价值函数

“价值函数”是一个人工智能，特别是强化学习领域的专业概念，但其核心思想其实非常贴近我们常说的“趋利避害”。今天，我们就来深入浅出地聊聊这个有趣的“价值函数”。

引言：为什么AI需要“懂得”价值？

想象一下，你正在玩一个寻宝游戏。你每走一步，都需要决定是往左走、往右走，还是向前走。你最终的目标是找到宝藏，但一路上可能会遇到陷阱（惩罚）或者得到一些小奖励（线索）。你如何才能做出最好的选择，以最快、最安全的方式找到宝藏呢？

对于人类来说，我们有经验、有直觉，可以评估每一步可能带来的“好”与“坏”。但对于AI来说，它需要一个量化的标准来“衡量”这些“好”与“坏”，这个标准就是我们今天要讲的——价值函数。

一、 什么是价值函数？—— 给“好坏”打分

在人工智能，尤其是强化学习（Reinforcement Learning）领域中，“价值函数”（Value Function）是一个核心概念。简单来说，价值函数就是一个给特定“状态”或“行为”打分的“评分系统”。这个分数代表的不是即时的奖励或惩罚，而是未来预期获得的累积总奖励。

打个比方：

  • 股市投资： 你手里的股票现在的价格（即时状态）是一方面，但你更关心的是这只股票未来能给你带来多少收益，它的“潜力”有多大。这个“潜力”，就是它的“价值”。AI在做决策时，就如同一个投资者，它看到的不仅是当前的“即时收益”，更要评估一个“状态”或“动作”带来的“长期总价值”.
  • 玩游戏： 在玩像国际象棋这样的策略游戏时，你当前棋盘的局面（一个状态）本身并没有直接的得分。但你会判断这个局面是“好”是“坏”，因为它可能导向胜利（高价值）或者失败（低价值）。这里的“好坏”就是价值函数在评估。

所以，价值函数不是告诉你“立即能得到什么”，而是告诉你“长远来看，这样做好不好，能获得多少收益”。

二、 为什么需要价值函数？—— 指引AI做出明智选择

AI在复杂的环境中做决策时，常常像一个初学走路的孩子，需要指导。它的目标通常是最大化它能获得的总奖励。但仅仅依靠眼前的奖励往往是不够的，因为眼前的“甜头”可能导致长远的“苦果”。价值函数的作用就在于：

  1. 评估优劣： 帮助AI判断当前所处的状态有多“好”，或者在当前状态下采取某个行动有多“好”.
  2. 规划未来： 它让AI能够“展望未来”，而不仅仅是“活在当下”。通过考虑未来的奖励，AI可以选择那些短期内看似不好，但长期来看收益丰厚的行动。比如，在游戏中，为了布局而牺牲一颗小棋子，从短期看是“损失”，但价值函数会告诉AI，这可能带来更大的“价值”。
  3. 指导学习： AI在通过试错学习时，价值函数是其“学习指南”。它会根据自己行动后环境反馈的奖励来更新对不同状态或行动的“价值”评估，从而逐渐学会什么才是最优策略.

三、 价值函数的分类：状态价值 vs. 动作价值

在强化学习中，价值函数通常分为两种主要的类型:

  1. 状态价值函数 (State-Value Function, V(s))：

    • 比喻： 想象你在一个城市里旅行，每到一个地方（一个“状态”），你会问自己：“从这里出发，我能玩得有多开心，看到多少美景，总共能获得多少旅行体验积分？” 这个积分就是这个“地方”的“状态价值”。
    • 含义： 它评估的是一个_状态_本身的长期价值，即如果AI从某个状态s开始，并遵循某一策略（即一套行动规则）一直走下去，它预期能获得的未来累积奖励是多少.

  2. 动作价值函数 (Action-Value Function, Q(s,a))：

    • 比喻： 同样是旅行，你到了一个地方（状态s），现在有多种选择：坐地铁（动作a1）、打的（动作a2）或走路（动作a3）。你会评估“从这里坐地铁去，总共能获得多少体验积分？”或者“从这里打的去，总共能获得多少体验积分？”等等。这些就是不同“动作”的“动作价值”。
    • 含义： 它评估的是在某个_状态_s下采取某个_动作_a，然后继续遵循某一策略所能获得的未来累积奖励. 动作价值函数对于AI选择具体行动尤为重要。

四、 价值函数如何“学习”和“计算”？

AI通过与环境的不断互动，尝试各种行动，并观察获得的奖励，从而逐步“学习”和“估计”这些价值函数。这个过程类似于人类通过经验积累智慧。其中，贝尔曼方程（Bellman Equation）是计算和更新价值函数的基础数学工具，它将一个状态的价值与未来可能状态的价值关联起来，形成一个递归关系.

通俗理解贝尔曼方程：

你现在的位置的“价值”，等于你立即获得的奖励，加上你接下来将要到达的下一个位置的“打折”后的“价值”。之所以“打折”，是因为未来的事情不确定性更高，而且我们通常更看重眼前的收益。

AI反复进行这种计算和更新，就像一个人不断复盘自己的决策，总结经验教训，最终就能找到一个最优的“价值地图”，从而知道在任何情况下如何行动才能获得最大化的长期利益。

五、 最新发展：价值函数的演进与应用

价值函数在现代AI中依然是关键驱动力，尤其是在强化学习领域。

  • 深度学习与价值函数： 随着深度学习的发展，研究人员开始使用神经网络来近似复杂的价值函数。这使得AI能够处理更庞大、更抽象的状态空间，比如直接从游戏画面中学习棋局的价值，或者从原始传感器数据中判断自动驾驶车辆所处环境的“好坏”.
  • 多智能体强化学习： 在多个AI智能体相互协作或竞争的场景中，价值函数也被扩展应用，每个智能体都有自己的价值评估系统，以实现整体最优或个体利益最大化.
  • 大语言模型中的价值理念： 有趣的是，虽然不完全等同，但在大语言模型的某些最新研究中，也有类似价值函数的核心理念被探索。例如，香港科大的一项研究发现，在数学推理任务中，通过评估“随机策略的价值函数”来选择最优行动，效果甚至超越了复杂算法。这项研究表明，深入理解问题本质，并用简化方法利用“价值”概念，能带来意想不到的效果. 另外，大型科技公司如Meta也在利用AI基础投资来创造价值，例如通过AI驱动的推荐模型提高广告转化率等. 还有研究正探索如何让AI工程师更好地利用AI，通过“规范驱动开发”和“Agentic AI”等方法，让AI作为一个拥有“价值”判断的初级伙伴来协助代码开发，解决复杂问题.
  • 企业价值创造： 宏观来看，AI技术正在帮助企业在多个职能领域创造巨大价值，例如在营销、销售、产品开发、服务运营等方面提高效率和效益。企业正在重新设计工作流程，设定AI投资目标，以从AI中获取非凡价值.

总结：AI的“智慧指南”

价值函数，这个在AI领域听起来有些抽象的概念，实际上就像是AI的“智慧指南针”和“评分卡”。它让AI能够超越眼前的得失，学会“高瞻远瞩”，在复杂的环境中做出真正“明智”的长期决策。从自动玩游戏到辅助决策，再到驱动复杂的自动化系统，价值函数在幕后默默地指引着AI，使其变得越来越聪明，越来越有能力，为我们的生活创造更多的价值。未来，随着AI技术的不断演进，价值函数的探索和应用无疑还会迎来更多突破和创新。

Value Function

“Value Function” is a professional concept in the field of Artificial Intelligence, especially in Reinforcement Learning, but its core idea is actually very close to what we often say “seek advantages and avoid disadvantages”. Today, let’s talk about this interesting “Value Function” in simple terms.

Introduction: Why Does AI Need to “Understand” Value?

Imagine you are playing a treasure hunt game. With every step you take, you need to decide whether to go left, right, or forward. Your ultimate goal is to find the treasure, but along the way, you might encounter traps (punishments) or get some small rewards (clues). How can you make the best choice to find the treasure in the fastest and safest way?

For humans, we have experience and intuition to assess the “good” and “bad” that each step might bring. But for AI, it needs a quantified standard to “measure” these “good” and “bad”, and this standard is what we are going to talk about today — the Value Function.

I. What is a Value Function? — Scoring “Good or Bad”

In the field of Artificial Intelligence, especially Reinforcement Learning, “Value Function” is a core concept. Simply put, a Value Function is a “scoring system” that gives a score to a specific “state” or “action”. This score represents not the immediate reward or punishment, but the cumulative total reward expected to be obtained in the future.

Analogy:

  • Stock Investment: The current price of the stock you hold (immediate state) is one thing, but you care more about how much return this stock can bring you in the future and how big its “potential” is. This “potential” is its “value”. When AI makes decisions, just like an investor, it sees not only the current “immediate return” but also assesses the “long-term total value” brought by a “state” or “action”.
  • Playing Games: When playing strategy games like Chess, the current board situation (a state) itself has no direct score. But you will judge whether this situation is “good” or “bad” because it may lead to victory (high value) or defeat (low value). Here, the “good or bad” is what the value function is assessing.

So, the Value Function doesn’t tell you “what you can get immediately”, but tells you “in the long run, is this good or bad, and how much return can you get”.

II. Why Do We Need a Value Function? — Guiding AI to Make Wise Choices

When AI makes decisions in complex environments, it often acts like a toddler learning to walk and needs guidance. Its goal is usually to maximize the total reward it can get. But relying solely on immediate rewards is often not enough, because immediate “sweetness” may lead to long-term “bitterness”. The role of the value function lies in:

  1. Assessing Pros and Cons: Helps AI judge how “good” the current state is, or how “good” it is to take a certain action in the current state.
  2. Planning for the Future: It allows AI to “look ahead” rather than just “living in the moment”. By considering future rewards, AI can choose actions that seem bad in the short term but yield rich returns in the long term. For example, in a game, sacrificing a small pawn for layout is a “loss” in the short term, but the value function will tell AI that this may bring greater “value”.
  3. Guiding Learning: When AI learns through trial and error, the value function is its “learning guide”. It updates its assessment of the “value” of different states or actions based on the rewards fed back from the environment after its actions, thereby gradually learning what the optimal strategy is.

III. Classification of Value Functions: State Value vs. Action Value

In Reinforcement Learning, value functions are usually divided into two main types:

  1. State-Value Function (V(s)):

    • Analogy: Imagine you are traveling in a city. Whenever you arrive at a place (a “state”), you ask yourself: “Starting from here, how happy can I be, how many beautiful sceneries can I see, and how many total travel experience points can I get?” This score is the “state value” of this “place”.
    • Meaning: It assesses the long-term value of a state itself, that is, if AI starts from a state s and follows a certain strategy (i.e., a set of action rules) all the way, what is the expected future cumulative reward it can get.

  2. Action-Value Function (Q(s,a)):

    • Analogy: Also traveling, you arrive at a place (state s), and now there are multiple choices: take the subway (action a1), take a taxi (action a2), or walk (action a3). You will assess “How many experience points can I get in total if I take the subway from here?” or “How many experience points can I get in total if I take a taxi from here?”, etc. These are the “action values” of different “actions”.
    • Meaning: It assesses the future cumulative reward that can be obtained by taking a certain action a in a certain state s and then continuing to follow a certain strategy. The Action-Value Function is particularly important for AI to choose specific actions.

IV. How Does the Value Function “Learn” and “Calculate”?

AI gradually “learns” and “estimates” these value functions by constantly interacting with the environment, trying various actions, and observing the rewards obtained. This process is similar to humans accumulating wisdom through experience. Among them, the Bellman Equation is the basic mathematical tool for calculating and updating value functions. It relates the value of a state to the value of possible future states, forming a recursive relationship.

Understanding Bellman Equation simply:

The “value” of your current position equals the immediate reward you get, plus the “discounted” value of the next position you will reach. It is “discounted” because future events have higher uncertainty, and we usually value immediate gains more.

AI repeats this calculation and update process, just like a person constantly reviewing their decisions and summarizing lessons learned, and finally can find an optimal “value map” to know how to act in any situation to maximize long-term benefits.

V. Latest Development: Evolution and Application of Value Functions

Value functions remain a key driving force in modern AI, especially in the field of Reinforcement Learning.

  • Deep Learning and Value Functions: With the development of deep learning, researchers began to use neural networks to approximate complex value functions. This allows AI to handle larger and more abstract state spaces, such as learning the value of a chess game directly from game screens, or judging the “good or bad” of the environment where an autonomous vehicle is located from raw sensor data.
  • Multi-Agent Reinforcement Learning: In scenarios where multiple AI agents collaborate or compete with each other, value functions are also extended and applied. Each agent has its own value assessment system to achieve overall optimality or maximize individual interests.
  • Value Concepts in Large Language Models: Interestingly, although not exactly the same, similar core concepts of value functions are also being explored in some of the latest research on large language models. For example, a study from HKUST found that in mathematical reasoning tasks, choosing the optimal action by evaluating the “value function of a random policy” even surpassed complex algorithms. This study shows that deep understanding of the problem essence and using simplified methods to utilize the “value” concept can bring unexpected results. In addition, large tech companies like Meta are also using AI infrastructure investments to create value, such as improving ad conversion rates through AI-driven recommendation models. There are also researches exploring how to let AI engineers better use AI, through methods like “Specification-Driven Development” and “Agentic AI”, letting AI assist in code development as a junior partner with “value” judgment to solve complex problems.
  • Enterprise Value Creation: From a macro perspective, AI technology is helping enterprises create huge value in multiple functional areas, such as improving efficiency and effectiveness in marketing, sales, product development, service operations, etc. Enterprises are redesigning workflows and setting AI investment goals to obtain extraordinary value from AI.

Conclusion: AI’s “Wisdom Guide”

The Value Function, a concept that sounds somewhat abstract in the AI field, is actually like AI’s “wisdom compass” and “scorecard”. It allows AI to transcend immediate gains and losses, learn to be “far-sighted”, and make truly “wise” long-term decisions in complex environments. From automatic game playing to assisted decision-making, and then to driving complex automation systems, the Value Function silently guides AI behind the scenes, making it smarter, more capable, and creating more value for our lives. In the future, with the continuous evolution of AI technology, the exploration and application of Value Functions will undoubtedly usher in more breakthroughs and innovations.