The document discusses tools for artificial intelligence and their applications. It describes Olivier Teytaud's work at Tao, a research group in Paris focused on reservoir computing, optimal decision making under uncertainty, optimization, and machine learning. It then provides examples of applications for these tools in electricity generation, urban rivals, pokemons, minesweeper, and solving unsolved situations in the game of Go. Olivier suggests that breakthroughs in games can help open doors to applying these algorithms to more important real-world problems by building trust in the approaches.
Machine learning and artificial intelligence are explained. Machine learning uses algorithms and past data to allow computers to optimize performance and develop behaviors without being explicitly programmed. It is a branch of artificial intelligence that uses supervised and unsupervised algorithms to apply past information to new data or draw conclusions from datasets. Case studies show how machine learning reveals influences and predicts user preferences. Artificial intelligence aims to simulate human intelligence through computer science, psychology, and other fields. Industries like healthcare and finance will benefit from machine learning and artificial intelligence applications like disease prediction and financial recommendations.
Artificial Intelligence Machine Learning Deep Learning Ppt Powerpoint Present...SlideTeam
Choose our Artificial Intelligence Machine Learning Deep Learning PPT PowerPoint Presentation Slide Templates to understand this popular branch of computer science. Acquaint your audience with the process of building smart, capable machines that can perform intelligent tasks with the help of this neural network PPT presentation. Exhibit the difference between AI, machine learning, and deep learning through this informative robotics PPT design. Elaborate on the wide range of areas that can benefit from artificial intelligence like supply chain, customer experience, human resources, fraud detection, research, and development by taking the aid of this computer science PPT slideshow. Highlight the booming rate of AI business and its future revenue forecast by downloading this thought-provoking and indulging information technology PowerPoint graphics. Save your time and efforts with these pre-ready and professionally crafted content-specific slides. It will educate your audience about this complex process in an easy yet efficient way. Download this AI functioning PowerPoint deck to create a roadmap for the growth and expansion of your business. https://bit.ly/3x135nD
Artificial intelligence is a branch of computer science that aims to create intelligent machines that can think and act like humans. It uses techniques like neural networks and machine learning to solve complex problems. AI has many applications including healthcare, gaming, data security, social media, transportation, robotics, education and more. While it offers benefits like accuracy, speed and reliability, it also faces limitations such as high costs, limited abilities and lack of original creativity.
AI Vs ML Vs DL PowerPoint Presentation Slide Templates Complete DeckSlideTeam
AI Vs ML Vs DL PowerPoint Presentation Slide Templates Complete Deck is loaded with easy-to-follow content, and intuitive design. Introduce the types and levels of artificial intelligence using the highly-effective visuals featured in this PPT slide deck. Showcase the AI-subfield of machine learning, as well as deep learning through our comprehensive PowerPoint theme. Represent the differences, and interrelationship between AI, ML, and DL. Elaborate on the scope and use case of machine intelligence in healthcare, HR, banking, supply chain, or any other industry. Take advantage of the infographic-style layout to describe why AI is flourishing in today’s day and age. Elucidate AI trends such as robotic process automation, advanced cybersecurity, AI-powered chatbots, and more. Cover all the essentials of machine learning and deep learning with the help of this PPT slideshow. Outline the application, algorithms, use cases, significance, and selection criteria for machine learning. Highlight the deep learning process, types, limitations, and significance. Describe reinforcement training, neural network classifications, and a lot more. Hit download and begin personalization. Our AI Vs ML Vs DL PowerPoint Presentation Slide Templates Complete Deck are topically designed to provide an attractive backdrop to any subject. Use them to look like a presentation pro. https://bit.ly/3ngJCKf
Deep Learning - The Past, Present and Future of Artificial IntelligenceLukas Masuch
The document provides an overview of deep learning, including its history, key concepts, applications, and recent advances. It discusses the evolution of deep learning techniques like convolutional neural networks, recurrent neural networks, generative adversarial networks, and their applications in computer vision, natural language processing, and games. Examples include deep learning for image recognition, generation, segmentation, captioning, and more.
Introduction To Artificial Intelligence Powerpoint Presentation SlidesSlideTeam
Introduction to Artificial Intelligence is for the mid level managers giving information about what is AI, AI levels, types of AI, where AI is used. You can also know the difference between AI vs Machine learning vs Deep learning to understand expert system in a better way for business growth. https://bit.ly/2V0reNa
This talk overviews my background as a female data scientist, introduces many types of generative AI, discusses potential use cases, highlights the need for representation in generative AI, and showcases a few tools that currently exist.
Machine learning and artificial intelligence are explained. Machine learning uses algorithms and past data to allow computers to optimize performance and develop behaviors without being explicitly programmed. It is a branch of artificial intelligence that uses supervised and unsupervised algorithms to apply past information to new data or draw conclusions from datasets. Case studies show how machine learning reveals influences and predicts user preferences. Artificial intelligence aims to simulate human intelligence through computer science, psychology, and other fields. Industries like healthcare and finance will benefit from machine learning and artificial intelligence applications like disease prediction and financial recommendations.
Artificial Intelligence Machine Learning Deep Learning Ppt Powerpoint Present...SlideTeam
Choose our Artificial Intelligence Machine Learning Deep Learning PPT PowerPoint Presentation Slide Templates to understand this popular branch of computer science. Acquaint your audience with the process of building smart, capable machines that can perform intelligent tasks with the help of this neural network PPT presentation. Exhibit the difference between AI, machine learning, and deep learning through this informative robotics PPT design. Elaborate on the wide range of areas that can benefit from artificial intelligence like supply chain, customer experience, human resources, fraud detection, research, and development by taking the aid of this computer science PPT slideshow. Highlight the booming rate of AI business and its future revenue forecast by downloading this thought-provoking and indulging information technology PowerPoint graphics. Save your time and efforts with these pre-ready and professionally crafted content-specific slides. It will educate your audience about this complex process in an easy yet efficient way. Download this AI functioning PowerPoint deck to create a roadmap for the growth and expansion of your business. https://bit.ly/3x135nD
Artificial intelligence is a branch of computer science that aims to create intelligent machines that can think and act like humans. It uses techniques like neural networks and machine learning to solve complex problems. AI has many applications including healthcare, gaming, data security, social media, transportation, robotics, education and more. While it offers benefits like accuracy, speed and reliability, it also faces limitations such as high costs, limited abilities and lack of original creativity.
AI Vs ML Vs DL PowerPoint Presentation Slide Templates Complete DeckSlideTeam
AI Vs ML Vs DL PowerPoint Presentation Slide Templates Complete Deck is loaded with easy-to-follow content, and intuitive design. Introduce the types and levels of artificial intelligence using the highly-effective visuals featured in this PPT slide deck. Showcase the AI-subfield of machine learning, as well as deep learning through our comprehensive PowerPoint theme. Represent the differences, and interrelationship between AI, ML, and DL. Elaborate on the scope and use case of machine intelligence in healthcare, HR, banking, supply chain, or any other industry. Take advantage of the infographic-style layout to describe why AI is flourishing in today’s day and age. Elucidate AI trends such as robotic process automation, advanced cybersecurity, AI-powered chatbots, and more. Cover all the essentials of machine learning and deep learning with the help of this PPT slideshow. Outline the application, algorithms, use cases, significance, and selection criteria for machine learning. Highlight the deep learning process, types, limitations, and significance. Describe reinforcement training, neural network classifications, and a lot more. Hit download and begin personalization. Our AI Vs ML Vs DL PowerPoint Presentation Slide Templates Complete Deck are topically designed to provide an attractive backdrop to any subject. Use them to look like a presentation pro. https://bit.ly/3ngJCKf
Deep Learning - The Past, Present and Future of Artificial IntelligenceLukas Masuch
The document provides an overview of deep learning, including its history, key concepts, applications, and recent advances. It discusses the evolution of deep learning techniques like convolutional neural networks, recurrent neural networks, generative adversarial networks, and their applications in computer vision, natural language processing, and games. Examples include deep learning for image recognition, generation, segmentation, captioning, and more.
Introduction To Artificial Intelligence Powerpoint Presentation SlidesSlideTeam
Introduction to Artificial Intelligence is for the mid level managers giving information about what is AI, AI levels, types of AI, where AI is used. You can also know the difference between AI vs Machine learning vs Deep learning to understand expert system in a better way for business growth. https://bit.ly/2V0reNa
This talk overviews my background as a female data scientist, introduces many types of generative AI, discusses potential use cases, highlights the need for representation in generative AI, and showcases a few tools that currently exist.
The document summarizes the history of artificial intelligence from 1943 to present day in several periods:
1. The Gestation of AI from 1943-1955 which led to the birth of AI in 1956 at the Dartmouth conference where the field was named.
2. Early enthusiasm and great expectations from 1956-1969 but then a dose of reality from 1966-1973 as programs had little knowledge and many problems were difficult to solve.
3. Knowledge based systems emerged from 1969-1979 allowing more advanced reasoning in narrow domains.
4. AI became an industry from 1980 onwards with successful commercial systems, investment, and hundreds of companies despite limitations remaining.
5. Neural networks reemerged in 1986 and scientific
This document summarizes a lecture on the relationships between artificial intelligence and philosophy. It discusses how AI both relates to and improves upon philosophical inquiry. Specifically, it notes that AI can help clarify philosophical concepts and provide new examples to investigate philosophical questions. At the same time, philosophy helps clarify AI's goals and concepts. The document provides examples of how AI extends the philosophy of mind by allowing the design of varied mind types and clarifying the relationship between mind and body.
Artificial intelligence (AI) is the ability of digital computers or robots to perform tasks commonly associated with intelligent beings. The idea of AI has its origins in ancient Greece but the field began in the 1950s. Today, AI is used in applications like IBM's Watson, driverless cars, automated assembly lines, surgical robots, and traffic control systems. The future of AI depends on whether researchers can achieve human-level or superhuman intelligence through techniques like whole brain emulation. Critics argue key challenges remain in replicating general human intelligence and consciousness with technology.
Introduction To Artificial Intelligence PowerPoint Presentation SlidesSlideTeam
Introduction to Artificial Intelligence is for the mid level managers giving information about what is AI, AI levels, types of AI, where AI is used. You can also know the difference between AI vs Machine learning vs Deep learning to understand expert system in a better way for business growth. https://bit.ly/3er7KWI
The concept of intelligent system has emerged in information technology as a type of system derived from successful applications of artificial intelligence. The goal of this presentation is to give a general description of an intelligent system, which integrates classical approaches and recent advances in artificial intelligence. The presentation describes an intelligent system
in a generic way, identifying its main properties and functional components.
Artificial intelligence (AI) is the development of computer systems able to perform tasks normally requiring human intelligence, such as visual perception and decision-making. There are three types of AI: narrow AI, which is limited in scope; general AI at an advanced level similar to human intelligence; and super AI, which would surpass human intelligence. AI has many applications today including personal assistants on phones, gaming, robotics, and self-driving cars. While AI shows promise, it also presents risks if not developed responsibly, as machines currently lack human attributes like emotions and ethics.
An Introduction to Generative AI - May 18, 2023CoriFaklaris1
For this plenary talk at the Charlotte AI Institute for Smarter Learning, Dr. Cori Faklaris introduces her fellow college educators to the exciting world of generative AI tools. She gives a high-level overview of the generative AI landscape and how these tools use machine learning algorithms to generate creative content such as music, art, and text. She then shares some examples of generative AI tools and demonstrate how she has used some of these tools to enhance teaching and learning in the classroom and to boost her productivity in other areas of academic life.
This document provides an overview of artificial intelligence including:
1) It discusses what AI is, its history, and some of the key subfields like games playing, expert systems, natural language processing, and neural networks.
2) It outlines several applications of AI including in computer science, finance, medicine, heavy industry, transportation, telecommunications, toys/games, music, aviation, and news/publishing.
3) It provides a brief history of AI from the 15th century to modern day, highlighting milestones like the first mechanical calculator and Deep Blue's victory over Kasparov in chess.
The document discusses artificial intelligence and defines it as the science and engineering of making intelligent machines, especially intelligent computer programs. It notes two main approaches to AI: engineering and cognitive modeling. Intelligence is defined as the ability to learn and solve problems, specifically the ability to solve novel problems, act rationally, and act like humans. The document also discusses various applications and techniques in AI, including search algorithms, expert systems, fuzzy logic, robotics, and genetic algorithms.
Big data is large amounts of unstructured data that require new techniques and tools to analyze. Key drivers of big data growth are increased storage capacity, processing power, and data availability. Big data analytics can uncover hidden patterns to provide competitive advantages and better business decisions. Applications include healthcare, homeland security, finance, manufacturing, and retail. The global big data market is expected to grow significantly, with India's market projected to reach $1 billion by 2015. This growth will increase demand for data scientists and analysts to support big data solutions and technologies like Hadoop and NoSQL databases.
In which we try to explain why we consider artificial intelligence to be a subject most worthy of study, and in which we try to decide what exactly it is, this being a good thing to decide before embarking.
Artificial intelligence (AI) is defined as making computers do intelligent tasks like humans. It works using artificial neurons that mimic biological neurons. Neural networks are composed of interconnected artificial neurons. The Turing test tests a machine's ability to demonstrate intelligence comparable to a human. There are different types of AI like expert systems, machine learning, and intelligent agents. While AI can process large amounts of data fast without human limitations, it lacks common sense, intuition, and creativity that humans possess. Overall, AI aims to supplement natural human intelligence by performing tasks through machines to reduce human labor and mistakes.
Neural networks are computational models inspired by the human brain. They consist of interconnected nodes that process information using a principle called neural learning. The document discusses the history and evolution of neural networks. It also provides examples of applications like image recognition, medical diagnosis, and predictive analytics. Neural networks are well-suited for problems that are difficult to solve with traditional algorithms like pattern recognition and classification.
Artificial intelligence is applied in many domains including finance, hospitals, heavy industry, telecommunications, gaming, music, and antivirus software. In finance, AI is used for operations, investing, loan investigations and ATM design. In hospitals, AI organizes bed schedules, staff rotation, and provides medical information. Robots are effectively used in heavy industry for dangerous, repetitive, or degrading jobs. Telecommunications companies use AI for workforce scheduling. AI is also applied to video games through bots and to music composition, performance, and sound processing. Antivirus detection has increasingly integrated AI techniques to improve performance.
Introduction to Artificial Intelligence | AI using Deep Learning | EdurekaEdureka!
The document discusses artificial intelligence and deep learning. It begins with defining AI and its applications, and then discusses machine learning as a subset of AI. Deep learning is presented as a solution to the limitations of machine learning for complex tasks like image recognition. Deep learning uses neural networks with multiple layers to learn representations of data with little human guidance. Examples of deep learning applications discussed include machine translation, image classification, and Google Lens.
Artificial intelligence and machine learning are discussed. AI is defined as making computers intelligent like humans through understanding, reasoning, planning, communication and perception. Machine learning is a subset of AI that allows machines to learn from experience without being explicitly programmed. The document provides background on AI and ML, including definitions, history, and discussions of intelligence and applications.
Branch of computer science that develops machines and software with human-like intelligence
top 5 artificial intelligence stocks
artificial intelligence technology
artificial intelligence articles
artificial intelligence companies
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1. The document discusses various methods for continuous optimization, including rates of convergence for noise-free and noisy settings.
2. In noise-free settings, methods like Newton's method and BFGS have quadratic or superlinear convergence rates, while evolutionary strategies (ES) have linear convergence rates.
3. Lower bounds on optimization complexity are also discussed, showing minimum comparisons or evaluations needed depending on problem properties like domain size and precision required.
Combining UCT and Constraint Satisfaction Problems for MinesweeperOlivier Teytaud
@inproceedings{buffet:hal-00750577,
hal_id = {hal-00750577},
url = {http://hal.inria.fr/hal-00750577},
title = {{Optimistic Heuristics for MineSweeper}},
author = {Buffet, Olivier and Lee, Chang-Shing and Lin, Woanting and Teytaud, Olivier},
abstract = {{We present a combination of Upper Con dence Tree (UCT) and domain speci c solvers, aimed at improving the behavior of UCT for long term aspects of a problem. Results improve the state of the art, combining top performance on small boards (where UCT is the state of the art) and on big boards (where variants of CSP rule).}},
language = {Anglais},
affiliation = {MAIA - INRIA Nancy - Grand Est / LORIA , Department of Computer Science and Information Engineering - CSIE , National University of Tainan - NUTN , TAO - INRIA Saclay - Ile de France , Laboratoire de Recherche en Informatique - LRI , Department of Electrical Engineering and Computer Science - Institut Montefiore},
booktitle = {{International Computer Symposium}},
address = {Hualien, Ta{\"\i}wan, Province De Chine},
audience = {internationale },
year = {2012},
pdf = {http://hal.inria.fr/hal-00750577/PDF/mines3.pdf},
}
The document summarizes the history of artificial intelligence from 1943 to present day in several periods:
1. The Gestation of AI from 1943-1955 which led to the birth of AI in 1956 at the Dartmouth conference where the field was named.
2. Early enthusiasm and great expectations from 1956-1969 but then a dose of reality from 1966-1973 as programs had little knowledge and many problems were difficult to solve.
3. Knowledge based systems emerged from 1969-1979 allowing more advanced reasoning in narrow domains.
4. AI became an industry from 1980 onwards with successful commercial systems, investment, and hundreds of companies despite limitations remaining.
5. Neural networks reemerged in 1986 and scientific
This document summarizes a lecture on the relationships between artificial intelligence and philosophy. It discusses how AI both relates to and improves upon philosophical inquiry. Specifically, it notes that AI can help clarify philosophical concepts and provide new examples to investigate philosophical questions. At the same time, philosophy helps clarify AI's goals and concepts. The document provides examples of how AI extends the philosophy of mind by allowing the design of varied mind types and clarifying the relationship between mind and body.
Artificial intelligence (AI) is the ability of digital computers or robots to perform tasks commonly associated with intelligent beings. The idea of AI has its origins in ancient Greece but the field began in the 1950s. Today, AI is used in applications like IBM's Watson, driverless cars, automated assembly lines, surgical robots, and traffic control systems. The future of AI depends on whether researchers can achieve human-level or superhuman intelligence through techniques like whole brain emulation. Critics argue key challenges remain in replicating general human intelligence and consciousness with technology.
Introduction To Artificial Intelligence PowerPoint Presentation SlidesSlideTeam
Introduction to Artificial Intelligence is for the mid level managers giving information about what is AI, AI levels, types of AI, where AI is used. You can also know the difference between AI vs Machine learning vs Deep learning to understand expert system in a better way for business growth. https://bit.ly/3er7KWI
The concept of intelligent system has emerged in information technology as a type of system derived from successful applications of artificial intelligence. The goal of this presentation is to give a general description of an intelligent system, which integrates classical approaches and recent advances in artificial intelligence. The presentation describes an intelligent system
in a generic way, identifying its main properties and functional components.
Artificial intelligence (AI) is the development of computer systems able to perform tasks normally requiring human intelligence, such as visual perception and decision-making. There are three types of AI: narrow AI, which is limited in scope; general AI at an advanced level similar to human intelligence; and super AI, which would surpass human intelligence. AI has many applications today including personal assistants on phones, gaming, robotics, and self-driving cars. While AI shows promise, it also presents risks if not developed responsibly, as machines currently lack human attributes like emotions and ethics.
An Introduction to Generative AI - May 18, 2023CoriFaklaris1
For this plenary talk at the Charlotte AI Institute for Smarter Learning, Dr. Cori Faklaris introduces her fellow college educators to the exciting world of generative AI tools. She gives a high-level overview of the generative AI landscape and how these tools use machine learning algorithms to generate creative content such as music, art, and text. She then shares some examples of generative AI tools and demonstrate how she has used some of these tools to enhance teaching and learning in the classroom and to boost her productivity in other areas of academic life.
This document provides an overview of artificial intelligence including:
1) It discusses what AI is, its history, and some of the key subfields like games playing, expert systems, natural language processing, and neural networks.
2) It outlines several applications of AI including in computer science, finance, medicine, heavy industry, transportation, telecommunications, toys/games, music, aviation, and news/publishing.
3) It provides a brief history of AI from the 15th century to modern day, highlighting milestones like the first mechanical calculator and Deep Blue's victory over Kasparov in chess.
The document discusses artificial intelligence and defines it as the science and engineering of making intelligent machines, especially intelligent computer programs. It notes two main approaches to AI: engineering and cognitive modeling. Intelligence is defined as the ability to learn and solve problems, specifically the ability to solve novel problems, act rationally, and act like humans. The document also discusses various applications and techniques in AI, including search algorithms, expert systems, fuzzy logic, robotics, and genetic algorithms.
Big data is large amounts of unstructured data that require new techniques and tools to analyze. Key drivers of big data growth are increased storage capacity, processing power, and data availability. Big data analytics can uncover hidden patterns to provide competitive advantages and better business decisions. Applications include healthcare, homeland security, finance, manufacturing, and retail. The global big data market is expected to grow significantly, with India's market projected to reach $1 billion by 2015. This growth will increase demand for data scientists and analysts to support big data solutions and technologies like Hadoop and NoSQL databases.
In which we try to explain why we consider artificial intelligence to be a subject most worthy of study, and in which we try to decide what exactly it is, this being a good thing to decide before embarking.
Artificial intelligence (AI) is defined as making computers do intelligent tasks like humans. It works using artificial neurons that mimic biological neurons. Neural networks are composed of interconnected artificial neurons. The Turing test tests a machine's ability to demonstrate intelligence comparable to a human. There are different types of AI like expert systems, machine learning, and intelligent agents. While AI can process large amounts of data fast without human limitations, it lacks common sense, intuition, and creativity that humans possess. Overall, AI aims to supplement natural human intelligence by performing tasks through machines to reduce human labor and mistakes.
Neural networks are computational models inspired by the human brain. They consist of interconnected nodes that process information using a principle called neural learning. The document discusses the history and evolution of neural networks. It also provides examples of applications like image recognition, medical diagnosis, and predictive analytics. Neural networks are well-suited for problems that are difficult to solve with traditional algorithms like pattern recognition and classification.
Artificial intelligence is applied in many domains including finance, hospitals, heavy industry, telecommunications, gaming, music, and antivirus software. In finance, AI is used for operations, investing, loan investigations and ATM design. In hospitals, AI organizes bed schedules, staff rotation, and provides medical information. Robots are effectively used in heavy industry for dangerous, repetitive, or degrading jobs. Telecommunications companies use AI for workforce scheduling. AI is also applied to video games through bots and to music composition, performance, and sound processing. Antivirus detection has increasingly integrated AI techniques to improve performance.
Introduction to Artificial Intelligence | AI using Deep Learning | EdurekaEdureka!
The document discusses artificial intelligence and deep learning. It begins with defining AI and its applications, and then discusses machine learning as a subset of AI. Deep learning is presented as a solution to the limitations of machine learning for complex tasks like image recognition. Deep learning uses neural networks with multiple layers to learn representations of data with little human guidance. Examples of deep learning applications discussed include machine translation, image classification, and Google Lens.
Artificial intelligence and machine learning are discussed. AI is defined as making computers intelligent like humans through understanding, reasoning, planning, communication and perception. Machine learning is a subset of AI that allows machines to learn from experience without being explicitly programmed. The document provides background on AI and ML, including definitions, history, and discussions of intelligence and applications.
Branch of computer science that develops machines and software with human-like intelligence
top 5 artificial intelligence stocks
artificial intelligence technology
artificial intelligence articles
artificial intelligence companies
artificial intelligence stocks to buy
artificial intelligence robots
artificial intelligence in medicine
artificial intelligence wikipedia
1. The document discusses various methods for continuous optimization, including rates of convergence for noise-free and noisy settings.
2. In noise-free settings, methods like Newton's method and BFGS have quadratic or superlinear convergence rates, while evolutionary strategies (ES) have linear convergence rates.
3. Lower bounds on optimization complexity are also discussed, showing minimum comparisons or evaluations needed depending on problem properties like domain size and precision required.
Combining UCT and Constraint Satisfaction Problems for MinesweeperOlivier Teytaud
@inproceedings{buffet:hal-00750577,
hal_id = {hal-00750577},
url = {http://hal.inria.fr/hal-00750577},
title = {{Optimistic Heuristics for MineSweeper}},
author = {Buffet, Olivier and Lee, Chang-Shing and Lin, Woanting and Teytaud, Olivier},
abstract = {{We present a combination of Upper Con dence Tree (UCT) and domain speci c solvers, aimed at improving the behavior of UCT for long term aspects of a problem. Results improve the state of the art, combining top performance on small boards (where UCT is the state of the art) and on big boards (where variants of CSP rule).}},
language = {Anglais},
affiliation = {MAIA - INRIA Nancy - Grand Est / LORIA , Department of Computer Science and Information Engineering - CSIE , National University of Tainan - NUTN , TAO - INRIA Saclay - Ile de France , Laboratoire de Recherche en Informatique - LRI , Department of Electrical Engineering and Computer Science - Institut Montefiore},
booktitle = {{International Computer Symposium}},
address = {Hualien, Ta{\"\i}wan, Province De Chine},
audience = {internationale },
year = {2012},
pdf = {http://hal.inria.fr/hal-00750577/PDF/mines3.pdf},
}
This document discusses using Meta-Monte Carlo Tree Search (Meta-MCTS) to build an opening book for 7x7 Go. Meta-MCTS improved its play against a sparring partner that incorporated human variations. While Meta-MCTS won all games as black and white against professionals, humans found at least one variation where it did not play correctly. The document concludes that Meta-MCTS performed well but incorporating human data helped, and exactly solving 7x7 Go would require immense work collecting and solving all leaf variations.
Stochastic modelling and quasi-random numbersOlivier Teytaud
Stochastic models use random numbers to simulate random variables and processes. However, random numbers can be disappointing as they do not cover the space uniformly. Quasi-random numbers provide an alternative by being more uniformly distributed. The document discusses using quasi-random numbers instead of purely random numbers in stochastic models to generate sequences that better cover the sample space.
Introductory talk
more technicities in
@inproceedings{schoenauer:inria-00625855,
hal_id = {inria-00625855},
url = {http://hal.inria.fr/inria-00625855},
title = {{A Rigorous Runtime Analysis for Quasi-Random Restarts and Decreasing Stepsize}},
author = {Schoenauer, Marc and Teytaud, Fabien and Teytaud, Olivier},
abstract = {{Multi-Modal Optimization (MMO) is ubiquitous in engineer- ing, machine learning and artificial intelligence applications. Many algo- rithms have been proposed for multimodal optimization, and many of them are based on restart strategies. However, only few works address the issue of initialization in restarts. Furthermore, very few comparisons have been done, between different MMO algorithms, and against simple baseline methods. This paper proposes an analysis of restart strategies, and provides a restart strategy for any local search algorithm for which theoretical guarantees are derived. This restart strategy is to decrease some 'step-size', rather than to increase the population size, and it uses quasi-random initialization, that leads to a rigorous proof of improve- ment with respect to random restarts or restarts with constant initial step-size. Furthermore, when this strategy encapsulates a (1+1)-ES with 1/5th adaptation rule, the resulting algorithm outperforms state of the art MMO algorithms while being computationally faster.}},
language = {Anglais},
affiliation = {TAO - INRIA Saclay - Ile de France , Microsoft Research - Inria Joint Centre - MSR - INRIA , Laboratoire de Recherche en Informatique - LRI},
booktitle = {{Artificial Evolution}},
address = {Angers, France},
audience = {internationale },
year = {2011},
month = Oct,
pdf = {http://hal.inria.fr/inria-00625855/PDF/qrrsEA.pdf},
}
Introduction to the TAO Uct Sig, a team working on computational intelligence...Olivier Teytaud
The document discusses research from Tao-Uctsig, a special interest group within Tao focused on artificial intelligence. Tao has 11 permanent staff and around 22 PhD students/postdocs working across various fields of mathematics, computer science, and sciences. The SIG works on problems where computers make decisions, particularly challenges where humans are currently better than computers. Their work involves games, important applications, and previously included mathematics. Specific applications discussed include controlling a robot arm, analyzing strategy in Pokemon and Urban Rivals, solving Minesweeper puzzles, and Go. Industrial applications include helping optimize France's major electricity industry.
Weather, opponents, geopolitics: so many uncertainties in such a case ? How to manage power systems in spite of these uncertainties, and how to decide investments.
Talk at Saint-Etienne in 2015; thanks to R. Leriche and to the "games and optimizations" days in Saint-Etienne.
Complexity of planning and games with partial informationOlivier Teytaud
Survey of computational complexity or computability of sequential decision making (games, planning)
contains two more detailed proofs:
- EXPSPACE completeness of unobservable adversarial planning for existence of 100% winning strategy (Hasslum et al)
- undecidability of unobservable adversarial planning for arbitrary winning rate (including optimal play in the Nash sense)
Dynamic Optimization without Markov Assumptions: application to power systemsOlivier Teytaud
Ilab METIS is a collaboration between TAO, a machine learning and optimization team at INRIA, and Artelys, an SME focused on optimization. They work on optimizing energy policies through modeling power systems and simulating operational and investment decisions. Their methodologies hybridize reinforcement learning, mathematical programming, and direct policy search to optimize complex, constrained problems with uncertainties while minimizing model error. They have applied these techniques to problems involving European-scale power grids with stochastic renewables.
Computers have made progress playing the game of Go but still have weaknesses. In 19x19 Go, computers have beaten professionals with handicaps of 6-9 stones. In 9x9 Go, computers have reached human professional level by beating professionals without handicaps. However, in 19x19 Go computers still require at least a 6 stone handicap against top professionals. Future improvements may allow computers to reach professional human level in 19x19 Go without handicaps.
This document discusses the go variant "killall go" where black wins by capturing all white stones, and proposes different board sizes and handicap placements to test balance. It analyzes MoGo evaluations of some placements, finding discrepancies between single-game evaluations and full-game results. It concludes more research could be done on MCTS opening evaluations, Batoo variants where players take turns placing stones, and using bandits to learn balanced handicap placements.
The document discusses energy management in France and Taiwan. It notes that both countries have a long history in energy but differ in their approaches. France relies heavily on nuclear power through large state-owned companies while Taiwan has focused more recently on renewable resources like solar, wind, and ocean currents. The challenges of energy management are outlined as deciding how to operate existing power sources and plan new investments over decades to improve the system under uncertainty. Optimization methods that incorporate stochastic modeling are proposed to help with these long-term planning problems.
This document provides an overview of statistical concepts related to item response theory (IRT), including posterior probability, Bayes' theorem, maximum a posteriori (MAP) estimation, and the Jacobi algorithm. It discusses how to initialize IRT parameters like student abilities and item parameters, and evaluates options for fitting IRT models like R and Octave packages.
Machine learning 2016: deep networks and Monte Carlo Tree SearchOlivier Teytaud
This talk describes two key machine learning algorithms, namely MCTS and Deep Networks (DN), presented as the main AI innovations from the last 20 years. Interestingly, the talk was given a few days before a combination MCTS+DN was used by Google DeepMind for winning against a pro (https://docs.google.com/document/d/1ZjniEJiotdCfvBYI3MTBpjtOTSlUvf3ma7V8DHVmjhk/edit#)
Talk ENS-Lyon at "Sept Laux"
The document discusses the research focus of the TAO group at Inria Saclay, which includes machine learning and optimization applications for energy management. The group has one permanent member and others part-time. It collaborates closely with partners in Taiwan and the company Artelys. The research aims to address challenges in power grid simulation like variable demand and renewable energy sources using techniques like mathematical programming, reinforcement learning, and direct policy search combined with heuristics and Monte Carlo tree search.
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Tools for artificial intelligence
1. SOME TOOLS
FOR ARTIFICIAL INTELLIGENCE
Olivier Teytaud --- olivier.teytaud@gmail.com
NUTN, Tainan, 2011
2. Tao (Inria, Cnrs, Lri, Paris-Sud)
People:
Permanent staff: 11
~15 ph.D. Students
In Université Paris-Sud
Largest campus in France
Faculty of sciences: mathematics, computer
science, physics, chemistry, biology, earth and
space sciences ==> 12000 students
Inria affiliation:
Around 50 years old
Devoted to research in comp. science
3. Tao (Inria, Cnrs, Lri, Paris-Sud)
Reservoir computing
Optimal decision making under uncertainty
Optimization
Autonomic computer
Machine learning
4. Communication not always so easy:
● Many of you speak Chinese + Taiwanese.
So English = third language.
I am French.
English = second language.
● I work mainly in mathematical aspects
of computer science, more than computer science.
Difficulties might also be an enrichment.
Feel free to interrupt me as much as useful.
NUTN, Tainan, 2011
5. Communication not always so easy:
● Many of you speak Chinese + Taiwanese.
So English = third language.
I am French.
English = second language.
● I work mainly in mathematical aspects
of computer science, more than computer science.
Difficulties might also be an enrichment.
Feel free to interrupt me as much as useful.
NUTN, Tainan, 2011
6. Vita in a nutshell:
1) First research: mathematical logic
2) I had fun, but I wanted to be “directly” useful. I switched
to Statistics.
3) I had fun, but I wanted to be “more directly” useful. Switched
to Operational Research, in industry.
- Many applications.
- My favorite: electricity generation.
4) Now (40 dangerously approaching), Artificial Intelligence:
- Mathematics.
- Challenges (in particular games).
- Applications.
7. Vita in a nutshell:
1) First research: mathematical logic
2) I had fun, but I wanted to be “directly” useful. I switched
to Statistics.
3) I had fun, but I wanted to be “more directly” useful. Switched
to Operational Research, in industry.
- Many applications.
- My favorite: electricity generation.
4) Now (40 dangerously approaching), Artificial Intelligence:
- Mathematics.
- Challenges (in particular games).
- Applications.
8. Vita in a nutshell:
1) First research: mathematical logic
2) I had fun, but I wanted to be “directly” useful. I switched
to Statistics.
3) I had fun, but I wanted to be “more directly” useful.
Switched to Operation Research, in industry.
- Many applications.
- My favorite: electricity generation.
4) Now (40 dangerously approaching), Artificial Intelligence:
- Mathematics. Goes back to military
- Challenges application around world war II,
(in particular games).
- Applications. UK resisted to Hitler thanks
when
to optimized radars.
Now essentially civil applications.
9. Vita in a nutshell:
1) First research: mathematical logic
2) I had fun, but I wanted to be “directly” useful. I switched
to Statistics.
3) I had fun, but I wanted to be “more directly” useful. Switched
to Operational Research, in industry.
- Many applications.
- My favorite: electricity generation.
4) Now (40 years old soon...), Artificial Intelligence:
- Mathematics.
- Beautiful challenges (in particular games).
- Applications.
10. Outline of what I'll discuss:
1) Some concepts:
- simplified problems
- toolboxes for these problems
2) Principle:
- reducing real problems to groups of artificial problems
- small problems might be considered as artificial
and useless when considered alone.
- but when you solve a clearly stated small problem, usually
you can find an application for this solution.
- we will see applications as well.
==> For the moment let's see “big” applications
3) I'll also show some works on which contributors are welcome.
13. ELECTRICITY GENERATION
The case of France
Data:
- climate model (stochastic)
- model of electricity demand (stochastic)
- model of power plants
Each day we receive:
- electricity consumption
- weather information
- info on faults
Each day, we decide how to distribute the production
among the power plants. (also: schedule long-term
investiments)
14. Data:
- climate model (stochastic)
- model of electricity demand (stochastic)
- model of power plants (PP): nuclear PP (NPP), thermal PP (TPP),
Hydroelectric PP (HPP)...
Each day we receive:
- electricity consumption
- weather information
- info on faults
Each day, we decide how to distribute the production among the power
plants.
Daily information
DATA
(climate, Electric
PROGRAM STRATEGY
plants, system
economy)
Decisions
15. One of the most important industrial problem you can imagine:
how to produce energy ?
France has specific elements:
- heavily nuclearized (most nuclearized country in the world)
- often cooled by rivers (do not work in case of droughts ==> hard
to predict)
- we must schedule maintenance
- we must take long-term decisions (building new NPP ? Removing ?)
- also hydroelectricity:
- should we use water now ?
- should we keep it for winter (in France, high consumption is in
winter)
Daily information
DATA
(climate, Electric
PROGRAM STRATEGY
plants, system
economy)
Decisions
16. Problem 1: Taiwan is very different from France :-)
● Almost no nuclear power plant ? Cooled by sea ?
● Electrically connected to other countries ? (France might
be connected to Africa)
● Sun sufficient for massive photo-voltaic units ?
● Wind much stronger than in France - can be used ?
● Other questions ?
● Electricity consumption dominated by air conditioning ?
● Maybe electric cars in the future ?
● Climate maybe more regular ? Problem easier than
in France ?
==> I don't know
==> I'd like to work on it (energy is an important
concern, in Taiwan as well – lack of independence ?)
==> Need Chinese-reading persons
==> Other (Taiwan-independent) concern: tackling partial
observation in energy generation problem
17. GOOD NEWS: we had a
GAME OF GO lot of progress with
**generic** algorithms
(with Nutn) (algorithms which can be
used for many things).
The revolution in Go which
occurred in 2007-2009 is a
major breakthrough in
Artificial Intelligence.
We'll see that in details.
I am a little bit tired of the
game of Go, because I
have no recent progress,
and recent progress in the
community comes from Go
expertise, which is only
useful for Go...
18. Problem 2: Solving unsolved situations in Go
● Now computers are much stronger than in the past.
● However, they still
misunderstand some
trivial situations
(in particular,
liberty races).
● You have an idea ?
Tell me :-)
● We have a solver in
France (not for playing Go;
aimed at provably solving),
that we would
like to test on various
situations. We do not
play Go. If you are 5kyu
or better, you can
contribute.
20. URBAN RIVALS
- Choose 4 cards, your opponent chooses 4
Cards
- Each player gets 12 “Pilz” (i.e. strength points)
- Each player gets health points.
- Each turn:
- each player chooses a card
- each player uses pilz
(each used pilz is
lost forever, but
it gives strength)
- read cards, apply rules
==> no more health point ?
==> you're dead.
21. Urban Rivals
==> Partial information
because you don't observe your opponent's decisions
==> There are “on the shell” algorithms and programs
for full information games,
but not for partial information games.
==> We used a (provable) combination of MCTS and EXP3
==> Immediately human level performance
==> suggests that maths can help
==> still possible works:
- automatic choice of cards ?
- reducing comp. cost ?
22. POKEMONS
皮卡丘
Second most lucrative video
game.
Meta-gaming: choosing your deck.
23. POKEMONS: Problem 3
Second most lucrative video
game.
Meta-gaming:
choosing your deck.
In-gaming: playing with your set of
cards.
24. Problem 4: Solving MineSweeper.
Find an optimal
move ?
● Looks like a trivial boring problem.
Certainly not indeed.
● Many papers with the same approach
(so-called CSP technique)
● We could outperform these algorithms thanks to
a probabilistic approach.
● But my approach only works on small board (or huge
computational cost) ==> we want to extend.
● Quite similar to electricity generation (yes, I believe in this)
25. Game applications can be considered as childish.
Shouldn't we focus on more important things ?
However:
- If you have a breakthrough in an important game,
people will trust you. Doors will be opened when you
will propose new algorithms for real-world applications.
- Testing ideas on a nuclear power plant is more dangerous
than testing ideas on a game of Go.
- It's easier to compare approaches in games than in
electricity generation.
28. ONE FUNDAMENTAL TOOL: ZERMELO
Consider the following game:
- there are 5 sticks;
- in turn, each player removes 1 or 2 sticks;
- the player which removes the last stick looses.
Example:
Player I: IIIII
Player II: III
Player I: I ==> looses!
How should I play ?
29. ONE FUNDAMENTAL TOOL: ZERMELO
Zermelo proposed a solution (for full-information games).
Born in 1871.
1900-1905: major contributions in logic.
1913: major contribution to games in 1913.
1931: Optimized navigation (from games to applications).
Resigned in 1935 (he did not like Hitler).
Died in 1953.
31. ZERMELO: I HAVE
THE OPTIMAL STRATEGY!
5
LOSS!
4 3
WIN!
WIN! 3 2 2 1
LOSS!
WIN! WIN!
1 2
WIN! LOSS!
32. ZERMELO: not limited to win/loss games.
Can work on games with continuous rewards.
New rule: if the game contains 4, reward is multiplied by 2.
YELLOW NODES: 5 BLUE NODES:
LABEL = MINIMUM 2 LABEL = MAXIMUM
OF CHILDREN's LABELS OF CHILDREN's LABELS
0
4 3
2
2 3 2 2 1
0
2 1
1 2
2 0
33. ZERMELO: C CODE
struct gameState
{
int *descriptionOfState;
int numberOfLegalMoves;
int * legalMoves;
int turn; // 1 if player 1 plays, -1 otherwise
int result; // final reward, if numberOfLegalMoves=0
};
struct gameState next(struct gameState s,int move) { RULES };
double zermeloValue(struct gameState s)
{
int i;double value;
double maxValue=-MAXDOUBLE;
if (s.numberOfLegalMoves==0) return(s.turn * s.result);
for (i=0;i<s.numberOfLegalMoves;i++)
{
value=s.turn*zermeloValue(next(s,s.legalMoves[i]));
if (value>maxValue) maxValue=value;
}
return s.turn*maxValue; //we return value for player 1
}
34. ZERMELO: C CODE
struct gameState
{
int *descriptionOfState;
int numberOfLegalMoves;
Int * legalMoves;
int turn; // 1 if player 1 plays, -1 otherwise
int result; // final reward, if numberOfLegalMoves=0
};
struct gameState next(struct gameState s,int move) { RULES };
double zermeloValue(struct gameState s)
{
int i;double value;
double maxValue=-MAXDOUBLE;
if (s.numberOfLegalMoves==0) return(s.turn * s.result);
for (i=0;i<s.numberOfLegalMoves;i++)
{
value=s.turn*zermeloValue(next(s,s.legalMoves[i]));
if (value>maxValue) maxValue=value;
}
return s.turn*maxValue; //we return value for player 1
}
35. Last week: Zermelo algorithm.
What is Zermelo ?
= Simplest algorithm for solving 1Player
or 2Player games.
= Recursive algorithm
= Conveniently (but slowly) implemented with “struct”
This week
= a bit more on Zermelo algorithm
= C development: “static” random variables
Future weeks
Still some C implementation (or other languages ? as you wish)
Still some (not always easy) algorithms
Models of applications
I hope I can convince you that
operational research / artificial intelligence
are useful and fun.
36. Zermelo again.
What does the “zermeloValue()” function returns ?
===> The reward in case of perfect play.
===> A perfect strategy.
===> Gods can run Zermelo algorithms: perfect play.
==> humans have no time for this.
==> Can we design a new version in case
it is too slow ?
37. Let's see a pseudo-code, instead of a code.
double zermeloValue(struct gameState s)
{
if (s is end of game) then return score.
else
{
If (play 1 plays) then
return max(zermeloValue(children))
Else
return min(zermeloValue(children))
}
}
39. ZERMELO: C CODE FOR THE DEPTH
double zermeloValue(struct gameState s)
{
static int depth=0;
int i;double value;
double maxValue=-MAXDOUBLE;
if (s.numberOfLegalMoves==0) return(s.turn * s.result);
depth++;
for (i=0;i<s.numberOfLegalMoves;i++)
{
value=s.turn*zermeloValue(next(s,s.legalMoves[i]));
if (value>maxValue) maxValue=value;
}
depth--;
return s.turn*maxValue; //we return value for player 1
}
43. We will not go But, what should
below this depth. zermeloFunction return ?
44. double zermeloValue(struct gameState s)
{
static int depth=0; Should we return
int i;double value; a random number ?
double maxValue=-MAXDOUBLE;
if (s.numberOfLegalMoves==0) return(s.turn * s.result);
if (depth>5) return drand48();
depth++;
for (i=0;i<s.numberOfLegalMoves;i++)
{
value=s.turn*zermeloValue(next(s,s.legalMoves[i]));
if (value>maxValue) maxValue=value;
}
depth--;
return s.turn*maxValue; //we return value for player 1
}
45. double zermeloValue(struct gameState s)
{
static int depth=0;
int i;double value;
double maxValue=-MAXDOUBLE;
if (s.numberOfLegalMoves==0) return(s.turn * s.result);
if (depth>5) return heuristicValue(s);
depth++;
for (i=0;i<s.numberOfLegalMoves;i++)
{ A function written
by some expert of
value=s.turn*zermeloValue(next(s,s.legalMoves[i]));
if (value>maxValue) maxValue=value; game.
the
}
depth--;
return s.turn*maxValue; //we return value for player 1
}
46. SHANNON and games
This idea is a main contribution
by Shannon (for European chess).
Shannon 1916-2001
Noble prize (not Nobel!)
Works in:
- Logic
- Games (also: artificial
mouse for mazes)
- Financial analysis
50. ALPHA-BETA
PRINCIPLE OF ALPHA-BETA:
In zermeloFunction, considering a opponent node, if I know:
- THAT AT PREVIOUS DEPTH,
I CAN REACH SCORE ALPHA=6,
- THAT IN CURRENT STATE
MY OPPONENT CAN ENSURE SCORE BETA<6,
I CAN STOP STUDYING THIS BRANCH.
==> THIS IS A “ALPHA-CUTOFF“
==> OTHER PLAYER:
“BETA-CUTOFF“ (just exchange players)
52. EXAMPLE OF GAME (we can
discuss why it is a good game)
- Randomly generate a 4x4 matrix with 0 and 1 (K=4).
0011
1001
0111
1000
- Player one removes top part or bottom part
0111
1000
- Player two removes left part or right part
01
10
- Player one removes top part of bottom part
01
- Player two removes left part or right part
0 ==> Player one wins if 1, player two wins if 0!
53. POSSIBLE HOME WORK
1) ZERMELO: can you implement it on a simple game ?
2) MINIMAX: can you add a heuristic function ?
Which heuristic function ?
Experiments: plot a graph:
X(depth) = computation time of minimax
(divided by Zermelo's computation time)
Y(depth) = win rate against Zermelo
3) ALPHA-BETA
Can you modify it ==> alpha-beta pruning ?
Plot a graph for various sizes:
X = number of visited nodes
Y = average winning rate of alpha-beta vs minimax
Or
X = depth
Y = average winning rate of a-b vs a-b with depth -1
54. APPLICATION OF ZERMELO
WE HAVE SEEN THE 5-STICKS GAME.
CAN WE FIND A REALLY USEFUL APPLICATION ?
55. APPLICATION OF ZERMELO
WE HAVE SEEN THE 5-STICKS GAME.
CAN WE FIND A REALLY USEFUL APPLICATION ?
I have:
- water
56. APPLICATION OF ZERMELO
WE HAVE SEEN THE 5-STICKS GAME.
CAN WE FIND A REALLY USEFUL APPLICATION ?
I have:
- water
- plants (which need water during summer's
heat wave)
57. APPLICATION OF ZERMELO
WE HAVE SEEN THE 5-STICKS GAME.
CAN WE FIND A REALLY USEFUL APPLICATION ?
I have:
- water
- plants (which need water during summer's
heat wave)
Actions = giving water to plants, or not.
58. APPLICATION OF ZERMELO
I have:
- water
- plants (which need water during summer's
heat wave)
Each day, I choose an action.
State = { date +water level in stock
+ water level in plants }
Reward = quality / quantity of production.
60. IMPORTANT REMARK:
- Maybe this does not look serious.
- But heat waves are a serious problem.
- Here the problem is simplified, but the concepts
for the real application are the same.
- Applying this just requires a computer and
datas/models about plants/water resources.
==> if you can apply Zermelo variants
correctly, you can help for a better world.
62. s.turn == 0: action is
randomly chosen.
double zermeloValue(struct gameState s)
{ This is Zermelo, adapted to
int i;double value; static int depth=0; stochastic games.
If (s.turn==0) References:
{ value=0; - Massé
double total=0; - Bellman
for (i=0;i<s.numberOfLegalMoves;i++)
value+=zermeloValue(next(s,s.legalMoves[i]));
return value/s.numberOfLegalMoves;
}
double maxValue=-MAXDOUBLE;
if (s.numberOfLegalMoves==0) return(s.turn * s.result);
if (depth>5) return heuristicValue(s);
depth++;
for (i=0;i<s.numberOfLegalMoves;i++)
{ value=s.turn*zermeloValue(next(s,s.legalMoves[i]));
if (value>maxValue) maxValue=value; }
depth--;
return s.turn*maxValue; //we return value for player 1
}
63. ONE MORE TOOL: MATRIX GAMES
The problem:
Solving Matrix Games.
A solution:
EXP3.
64. What is a (0-sum) Matrix Game ?
Example:
1 0 0
M= 0 1 1
1 0 1
- You choose (privately) a row (i is 1, 2 or 3).
- In same time, I choose (privately) a column (j=1, 2 or 3).
- My reward: M(i,j)
- Your reward: -M(i,j)
I want a 1, you want a 0.
Given M, how should I play ?
65. What is a (0-sum) Matrix Game ?
Example: rock-paper-scissor
Rock Paper Scissor
Rock 0 -1 1
M= Paper 1 0 -1
Scissor -1 1 0
- You choose (privately) a row (i is 1, 2 or 3).
- In same time, I choose (privately) a column (j=1, 2 or 3).
- My reward: M(i,j)
- Your reward: -M(i,j)
I want a 1, you want a 0.
Given M, how should I play ?
66. Given M, how should I play ?
Nash (diagnosed with paranoid schizophrenia)
got a Nobel prize for his work around that.
Principle of a Nash equilibrium:
- pure strategy = “fixed” strategy
(e.g. “play scissor”)
- mixed strategy = randomized strategy
(e.g. “play scissor with probability ½
and play rock with probability ½”
- choose the mixed strategy such that
“The worst possible score against
any opponent strategy is maximum”
==> “Nash” strategy
==> EXP3: algorithm for finding Nash strategies.
67. IMPORTANT FACTS ON GAMES:
- Turn-based, full-information games,
solvers exist:
- Too slow for chess, Go.
- Ok for 8x8 checkers.
==> Zermelo
==> variants: Minimax, Alpha-beta, play
reasonably well many games
- Matrix games:
- Nash strategies = wort-case optimal
- Nash strategies = randomized strategies
68. A BETTER EXAMPLE ? POKEMON.
Each player chooses 2 pokemons among
the 3 possible ones (real life: 3 or 4
among hundreds).
70. A BETTER EXAMPLE ? POKEMON.
Three possibilities (the same as choosing
a row in a 3x3 matrix
game):
Player 2
Player 1 Check who
wins (by some
full-observation
game-solver).
71. A BETTER EXAMPLE ? POKEMON.
Three possibilities (the same as choosing
a row in a 3x3 matrix
game):
Player 2
Player 1
P1 P2 P2
P2 P1 P1
P1 P2 P1
72. A BETTER EXAMPLE ? POKEMON.
Three possibilities (the same as choosing
a row in a 3x3 matrix
game):
Player 2
Player 1
1 0 0
0 1 1
1 0 1
73. EXP3 principle for Nash equilibrium of KxK matrix M:
- choose a number N of iterations
- S1=null vector
- S2=null vector
- at each iteration t=1, ..., t=N:
{
- compute p1 as a function of S1 // we will see how
- compute p2 as a function of S2 // we will see how
- randomly draw i according to probability distribution p1
- randomly draw j according to probability distribution p2
- define r=M(i,j) in the matrix
- S1(i)+= r / p1(i)
- S2(j)+=(1-r) / p2(j)
- Player1Nash(i)+= (1/N);
- Player2Nash(j)+= (1/N);
}
74. EXP3 principle for Nash equilibrium of KxK matrix M:
- choose a number N of iterations
- S1=null vector
- S2=null vector
- at each iteration t=1, ..., t=N:
{
- compute p1 as a function of S1 // we will see how
- compute p2 as a function of S2 // we will see how
- randomly draw i according to probability distribution p1
- randomly draw j according to probability distribution p2
- define r=M(i,j) in the matrix
- S1(i)+= r / p1(i)
- S2(j)+=(1-r) / p2(j)
- Player1Nash(i)+= (1/N);
- Player2Nash(j)+= (1/N);
}
76. Q&A: (my questions, and also yours)
Q: Who cares about matrix games ?
A: Useful for many things. Unfortunately, it's usually
a building block inside more complex algorithms.
We will see examples, but later.
Q: Is a Nash strategy optimal ?
A: It depends for what... It is optimal in a worst case sense
(i.e. against a very strong opponent).
Not necessarily very good against a weak opponent.