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113-457: AlphaZero is a computer program developed by artificial intelligence research company DeepMind to master the games of chess , shogi and go . This algorithm uses an approach similar to AlphaGo Zero . On December 5, 2017, the DeepMind team released a preprint paper introducing AlphaZero, which would soon play three games by defeating world-champion chess engines Stockfish , Elmo , and

226-415: A {\displaystyle a} and a policy π {\displaystyle \pi } , the action-value of the pair ( s , a ) {\displaystyle (s,a)} under π {\displaystyle \pi } is defined by where G {\displaystyle G} now stands for the random discounted return associated with first taking action

339-552: A {\displaystyle a} in state s {\displaystyle s} and following π {\displaystyle \pi } , thereafter. The theory of Markov decision processes states that if π ∗ {\displaystyle \pi ^{*}} is an optimal policy, we act optimally (take the optimal action) by choosing the action from Q π ∗ ( s , ⋅ ) {\displaystyle Q^{\pi ^{*}}(s,\cdot )} with

452-564: A {\displaystyle a} when in state s {\displaystyle s} . There are also deterministic policies. The state-value function V π ( s ) {\displaystyle V_{\pi }(s)} is defined as, expected discounted return starting with state s {\displaystyle s} , i.e. S 0 = s {\displaystyle S_{0}=s} , and successively following policy π {\displaystyle \pi } . Hence, roughly speaking,

565-555: A ) {\displaystyle (s,a)} are obtained by linearly combining the components of ϕ ( s , a ) {\displaystyle \phi (s,a)} with some weights θ {\displaystyle \theta } : The algorithms then adjust the weights, instead of adjusting the values associated with the individual state-action pairs. Methods based on ideas from nonparametric statistics (which can be seen to construct their own features) have been explored. Value iteration can also be used as

678-402: A ) = Pr ( A t = a ∣ S t = s ) {\displaystyle \pi (s,a)=\Pr(A_{t}=a\mid S_{t}=s)} that maximizes the expected cumulative reward. Formulating the problem as a Markov decision process assumes the agent directly observes the current environmental state; in this case, the problem is said to have full observability . If

791-462: A list of integers could be called integer_list . In object-oriented jargon, abstract datatypes are called classes . However, a class is only a definition; no memory is allocated. When memory is allocated to a class and bound to an identifier , it is called an object . Object-oriented imperative languages developed by combining the need for classes and the need for safe functional programming . A function, in an object-oriented language,

904-422: A programming language . Programming language features exist to provide building blocks to be combined to express programming ideals. Ideally, a programming language should: The programming style of a programming language to provide these building blocks may be categorized into programming paradigms . For example, different paradigms may differentiate: Each of these programming styles has contributed to

1017-428: A store which consisted of memory to hold 1,000 numbers of 50 decimal digits each. Numbers from the store were transferred to the mill for processing. The engine was programmed using two sets of perforated cards. One set directed the operation and the other set inputted the variables. However, the thousands of cogged wheels and gears never fully worked together. Ada Lovelace worked for Charles Babbage to create

1130-563: A 32 GB hash size. Instead of a fixed time control of one move per minute, both engines were given 3 hours plus 15 seconds per move to finish the game. AlphaZero ran on a machine with four TPUs in addition to 44 CPU cores. In a 1000-game match, AlphaZero won with a score of 155 wins, 6 losses, and 839 draws. DeepMind also played a series of games using the TCEC opening positions; AlphaZero also won convincingly. Stockfish needed 10-to-1 time odds to match AlphaZero. Similar to Stockfish, Elmo ran under

1243-604: A description of the Analytical Engine (1843). The description contained Note G which completely detailed a method for calculating Bernoulli numbers using the Analytical Engine. This note is recognized by some historians as the world's first computer program . In 1936, Alan Turing introduced the Universal Turing machine , a theoretical device that can model every computation. It is a finite-state machine that has an infinitely long read/write tape. The machine can move

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1356-414: A dynamic environment in order to maximize a reward signal. Reinforcement learning is one of the three basic machine learning paradigms , alongside supervised learning and unsupervised learning . Q-learning at its simplest stores data in tables. This approach becomes infeasible as the number of states/actions increases (e.g., if the state space or action space were continuous), as the probability of

1469-435: A function of the parameter vector θ {\displaystyle \theta } . If the gradient of ρ {\displaystyle \rho } was known, one could use gradient ascent . Since an analytic expression for the gradient is not available, only a noisy estimate is available. Such an estimate can be constructed in many ways, giving rise to algorithms such as Williams' REINFORCE method (which

1582-580: A language's basic syntax . The syntax of the language BASIC (1964) was intentionally limited to make the language easy to learn. For example, variables are not declared before being used. Also, variables are automatically initialized to zero. Here is an example computer program, in Basic, to average a list of numbers: Once the mechanics of basic computer programming are learned, more sophisticated and powerful languages are available to build large computer systems. Improvements in software development are

1695-624: A mapping from a finite-dimensional (parameter) space to the space of policies: given the parameter vector θ {\displaystyle \theta } , let π θ {\displaystyle \pi _{\theta }} denote the policy associated to θ {\displaystyle \theta } . Defining the performance function by ρ ( θ ) = ρ π θ {\displaystyle \rho (\theta )=\rho ^{\pi _{\theta }}} under mild conditions this function will be differentiable as

1808-471: A match against the latest version of Stockfish, Stockfish 10, under Top Chess Engine Championship (TCEC) conditions. Kaufman argued that the only advantage of neural network–based engines was that they used a GPU, so if there was no regard for power consumption (e.g. in an equal-hardware contest where both engines had access to the same CPU and GPU) then anything the GPU achieved was "free". Based on this, he stated that

1921-423: A match that's comparable you have to have Stockfish running on a supercomputer as well." Top US correspondence chess player Wolff Morrow was also unimpressed, claiming that AlphaZero would probably not make the semifinals of a fair competition such as TCEC where all engines play on equal hardware. Morrow further stated that although he might not be able to beat AlphaZero if AlphaZero played drawish openings such as

2034-466: A match with more normal conditions. Computer program A computer program in its human-readable form is called source code . Source code needs another computer program to execute because computers can only execute their native machine instructions . Therefore, source code may be translated to machine instructions using a compiler written for the language. ( Assembly language programs are translated using an assembler .) The resulting file

2147-455: A model capable of generating sample transitions is required, rather than a full specification of transition probabilities , which is necessary for dynamic programming methods. Monte Carlo methods apply to episodic tasks, where experience is divided into episodes that eventually terminate. Policy and value function updates occur only after the completion of an episode, making these methods incremental on an episode-by-episode basis, though not on

2260-411: A policy that maximizes the discounted return by maintaining a set of estimates of expected discounted returns E ⁡ [ G ] {\displaystyle \operatorname {\mathbb {E} } [G]} for some policy (usually either the "current" [on-policy] or the optimal [off-policy] one). These methods rely on the theory of Markov decision processes, where optimality is defined in

2373-521: A profound influence on programming language design. Emerging from a committee of European and American programming language experts, it used standard mathematical notation and had a readable, structured design. Algol was first to define its syntax using the Backus–Naur form . This led to syntax-directed compilers. It added features like: Algol's direct descendants include Pascal , Modula-2 , Ada , Delphi and Oberon on one branch. On another branch

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2486-406: A queen and bishop to exploit a positional advantage. "It's like chess from another dimension." Given the difficulty in chess of forcing a win against a strong opponent , the +28 –0 =72 result is a significant margin of victory. However, some grandmasters, such as Hikaru Nakamura and Komodo developer Larry Kaufman , downplayed AlphaZero's victory, arguing that the match would have been closer if

2599-463: A remarkable achievement, even if we should have expected it after AlphaGo." Grandmaster Hikaru Nakamura was less impressed, stating: "I don't necessarily put a lot of credibility in the results simply because my understanding is that AlphaZero is basically using the Google supercomputer and Stockfish doesn't run on that hardware; Stockfish was basically running on what would be my laptop. If you wanna have

2712-557: A result, the computer could be programmed quickly and perform calculations at very fast speeds. Presper Eckert and John Mauchly built the ENIAC. The two engineers introduced the stored-program concept in a three-page memo dated February 1944. Later, in September 1944, John von Neumann began working on the ENIAC project. On June 30, 1945, von Neumann published the First Draft of a Report on

2825-429: A schedule (making the agent explore progressively less), or adaptively based on heuristics. Even if the issue of exploration is disregarded and even if the state was observable (assumed hereafter), the problem remains to use past experience to find out which actions lead to higher cumulative rewards. The agent's action selection is modeled as a map called policy : The policy map gives the probability of taking action

2938-470: A sense stronger than the one above: A policy is optimal if it achieves the best-expected discounted return from any initial state (i.e., initial distributions play no role in this definition). Again, an optimal policy can always be found among stationary policies. To define optimality in a formal manner, define the state-value of a policy π {\displaystyle \pi } by where G {\displaystyle G} stands for

3051-465: A starting point, giving rise to the Q-learning algorithm and its many variants. Including Deep Q-learning methods when a neural network is used to represent Q, with various applications in stochastic search problems. The problem with using action-values is that they may need highly precise estimates of the competing action values that can be hard to obtain when the returns are noisy, though this problem

3164-433: A step-by-step (online) basis. The term “Monte Carlo” generally refers to any method involving random sampling ; however, in this context, it specifically refers to methods that compute averages from complete returns, rather than partial returns. These methods function similarly to the bandit algorithms , in which returns are averaged for each state-action pair. The key difference is that actions taken in one state affect

3277-589: A unified system that played excellent chess, shogi, and go, as well as games in the Atari Learning Environment, without being pre-programmed with their rules. The match results by themselves are not particularly meaningful because of the rather strange choice of time controls and Stockfish parameter settings: The games were played at a fixed time of 1 minute/move, which means that Stockfish has no use of its time management heuristics (lot of effort has been put into making Stockfish identify critical points in

3390-564: Is stationary if the action-distribution returned by it depends only on the last state visited (from the observation agent's history). The search can be further restricted to deterministic stationary policies. A deterministic stationary policy deterministically selects actions based on the current state. Since any such policy can be identified with a mapping from the set of states to the set of actions, these policies can be identified with such mappings with no loss of generality. The brute force approach entails two steps: One problem with this

3503-429: Is a generic reinforcement learning algorithm – originally devised for the game of go – that achieved superior results within a few hours, searching a thousand times fewer positions, given no domain knowledge except the rules." DeepMind's Demis Hassabis , a chess player himself, called AlphaZero's play style "alien": It sometimes wins by offering counterintuitive sacrifices, like offering up

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3616-430: Is a state randomly sampled from the distribution μ {\displaystyle \mu } of initial states (so μ ( s ) = Pr ( S 0 = s ) {\displaystyle \mu (s)=\Pr(S_{0}=s)} ). Although state-values suffice to define optimality, it is useful to define action-values. Given a state s {\displaystyle s} , an action

3729-409: Is able to play shogi and chess as well as Go . Differences between AZ and AGZ include: Comparing Monte Carlo tree search searches, AlphaZero searches just 80,000 positions per second in chess and 40,000 in shogi, compared to 70 million for Stockfish and 35 million for Elmo. AlphaZero compensates for the lower number of evaluations by using its deep neural network to focus much more selectively on

3842-507: Is allowed to change, A policy that achieves these optimal state-values in each state is called optimal . Clearly, a policy that is optimal in this sense is also optimal in the sense that it maximizes the expected discounted return, since V ∗ ( s ) = max π E [ G ∣ s , π ] {\displaystyle V^{*}(s)=\max _{\pi }\mathbb {E} [G\mid s,\pi ]} , where s {\displaystyle s}

3955-425: Is already obsolete compared with newer programs. Papers headlined that the chess training took only four hours: "It was managed in little more than the time between breakfast and lunch." Wired described AlphaZero as "the first multi-skilled AI board-game champ". AI expert Joanna Bryson noted that Google's "knack for good publicity" was putting it in a strong position against challengers. "It's not only about hiring

4068-418: Is assigned to a class. An assigned function is then referred to as a method , member function , or operation . Object-oriented programming is executing operations on objects . Object-oriented languages support a syntax to model subset/superset relationships. In set theory , an element of a subset inherits all the attributes contained in the superset. For example, a student is a person. Therefore,

4181-399: Is called an executable . Alternatively, source code may execute within an interpreter written for the language. If the executable is requested for execution, then the operating system loads it into memory and starts a process . The central processing unit will soon switch to this process so it can fetch, decode, and then execute each machine instruction. If the source code

4294-446: Is chosen, and the agent chooses the action that it believes has the best long-term effect (ties between actions are broken uniformly at random). Alternatively, with probability ε {\displaystyle \varepsilon } , exploration is chosen, and the action is chosen uniformly at random. ε {\displaystyle \varepsilon } is usually a fixed parameter but can be adjusted either according to

4407-455: Is mitigated to some extent by temporal difference methods. Using the so-called compatible function approximation method compromises generality and efficiency. An alternative method is to search directly in (some subset of) the policy space, in which case the problem becomes a case of stochastic optimization . The two approaches available are gradient-based and gradient-free methods. Gradient -based methods ( policy gradient methods ) start with

4520-402: Is requested for execution, then the operating system loads the corresponding interpreter into memory and starts a process. The interpreter then loads the source code into memory to translate and execute each statement . Running the source code is slower than running an executable . Moreover, the interpreter must be installed on the computer. The "Hello, World!" program is used to illustrate

4633-487: Is that the latter do not assume knowledge of an exact mathematical model of the Markov decision process, and they target large MDPs where exact methods become infeasible. Due to its generality, reinforcement learning is studied in many disciplines, such as game theory , control theory , operations research , information theory , simulation-based optimization , multi-agent systems , swarm intelligence , and statistics . In

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4746-508: Is that the number of policies can be large, or even infinite. Another is that the variance of the returns may be large, which requires many samples to accurately estimate the discounted return of each policy. These problems can be ameliorated if we assume some structure and allow samples generated from one policy to influence the estimates made for others. The two main approaches for achieving this are value function estimation and direct policy search . Value function approaches attempt to find

4859-440: Is the discount rate . γ {\displaystyle \gamma } is less than 1, so rewards in the distant future are weighted less than rewards in the immediate future. The algorithm must find a policy with maximum expected discounted return. From the theory of Markov decision processes it is known that, without loss of generality, the search can be restricted to the set of so-called stationary policies. A policy

4972-548: Is to alter the electrical resistivity and conductivity of a semiconductor junction . First, naturally occurring silicate minerals are converted into polysilicon rods using the Siemens process . The Czochralski process then converts the rods into a monocrystalline silicon , boule crystal . The crystal is then thinly sliced to form a wafer substrate . The planar process of photolithography then integrates unipolar transistors, capacitors , diodes , and resistors onto

5085-538: The new statement. A module's other file is the source file . Here is a C++ source file for the GRADE class in a simple school application: Here is a C++ header file for the PERSON class in a simple school application: Reinforcement learning Reinforcement learning ( RL ) is an interdisciplinary area of machine learning and optimal control concerned with how an intelligent agent should take actions in

5198-604: The IBM System/360 (1964) had a CPU made from circuit boards containing discrete components on ceramic substrates . The Intel 4004 (1971) was a 4- bit microprocessor designed to run the Busicom calculator. Five months after its release, Intel released the Intel 8008 , an 8-bit microprocessor. Bill Pentz led a team at Sacramento State to build the first microcomputer using the Intel 8008:

5311-500: The Petroff Defence , AlphaZero would not be able to beat him in a correspondence chess game either. Motohiro Isozaki, the author of YaneuraOu, noted that although AlphaZero did comprehensively beat Elmo, the rating of AlphaZero in shogi stopped growing at a point which is at most 100–200 higher than Elmo. This gap is not that high, and Elmo and other shogi software should be able to catch up in 1–2 years. DeepMind addressed many of

5424-480: The Sac State 8008 (1972). Its purpose was to store patient medical records. The computer supported a disk operating system to run a Memorex , 3- megabyte , hard disk drive . It had a color display and keyboard that was packaged in a single console. The disk operating system was programmed using IBM's Basic Assembly Language (BAL) . The medical records application was programmed using a BASIC interpreter. However,

5537-550: The circuits . At its core, it was a series of Pascalines wired together. Its 40 units weighed 30 tons, occupied 1,800 square feet (167 m ), and consumed $ 650 per hour ( in 1940s currency ) in electricity when idle. It had 20 base-10 accumulators . Programming the ENIAC took up to two months. Three function tables were on wheels and needed to be rolled to fixed function panels. Function tables were connected to function panels by plugging heavy black cables into plugboards . Each function table had 728 rotating knobs. Programming

5650-492: The multi-armed bandit problem and for finite state space Markov decision processes in Burnetas and Katehakis (1997). Reinforcement learning requires clever exploration mechanisms; randomly selecting actions, without reference to an estimated probability distribution, shows poor performance. The case of (small) finite Markov decision processes is relatively well understood. However, due to the lack of algorithms that scale well with

5763-404: The programming environment to advance from a computer terminal (until the 1990s) to a graphical user interface (GUI) computer. Computer terminals limited programmers to a single shell running in a command-line environment . During the 1970s, full-screen source code editing became possible through a text-based user interface . Regardless of the technology available, the goal is to program in

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5876-452: The Bellman equations. This can be effective in palliating this issue. In order to address the fifth issue, function approximation methods are used. Linear function approximation starts with a mapping ϕ {\displaystyle \phi } that assigns a finite-dimensional vector to each state-action pair. Then, the action values of a state-action pair ( s ,

5989-494: The EDVAC , which equated the structures of the computer with the structures of the human brain. The design became known as the von Neumann architecture . The architecture was simultaneously deployed in the constructions of the EDVAC and EDSAC computers in 1949. The IBM System/360 (1964) was a family of computers, each having the same instruction set architecture . The Model 20 was

6102-433: The ENIAC also involved setting some of the 3,000 switches. Debugging a program took a week. It ran from 1947 until 1955 at Aberdeen Proving Ground , calculating hydrogen bomb parameters, predicting weather patterns, and producing firing tables to aim artillery guns. Instead of plugging in cords and turning switches, a stored-program computer loads its instructions into memory just like it loads its data into memory. As

6215-881: The absence of a mathematical model of the environment). Basic reinforcement learning is modeled as a Markov decision process : The purpose of reinforcement learning is for the agent to learn an optimal (or near-optimal) policy that maximizes the reward function or other user-provided reinforcement signal that accumulates from immediate rewards. This is similar to processes that appear to occur in animal psychology. For example, biological brains are hardwired to interpret signals such as pain and hunger as negative reinforcements, and interpret pleasure and food intake as positive reinforcements. In some circumstances, animals learn to adopt behaviors that optimize these rewards. This suggests that animals are capable of reinforcement learning. A basic reinforcement learning agent interacts with its environment in discrete time steps. At each time step t ,

6328-406: The agent only has access to a subset of states, or if the observed states are corrupted by noise, the agent is said to have partial observability , and formally the problem must be formulated as a partially observable Markov decision process . In both cases, the set of actions available to the agent can be restricted. For example, the state of an account balance could be restricted to be positive; if

6441-461: The agent receives the current state S t {\displaystyle S_{t}} and reward R t {\displaystyle R_{t}} . It then chooses an action A t {\displaystyle A_{t}} from the set of available actions, which is subsequently sent to the environment. The environment moves to a new state S t + 1 {\displaystyle S_{t+1}} and

6554-403: The agent visiting a particular state and performing a particular action diminishes. Reinforcement learning differs from supervised learning in not needing labelled input-output pairs to be presented, and in not needing sub-optimal actions to be explicitly corrected. Instead, the focus is on finding a balance between exploration (of uncharted territory) and exploitation (of current knowledge) with

6667-442: The batch). Batch methods, such as the least-squares temporal difference method, may use the information in the samples better, while incremental methods are the only choice when batch methods are infeasible due to their high computational or memory complexity. Some methods try to combine the two approaches. Methods based on temporal differences also overcome the fourth issue. Another problem specific to TD comes from their reliance on

6780-580: The best programmers. It's also very political, as it helps make Google as strong as possible when negotiating with governments and regulators looking at the AI sector." Human chess grandmasters generally expressed excitement about AlphaZero. Danish grandmaster Peter Heine Nielsen likened AlphaZero's play to that of a superior alien species. Norwegian grandmaster Jon Ludvig Hammer characterized AlphaZero's play as "insane attacking chess" with profound positional understanding. Former champion Garry Kasparov said, "It's

6893-640: The cheaper Intel 8088 . IBM embraced the Intel 8088 when they entered the personal computer market (1981). As consumer demand for personal computers increased, so did Intel's microprocessor development. The succession of development is known as the x86 series . The x86 assembly language is a family of backward-compatible machine instructions . Machine instructions created in earlier microprocessors were retained throughout microprocessor upgrades. This enabled consumers to purchase new computers without having to purchase new application software . The major categories of instructions are: VLSI circuits enabled

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7006-516: The chess games, each program got one minute per move, and Elmo was given 64 threads and a hash size of 1 GB. After 34 hours of self-learning of Go and against AlphaGo Zero, AlphaZero won 60 games and lost 40. DeepMind stated in its preprint, "The game of chess represented the pinnacle of AI research over several decades. State-of-the-art programs are based on powerful engines that search many millions of positions, leveraging handcrafted domain expertise and sophisticated domain adaptations. AlphaZero

7119-419: The computer was an evolutionary dead-end because it was extremely expensive. Also, it was built at a public university lab for a specific purpose. Nonetheless, the project contributed to the development of the Intel 8080 (1974) instruction set . In 1978, the modern software development environment began when Intel upgraded the Intel 8080 to the Intel 8086 . Intel simplified the Intel 8086 to manufacture

7232-537: The configuration, an execute button was pressed. This process was then repeated. Computer programs also were automatically inputted via paper tape , punched cards or magnetic-tape . After the medium was loaded, the starting address was set via switches, and the execute button was pressed. A major milestone in software development was the invention of the Very Large Scale Integration (VLSI) circuit (1964). Following World War II , tube-based technology

7345-580: The criticisms in their final version of the paper, published in December 2018 in Science . They further clarified that AlphaZero was not running on a supercomputer; it was trained using 5,000 tensor processing units (TPUs), but only ran on four TPUs and a 44-core CPU in its matches. In the final results, Stockfish 9 dev ran under the same conditions as in the TCEC superfinal: 44 CPU cores, Syzygy endgame tablebases , and

7458-416: The current value of the state is 3 and the state transition attempts to reduce the value by 4, the transition will not be allowed. When the agent's performance is compared to that of an agent that acts optimally, the difference in performance yields the notion of regret . In order to act near optimally, the agent must reason about long-term consequences of its actions (i.e., maximize future rewards), although

7571-434: The descendants include C , C++ and Java . BASIC (1964) stands for "Beginner's All-Purpose Symbolic Instruction Code". It was developed at Dartmouth College for all of their students to learn. If a student did not go on to a more powerful language, the student would still remember Basic. A Basic interpreter was installed in the microcomputers manufactured in the late 1970s. As the microcomputer industry grew, so did

7684-459: The discounted return associated with following π {\displaystyle \pi } from the initial state s {\displaystyle s} . Defining V ∗ ( s ) {\displaystyle V^{*}(s)} as the maximum possible state-value of V π ( s ) {\displaystyle V^{\pi }(s)} , where π {\displaystyle \pi }

7797-428: The environment’s dynamics, Monte Carlo methods rely solely on actual or simulated experience—sequences of states, actions, and rewards obtained from interaction with an environment. This makes them applicable in situations where the complete dynamics are unknown. Learning from actual experience does not require prior knowledge of the environment and can still lead to optimal behavior. When using simulated experience, only

7910-460: The first Fortran standard in 1966. In 1978, Fortran 77 became the standard until 1991. Fortran 90 supports: COBOL (1959) stands for "COmmon Business Oriented Language". Fortran manipulated symbols. It was soon realized that symbols did not need to be numbers, so strings were introduced. The US Department of Defense influenced COBOL's development, with Grace Hopper being a major contributor. The statements were English-like and verbose. The goal

8023-399: The game and decide when to spend some extra time on a move; at a fixed time per move, the strength will suffer significantly). The version of Stockfish used is one year old, was playing with far more search threads than has ever received any significant amount of testing, and had way too small hash tables for the number of threads. I believe the percentage of draws would have been much higher in

8136-455: The goal of maximizing the cumulative reward (the feedback of which might be incomplete or delayed). The search for this balance is known as the exploration-exploitation dilemma . The environment is typically stated in the form of a Markov decision process (MDP), as many reinforcement learning algorithms use dynamic programming techniques. The main difference between classical dynamic programming methods and reinforcement learning algorithms

8249-415: The highest action-value at each state, s {\displaystyle s} . The action-value function of such an optimal policy ( Q π ∗ {\displaystyle Q^{\pi ^{*}}} ) is called the optimal action-value function and is commonly denoted by Q ∗ {\displaystyle Q^{*}} . In summary, the knowledge of

8362-454: The immediate reward associated with this might be negative. Thus, reinforcement learning is particularly well-suited to problems that include a long-term versus short-term reward trade-off. It has been applied successfully to various problems, including energy storage , robot control , photovoltaic generators , backgammon , checkers , Go ( AlphaGo ), and autonomous driving systems . Two elements make reinforcement learning powerful:

8475-475: The language BCPL was replaced with B , and AT&T Bell Labs called the next version "C". Its purpose was to write the UNIX operating system . C is a relatively small language, making it easy to write compilers. Its growth mirrored the hardware growth in the 1980s. Its growth also was because it has the facilities of assembly language , but uses a high-level syntax . It added advanced features like: C allows

8588-400: The language. Basic pioneered the interactive session . It offered operating system commands within its environment: However, the Basic syntax was too simple for large programs. Recent dialects added structure and object-oriented extensions. Microsoft's Visual Basic is still widely used and produces a graphical user interface . C programming language (1973) got its name because

8701-485: The matrix was to burn out the unneeded connections. There were so many connections, firmware programmers wrote a computer program on another chip to oversee the burning. The technology became known as Programmable ROM . In 1971, Intel installed the computer program onto the chip and named it the Intel 4004 microprocessor . The terms microprocessor and central processing unit (CPU) are now used interchangeably. However, CPUs predate microprocessors. For example,

8814-471: The most promising variation. AlphaZero was made & trained by it simply playing against itself multiple times, using 5,000 first-generation TPUs to generate the games and 64 second-generation TPUs to train the neural networks . Training took several days, totaling about 41 TPU-years. In parallel, the in-training AlphaZero was periodically matched against its benchmark (Stockfish, Elmo, or AlphaGo Zero) in brief one-second-per-move games to determine how well

8927-511: The number of states (or scale to problems with infinite state spaces), simple exploration methods are the most practical. One such method is ε {\displaystyle \varepsilon } -greedy, where 0 < ε < 1 {\displaystyle 0<\varepsilon <1} is a parameter controlling the amount of exploration vs. exploitation. With probability 1 − ε {\displaystyle 1-\varepsilon } , exploitation

9040-451: The operations research and control literature, RL is called approximate dynamic programming , or neuro-dynamic programming. The problems of interest in RL have also been studied in the theory of optimal control , which is concerned mostly with the existence and characterization of optimal solutions, and algorithms for their exact computation, and less with learning or approximation (particularly in

9153-625: The optimal action-value function alone suffices to know how to act optimally. Assuming full knowledge of the Markov decision process, the two basic approaches to compute the optimal action-value function are value iteration and policy iteration . Both algorithms compute a sequence of functions Q k {\displaystyle Q_{k}} ( k = 0 , 1 , 2 , … {\displaystyle k=0,1,2,\ldots } ) that converge to Q ∗ {\displaystyle Q^{*}} . Computing these functions involves computing expectations over

9266-606: The prediction problem and then extending to policy improvement and control, all based on sampled experience. The first problem is corrected by allowing the procedure to change the policy (at some or all states) before the values settle. This too may be problematic as it might prevent convergence. Most current algorithms do this, giving rise to the class of generalized policy iteration algorithms. Many actor-critic methods belong to this category. The second issue can be corrected by allowing trajectories to contribute to any state-action pair in them. This may also help to some extent with

9379-443: The programmer to control which region of memory data is to be stored. Global variables and static variables require the fewest clock cycles to store. The stack is automatically used for the standard variable declarations . Heap memory is returned to a pointer variable from the malloc() function. In the 1970s, software engineers needed language support to break large projects down into modules . One obvious feature

9492-494: The programs had access to an opening database (since Stockfish was optimized for that scenario). Romstad additionally pointed out that Stockfish is not optimized for rigidly fixed-time moves and the version used was a year old. Similarly, some shogi observers argued that the Elmo hash size was too low, that the resignation settings and the "EnteringKingRule" settings (cf. shogi § Entering King ) may have been inappropriate, and that Elmo

9605-457: The public, the algorithm described in the paper has been implemented in publicly available software. In 2019, DeepMind published a new paper detailing MuZero , a new algorithm able to generalize AlphaZero's work, playing both Atari and board games without knowledge of the rules or representations of the game. AlphaZero (AZ) is a more generalized variant of the AlphaGo Zero (AGZ) algorithm , and

9718-407: The recursive Bellman equation. Most TD methods have a so-called λ {\displaystyle \lambda } parameter ( 0 ≤ λ ≤ 1 ) {\displaystyle (0\leq \lambda \leq 1)} that can continuously interpolate between Monte Carlo methods that do not rely on the Bellman equations and the basic TD methods that rely entirely on

9831-482: The remaining 72. In a series of twelve, 100-game matches (of unspecified time or resource constraints) against Stockfish starting from the 12 most popular human openings, AlphaZero won 290, drew 886 and lost 24. AlphaZero was trained on shogi for a total of two hours before the tournament. In 100 shogi games against Elmo (World Computer Shogi Championship 27 summer 2017 tournament version with YaneuraOu 4.73 search), AlphaZero won 90 times, lost 8 times and drew twice. As in

9944-486: The result of improvements in computer hardware . At each stage in hardware's history, the task of computer programming changed dramatically. In 1837, Jacquard's loom inspired Charles Babbage to attempt to build the Analytical Engine . The names of the components of the calculating device were borrowed from the textile industry. In the textile industry, yarn was brought from the store to be milled. The device had

10057-546: The returns of subsequent states within the same episode, making the problem non-stationary . To address this non-stationarity, Monte Carlo methods use the framework of general policy iteration (GPI). While dynamic programming computes value functions using full knowledge of the Markov decision process (MDP), Monte Carlo methods learn these functions through sample returns. The value functions and policies interact similarly to dynamic programming to achieve optimality , first addressing

10170-577: The reward R t + 1 {\displaystyle R_{t+1}} associated with the transition ( S t , A t , S t + 1 ) {\displaystyle (S_{t},A_{t},S_{t+1})} is determined. The goal of a reinforcement learning agent is to learn a policy : π : S × A → [ 0 , 1 ] {\displaystyle \pi :{\mathcal {S}}\times {\mathcal {A}}\rightarrow [0,1]} , π ( s ,

10283-479: The same conditions as in the 2017 CSA championship. The version of Elmo used was WCSC27 in combination with YaneuraOu 2017 Early KPPT 4.79 64AVX2 TOURNAMENT. Elmo operated on the same hardware as Stockfish: 44 CPU cores and a 32 GB hash size. AlphaZero won 98.2% of games when playing sente (i.e. having the first move) and 91.2% overall. Human grandmasters were generally impressed with AlphaZero's games against Stockfish. Former world champion Garry Kasparov said it

10396-438: The set of students is a subset of the set of persons. As a result, students inherit all the attributes common to all persons. Additionally, students have unique attributes that other people do not have. Object-oriented languages model subset/superset relationships using inheritance . Object-oriented programming became the dominant language paradigm by the late 1990s. C++ (1985) was originally called "C with Classes". It

10509-467: The smallest and least expensive. Customers could upgrade and retain the same application software . The Model 195 was the most premium. Each System/360 model featured multiprogramming —having multiple processes in memory at once. When one process was waiting for input/output , another could compute. IBM planned for each model to be programmed using PL/1 . A committee was formed that included COBOL , Fortran and ALGOL programmers. The purpose

10622-415: The strongest engine was likely to be a hybrid with neural networks and standard alpha–beta search . AlphaZero inspired the computer chess community to develop Leela Chess Zero , using the same techniques as AlphaZero. Leela contested several championships against Stockfish, where it showed roughly similar strength to Stockfish, although Stockfish has since pulled away. In 2019 DeepMind published MuZero ,

10735-430: The synthesis of different programming languages . A programming language is a set of keywords , symbols , identifiers , and rules by which programmers can communicate instructions to the computer. They follow a set of rules called a syntax . Programming languages get their basis from formal languages . The purpose of defining a solution in terms of its formal language is to generate an algorithm to solve

10848-447: The tape back and forth, changing its contents as it performs an algorithm . The machine starts in the initial state, goes through a sequence of steps, and halts when it encounters the halt state. All present-day computers are Turing complete . The Electronic Numerical Integrator And Computer (ENIAC) was built between July 1943 and Fall 1945. It was a Turing complete , general-purpose computer that used 17,468 vacuum tubes to create

10961-446: The third problem, although a better solution when returns have high variance is Sutton's temporal difference (TD) methods that are based on the recursive Bellman equation . The computation in TD methods can be incremental (when after each transition the memory is changed and the transition is thrown away), or batch (when the transitions are batched and the estimates are computed once based on

11074-450: The three-day version of AlphaGo Zero. In each case it made use of custom tensor processing units (TPUs) that the Google programs were optimized to use. AlphaZero was trained solely via self-play using 5,000 first-generation TPUs to generate the games and 64 second-generation TPUs to train the neural networks , all in parallel , with no access to opening books or endgame tables . After four hours of training, DeepMind estimated AlphaZero

11187-507: The training was progressing. DeepMind judged that AlphaZero's performance exceeded the benchmark after around four hours of training for Stockfish, two hours for Elmo, and eight hours for AlphaGo Zero. In AlphaZero's chess match against Stockfish 8 (2016 TCEC world champion), each program was given one minute per move. AlphaZero was flying the English flag, while Stockfish the Norwegian. Stockfish

11300-553: The underlining problem. An algorithm is a sequence of simple instructions that solve a problem. The evolution of programming languages began when the EDSAC (1949) used the first stored computer program in its von Neumann architecture . Programming the EDSAC was in the first generation of programming language . Imperative languages specify a sequential algorithm using declarations , expressions , and statements : FORTRAN (1958)

11413-586: The use of samples to optimize performance, and the use of function approximation to deal with large environments. Thanks to these two key components, RL can be used in large environments in the following situations: The first two of these problems could be considered planning problems (since some form of model is available), while the last one could be considered to be a genuine learning problem. However, reinforcement learning converts both planning problems to machine learning problems. The exploration vs. exploitation trade-off has been most thoroughly studied through

11526-596: The value function estimates "how good" it is to be in a given state. where the random variable G {\displaystyle G} denotes the discounted return , and is defined as the sum of future discounted rewards: where R t + 1 {\displaystyle R_{t+1}} is the reward for transitioning from state S t {\displaystyle S_{t}} to S t + 1 {\displaystyle S_{t+1}} , 0 ≤ γ < 1 {\displaystyle 0\leq \gamma <1}

11639-448: The wafer to build a matrix of metal–oxide–semiconductor (MOS) transistors. The MOS transistor is the primary component in integrated circuit chips . Originally, integrated circuit chips had their function set during manufacturing. During the 1960s, controlling the electrical flow migrated to programming a matrix of read-only memory (ROM). The matrix resembled a two-dimensional array of fuses. The process to embed instructions onto

11752-472: The whole state-space, which is impractical for all but the smallest (finite) Markov decision processes. In reinforcement learning methods, expectations are approximated by averaging over samples and using function approximation techniques to cope with the need to represent value functions over large state-action spaces. Monte Carlo methods are used to solve reinforcement learning problems by averaging sample returns. Unlike methods that require full knowledge of

11865-416: Was a pleasure to watch AlphaZero play, especially since its style was open and dynamic like his own. In the computer chess community, Komodo developer Mark Lefler called it a "pretty amazing achievement", but also pointed out that the data was old, since Stockfish had gained a lot of strength since January 2018 (when Stockfish 8 was released). Fellow developer Larry Kaufman said AlphaZero would probably lose

11978-402: Was allocated 64 threads and a hash size of 1 GB, a setting that Stockfish's Tord Romstad later criticized as suboptimal. AlphaZero was trained on chess for a total of nine hours before the match. During the match, AlphaZero ran on a single machine with four application-specific TPUs . In 100 games from the normal starting position, AlphaZero won 25 games as White, won 3 as Black, and drew

12091-427: Was designed to expand C's capabilities by adding the object-oriented facilities of the language Simula . An object-oriented module is composed of two files. The definitions file is called the header file . Here is a C++ header file for the GRADE class in a simple school application: A constructor operation is a function with the same name as the class name. It is executed when the calling operation executes

12204-420: Was playing chess at a higher Elo rating than Stockfish 8; after nine hours of training, the algorithm defeated Stockfish 8 in a time-controlled 100-game tournament (28 wins, 0 losses, and 72 draws). The trained algorithm played on a single machine with four TPUs. DeepMind's paper on AlphaZero was published in the journal Science on 7 December 2018. While the actual AlphaZero program has not been released to

12317-436: Was replaced with point-contact transistors (1947) and bipolar junction transistors (late 1950s) mounted on a circuit board . During the 1960s , the aerospace industry replaced the circuit board with an integrated circuit chip . Robert Noyce , co-founder of Fairchild Semiconductor (1957) and Intel (1968), achieved a technological improvement to refine the production of field-effect transistors (1963). The goal

12430-405: Was to decompose large projects physically into separate files . A less obvious feature was to decompose large projects logically into abstract data types . At the time, languages supported concrete (scalar) datatypes like integer numbers, floating-point numbers, and strings of characters . Abstract datatypes are structures of concrete datatypes, with a new name assigned. For example,

12543-433: Was to design a language so managers could read the programs. However, the lack of structured statements hindered this goal. COBOL's development was tightly controlled, so dialects did not emerge to require ANSI standards. As a consequence, it was not changed for 15 years until 1974. The 1990s version did make consequential changes, like object-oriented programming . ALGOL (1960) stands for "ALGOrithmic Language". It had

12656-425: Was to develop a language that was comprehensive, easy to use, extendible, and would replace Cobol and Fortran. The result was a large and complex language that took a long time to compile . Computers manufactured until the 1970s had front-panel switches for manual programming. The computer program was written on paper for reference. An instruction was represented by a configuration of on/off settings. After setting

12769-423: Was unveiled as "The IBM Mathematical FORmula TRANslating system". It was designed for scientific calculations, without string handling facilities. Along with declarations , expressions , and statements , it supported: It succeeded because: However, non-IBM vendors also wrote Fortran compilers, but with a syntax that would likely fail IBM's compiler. The American National Standards Institute (ANSI) developed

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