这篇我们来详细讲讲AlphaGo的蒙特卡洛搜索。AlphaGo的智能体现在两个地方：一个是基于现有的深度学习和强化学习技术学习，通过自对弈和专家经验学习到的策略网络和值网络；另一个则是体现在实战阶段，AlphaGo并没有直接应用策略网络包含的知识进行对弈，而是将训练好的策略网络和值网络结合到蒙特卡洛搜索中，实现前瞻性的决策。我们先来捋顺一下AlphaGo中蒙特卡洛搜索的过程，然后解释下这种搜索的合理性。
蒙特卡洛搜索依托的数据结构首先是一棵树，树的根节点是当前AlphaGo需要进行决策的棋盘的状态s。这里需要注意的是，AlphaGo在决策每个落子的时候都会重新运行搜索，相应的也会重新建一棵搜索树。
我们考虑像这样的一棵搜索树都需要哪些量来确定呢？首先，根节点的孩子节点是什么呢？应该是棋盘的每一个可能的次状态，也就是说此时此刻每一个合法的落子都应该对应一个孩子节点。但是次状态太多，全部扩展的话，树的深度会受到限制。在蒙特卡洛搜索中，会根据指标选择一个动作作为对当前状态的扩展，扩展到新的状态后，再根据这个定量的指标选择一个新的动作，使用的定量指标如下
a_t = \arg\max_a(Q(s_t,a)+u(s_t,a)).每个量的含义后面分析，目前我们只需要知道针对每个棋盘的状态s_t，a_t 是怎么来的就行。按照这种规则不断扩展搜索树，直到达到树的最大深度，或者到达终止状态了，当然，对于围棋来讲，前者的可能性更大。假设到达了第一个不满足约束条件的叶节点，蒙特卡洛搜索的一次模拟就结束了，然后，蒙特卡洛搜索会从根节点开始继续模拟，而且是在之前生成的搜索树的基础上模拟，假设模拟了 n 次，n 应该是一个较大值，比如100,000。
接下来我们来说这个搜索树的边存储的变量以及相应的评估方式。搜索树的每条边都存储三个变量：Q(s_t,a)、u(s_t,a) 和 N(s_t,a)。其中，N(s_t,a) 表示在所有的 n 次模拟中，(s_t,a) 这条边被访问的次数，而 Q(s_t,a)和u(s_t,a)都是在这个次数的基础上定义的统计量。 Q(s_t,a) 表示沿着当前路径扩展搜索树获胜的数学期望，以获得的奖励的均值来统计
Q(s,a)=\frac{1}{N(s,a)}\sum_{i=1}^{n}1(s,a,i)V(s_L^i).1(s,a,i) 表示在第 i 次模拟中 (s,a) 这条边是否被使用过，而每条边的 N(s,a) 正是 \sum_{i=1}^{n}1(s,a,i)。所以，Q(s,a) 表示的正是奖励的期望。公式中的 V(s_L^i) 指的是第 i 次模拟得到的奖励值，s_L^i 则表示该次模拟到树的第 L 层停止后对应的叶节点，V(s_L^i) 由两部分组成
V(s_L)=(1-\lambda)v_\theta(s_L)+\lambda z_L.v_\theta(s_L) 是基于已经训练好的值网络的一次快速评估，评估在状态 s_L 下获胜的数学期望，z_L 是使用训练好的轻量级策略网络 p_\pi 进行快速的连续的决策，从而在短时间内从状态 s_L 到达某一方获胜的终止状态 s_T 后得到的奖励值。
在刚开始的时候，每个可能的次状态的 Q(s,a) 都是 \infty，因为 N(s,a) = 0。所以一开始就是随机选择一个，第一次模拟结束后，Q(s,a) 就不是 \infty 了，继而其他的次状态会被继续选中进行模拟，当众多状态都被模拟过一遍时候，就开始进入公平竞争了，谁的 Q 值大，谁被遍历的次数就多。
u(s,a) 是bonus
u(s,a) \propto \frac{P(s,a)}{1+N(s,a)},初始化为 P(s,a)，即根据专家经验学习的策略网络 p_\sigma 的对状态-动作对 (s,a) 的评估，而这个bonus会随着访问次数增加而递减，从而直接地维护了每个次状态被访问到的公平性，是exploration思想的一种体现。
在完成所有的 n 次遍历后，我们选择被访问次数最多的动作执行即可。
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Thomas, Ayanna K.; Bulevich, John B.; Loftus, Elizabeth F. (June 2003).
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Has Europe infected USA?
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George Edward Pegram, Chief Welfare Officer, Essex County Council.
Livingston, Christopher (August 14, 2014).
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Likewise, if the stock’s rate is lower than its real worth, then it is undervalued.
There are three main reasons that socialism gets combined up with its neighbors.
A Forex Internet trader doesn’t need to talk with a brokerage by telephone.
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Other countries have started emissions trading schemes that will set a price on carbon.
After every description is a report card exhibiting how the 1994 film and the 2005 movie evaluate towards the supply material.
In this kind buying and selling technique the traders can trade with the market development like you should purchase the stocks if the market trades within the lower range.
Strategically, the equal steadiness of destructive energy possessed by every aspect manifests within the doctrine of mutually assured destruction (MAD), which determines that a nuclear attack by one superpower would result in a nuclear counter-strike by the other.
The joint destabilization of its money and bond markets was further exacerbated by the yen’s appreciation, which shifted expectations on consumer prices and short-term rates, and brought with it nationwide deflation.
That means If in case you have 1,000 true fans you can do a crowdfunding marketing campaign, because by definition a true fan will grow to be a Kickstarter funder.
The conference will cover current issues in data management, and in database and knowledge systems analysis.
All the main stock indices of the future G7 bottomed out between September and December 1974, having lost at least 34 of their value in nominal terms and 43 in real terms.
Music therapists use music to help diagnose, treat and communicate with patients in a unique way.
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Based on Techwalla, a hacker can’t awaken and attack your Laptop whenever you leave it in sleep mode, as a result of in that state it doesn’t have an energetic connection to your community and the web.
This follows from a geometric structure formed by probabilistic representations of market views and threat situations.
It runs Android and was initially announced in 2013.
The road on which the location is located got here to be referred to as Dalal Road in Hindi (which means “Broker Road”) as a consequence of the placement of the change.
It’s not surprising, then, that many corporations, each overseas and domestic, will attempt to deceive People into thinking their merchandise were made domestically, when in actuality they aren’t.
The images these cameras capture are then projected onto a heads-up show on the car’s windshield.
The district’s board of schooling is comprised of 9 members, who are elected immediately by voters to serve three-yr terms of workplace on a staggered basis, with three seats up for election each year.
55, New Jersey League of Ladies Voters.
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Falk, Jeff (September 17, 2020).
What surprising findings have been discovered about restorative cities and mental health?
It is important for individuals to work closely with their healthcare provider to find the most effective medication regimen that minimizes side effects.
Board member of Family and kids Companies in Lebanon County.
Higher-rate tax payers have been hit hard as a result of the National Savings and Investment’s withdrawing its tax-free index-linked certificates, as it was previously offering the equivalent taxable gross return of 10 providing that the current Retail Prices Index (RPI) rate stayed at 5, giving savers more than double the returns that any standard savings accounts can offer.
Who was known as “Old Rough and Ready”?
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Pierce, Greg (September 22, 2008).
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Dell, who died by 1793 in Ontario, Canada.
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Draco Malfoy is the Seeker for the Slytherin Quidditch staff.
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Like a bank card, the borrower has a restrict on how a lot money is at his or her disposal.
22 December – Portugal reports its estimated budget deficit of 4.5 in 2011 will be substantially lower than expected and it will meet its 2012 target already a year earlier due to a one-off transfer of pension funds.
U.S. Division of Well being & Human Companies – Company for Healthcare Analysis and Quality.
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So, if the price of one stock falls it does not spell complete doom for you, whereas if you buy a stock and the price falls, you have lost everything.
Thermoresistors resist the circulation of electricity by a circuit at different ranges relying on temperature.
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Frank, Robert H. (2000).
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The marble desk’s grains additionally significantly contribute to the general appearance.
Crystal Raceway at some point.
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The tax charges that apply to lengthy-term capital good points are altering as properly.
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However, in early-March, Trapp suffered a thigh damage and was sidelined for 2 matches.
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Fastened capital is cash companies use to buy assets that will stay permanently in the enterprise and assist it make a revenue.
Falk, Jeff (September 17, 2020).
Census Bureau, measuring nearly three million observations per yr, spanning the great Recession in the U.S., from 2008 to 2013.
It is because Mutual Funds Are Sometimes Composed of a group of Related Stocks, Which Signifies that the overall Return of the Fund Will likely be Relatively Constant.
This page was final edited on 9 July 2024, at 00:23 (UTC).
Ashcroft v. the American Civil Liberties Union addressed the Little one Online Protection Act, which required pornography publishers to limit underage entry.
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8 (Castleford) Area, Yorkshire Division, National Coal Board.
Astrolabes are simple but highly effective astronomical devices used for the aim of observations, analog calculations and reckoning time.
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George GRAHAM, pastor of the primary United Methodist Church, officiating.
One of the costliest hurricanes in American history, Hurricane Katrina, unleashed its fury on the Gulf Coast in 2005.
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Clergyman: Dr Chas Evans of Sprague.
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In September 15, the CEO of CITIC Securities was suspected by Chinese language police of leaking and buying and selling on unspecified inside data.
It cost a total of $50,000 to be customized for the movies with the customization undertaken by Dean Jefferies.
In reality, telepsychiatry has confirmed to be a precious instrument for reaching and treating patients, allowing clinicians to broaden their apply beyond geographic boundaries.
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The Hitchhiker’s Information to the Galaxy was delivered to the stage by Ken Cambell.
Do you’ve got a dark aspect?
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