutionary (NE) method to replace RL for policy parameter updates but suffered from high sample complexity due to the large-scale problem of NLTH. In this work, we propose NE_RL, a novel method combing NE with RL for opponent exploitation in NLTH. Our method contains a hybrid framework that uses NE’s advantage of evolutionary computation with a long-term fitness metric to address the sparse rewards feedback in NLTH and retains RL’s gradient-based method for higher learning efficiency. Experimental results against multiple baseline opponents have proved the feasibility of our method with significant improvement compared to previous methods. We hope this paper provides an effective new approach for opponent exploitation in NLTH and other large-scale imperfect information games.

scholarly journals Computing Approximate Equilibria in Sequential Adversarial Games by Exploitability Descent

2019 ◽  
Author(s):  
Edward Lockhart ◽  
Marc Lanctot ◽  
Julien Pérolat ◽  
Jean-Baptiste Lespiau ◽  
Dustin Morrill ◽  
...  
Keyword(s):  
Function Approximation ◽  
Imperfect Information ◽  
Convergence Rates ◽  
Convergence Result ◽  
Extensive Form ◽  
Worst Case ◽  
Regret Minimization ◽  
Imperfect Information Games ◽  
Policy Optimization ◽  
Zero Sum

In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove that when following this optimization, the exploitability of a player's strategy converges asymptotically to zero, and hence when both players employ this optimization, the joint policies converge to a Nash equilibrium. Unlike fictitious play (XFP) and counterfactual regret minimization (CFR), our convergence result pertains to the policies being optimized rather than the average policies. Our experiments demonstrate convergence rates comparable to XFP and CFR in four benchmark games in the tabular case. Using function approximation, we find that our algorithm outperforms the tabular version in two of the games, which, to the best of our knowledge, is the first such result in imperfect information games among this class of algorithms.

scholarly journals Deep Reinforcement Learning from Self-Play in No-limit Texas Hold'em Poker

2021 ◽  
Vol 66 (2) ◽  
pp. 51
Author(s):  
T.-V. Pricope
Keyword(s):  
Nash Equilibrium ◽  
Imperfect Information ◽  
Large Scale ◽  
Adaptive Methods ◽  
Single Step ◽  
Random Factor ◽  
Approximate Nash Equilibrium ◽  
New Variant ◽  
Imperfect Information Games ◽  
Information Games

Imperfect information games describe many practical applications found in the real world as the information space is rarely fully available. This particular set of problems is challenging due to the random factor that makes even adaptive methods fail to correctly model the problem and find the best solution. Neural Fictitious Self Play (NFSP) is a powerful algorithm for learning approximate Nash equilibrium of imperfect information games from self-play. However, it uses only crude data as input and its most successful experiment was on the in-limit version of Texas Hold’em Poker. In this paper, we develop a new variant of NFSP that combines the established fictitious self-play with neural gradient play in an attempt to improve the performance on large-scale zero-sum imperfect information games and to solve the more complex no-limit version of Texas Hold’em Poker using powerful handcrafted metrics and heuristics alongside crude, raw data. When applied to no-limit Hold’em Poker, the agents trained through self-play outperformed the ones that used fictitious play with a normal-form single-step approach to the game. Moreover, we showed that our algorithm converges close to a Nash equilibrium within the limited training process of our agents with very limited hardware. Finally, our best self-play-based agent learnt a strategy that rivals expert human level.  

Multi-Resolution Autoregressive Graph-to-Graph Translation for Molecules

2019 ◽  
Author(s):  
Wengong Jin ◽  
Regina Barzilay ◽  
Tommi S Jaakkola
Keyword(s):  
Drug Discovery ◽  
State Of The Art ◽  
Molecular Graph ◽  
Biochemical Properties ◽  
Large Margin ◽  
Previous State ◽  
Translation Methods ◽  
Atom Level ◽  
Precursor Molecules ◽  
Prior State

The problem of accelerating drug discovery relies heavily on automatic tools to optimize precursor molecules to afford them with better biochemical properties. Our work in this paper substantially extends prior state-of-the-art on graph-to-graph translation methods for molecular optimization. In particular, we realize coherent multi-resolution representations by interweaving trees over substructures with the atom-level encoding of the original molecular graph. Moreover, our graph decoder is fully autoregressive, and interleaves each step of adding a new substructure with the process of resolving its connectivity to the emerging molecule. We evaluate our model on multiple molecular optimization tasks and show that our model outperforms previous state-of-the-art baselines by a large margin.

scholarly journals Documentary data and the study of past droughts: a global state of the art

2018 ◽  
Vol 14 (12) ◽  
pp. 1915-1960 ◽  
Author(s):  
Rudolf Brázdil ◽  
Andrea Kiss ◽  
Jürg Luterbacher ◽  
David J. Nash ◽  
Ladislava Řezníčková
Keyword(s):  
Large Scale ◽  
State Of The Art ◽  
Drought Indices ◽  
Documentary Evidence ◽  
Climatic Trends ◽  
Instrumental Observations ◽  
Spatio Temporal ◽  
Epigraphic Evidence ◽  
Administrative Evidence

Abstract. The use of documentary evidence to investigate past climatic trends and events has become a recognised approach in recent decades. This contribution presents the state of the art in its application to droughts. The range of documentary evidence is very wide, including general annals, chronicles, memoirs and diaries kept by missionaries, travellers and those specifically interested in the weather; records kept by administrators tasked with keeping accounts and other financial and economic records; legal-administrative evidence; religious sources; letters; songs; newspapers and journals; pictographic evidence; chronograms; epigraphic evidence; early instrumental observations; society commentaries; and compilations and books. These are available from many parts of the world. This variety of documentary information is evaluated with respect to the reconstruction of hydroclimatic conditions (precipitation, drought frequency and drought indices). Documentary-based drought reconstructions are then addressed in terms of long-term spatio-temporal fluctuations, major drought events, relationships with external forcing and large-scale climate drivers, socio-economic impacts and human responses. Documentary-based drought series are also considered from the viewpoint of spatio-temporal variability for certain continents, and their employment together with hydroclimate reconstructions from other proxies (in particular tree rings) is discussed. Finally, conclusions are drawn, and challenges for the future use of documentary evidence in the study of droughts are presented.

scholarly journals VIPPrint: Validating Synthetic Image Detection and Source Linking Methods on a Large Scale Dataset of Printed Documents

2021 ◽  
Vol 7 (3) ◽  
pp. 50
Author(s):  
Anselmo Ferreira ◽  
Ehsan Nowroozi ◽  
Mauro Barni
Keyword(s):  
Large Scale ◽  
State Of The Art ◽  
Child Pornography ◽  
Forensic Analysis ◽  
Synthetic Image ◽  
Image Detection ◽  
Face Images ◽  
Large Scale Dataset ◽  
Scanned Images ◽  
Analysis Of The Images

The possibility of carrying out a meaningful forensic analysis on printed and scanned images plays a major role in many applications. First of all, printed documents are often associated with criminal activities, such as terrorist plans, child pornography, and even fake packages. Additionally, printing and scanning can be used to hide the traces of image manipulation or the synthetic nature of images, since the artifacts commonly found in manipulated and synthetic images are gone after the images are printed and scanned. A problem hindering research in this area is the lack of large scale reference datasets to be used for algorithm development and benchmarking. Motivated by this issue, we present a new dataset composed of a large number of synthetic and natural printed face images. To highlight the difficulties associated with the analysis of the images of the dataset, we carried out an extensive set of experiments comparing several printer attribution methods. We also verified that state-of-the-art methods to distinguish natural and synthetic face images fail when applied to print and scanned images. We envision that the availability of the new dataset and the preliminary experiments we carried out will motivate and facilitate further research in this area.

scholarly journals SketchGNN: Semantic Sketch Segmentation with Graph Neural Networks

2021 ◽  
Vol 40 (3) ◽  
pp. 1-13
Author(s):  
Lumin Yang ◽  
Jiajie Zhuang ◽  
Hongbo Fu ◽  
Xiangzhi Wei ◽  
Kun Zhou ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Large Scale ◽  
State Of The Art ◽  
Semantic Segmentation ◽  
Structure Information ◽  
Graph Neural Networks ◽  
Node Labels ◽  
Point Level

We introduce SketchGNN , a convolutional graph neural network for semantic segmentation and labeling of freehand vector sketches. We treat an input stroke-based sketch as a graph with nodes representing the sampled points along input strokes and edges encoding the stroke structure information. To predict the per-node labels, our SketchGNN uses graph convolution and a static-dynamic branching network architecture to extract the features at three levels, i.e., point-level, stroke-level, and sketch-level. SketchGNN significantly improves the accuracy of the state-of-the-art methods for semantic sketch segmentation (by 11.2% in the pixel-based metric and 18.2% in the component-based metric over a large-scale challenging SPG dataset) and has magnitudes fewer parameters than both image-based and sequence-based methods.

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