什么是“没有免费午餐定理”？（What is the No Free Lunch Theorem?）

“没有免费午餐定理”是一个在优化、机器学习和决策理论中使用的数学概念。它表明，不存在一种方法能够同样有效地解决所有优化问题。实践者必须根据具体情况选择正确的方法，才能获得最佳结果。这一发现对机器学习中的过拟合和泛化以及计算、优化和决策的复杂性具有重要意义。（The No Free Lunch Theorem is a mathematical idea used in optimization, machine learning, and decision theory. It means that no one method can solve all optimization problems similarly. Practitioners must choose the right approach for each circumstance to get the greatest outcomes. This finding has significant consequences for overfitting and generalization in machine learning and the complexity of computing, optimization, and decision-making.）

“没有免费午餐定理”的解释（Explanation of the No-free Lunch Theorem）

NFL 定理阐述了该理论及其数学上的复杂性。它指出，对于每个优化问题，如果一个程序快速解决了某一组问题，那么它必然会更慢地解决另一组问题。在处理优化问题时，不存在一种方法优于所有其他方法。（The NFL Theorem tells you about the theory and how hard the math is. It says that for each optimization problem, if a program solves one group of problems quickly, it must solve another group of problems more slowly. When handling optimization problems, no single method is better than all the others.）

与过拟合和泛化的关系（Relation to Overfitting and Generalization）

在机器学习中，“没有免费午餐定理”的一个例子是过拟合和泛化。当一个模型在一个数据集上训练过度时，它在从未见过的新数据上的表现就会很差。这就是所谓的“过拟合”。另一方面，泛化是指模型在新数据上的表现能力。“没有免费午餐定理”表明，不存在一种方法在所有数据和任务上都优于其他方法。为了实现良好的泛化，必须仔细选择方法并比较它们在特定数据集上的性能。（Overfitting and expansion are examples of the No Free Lunch Theorem in machine learning. When a model is taught too well on one data set, it doesn't do well on new data it has never seen before. The term for this is "overfitting." On the other hand, extension is how well a model works with new material it has never seen before. The No Free Lunch Theorem says no method for data and jobs is better than all others. To generalize well, you must be careful about your methods and compare how well they work on a specific dataset.）

与计算复杂度的关系（Relation to Computational Complexity）

“没有免费午餐定理”对算法的性能有影响。由于优化和机器学习方法的应用存在固有的难度，“没有免费午餐定理”影响了它们的性能。某些方法可能比其他方法更有效地解决问题。可用的存储空间和 CPU 周期可能会影响所选算法。根据“没有免费午餐定理”，在选择算法时，必须权衡程序的处理能力需求和数据损失之间的关系。（The No Free Lunch Theorem has things to say about how well things work. The No Free Lunch Theorem affects how well optimization and machine learning methods work because it is hard to figure out how to use them. Some approaches might be more effective than others in resolving the issue. The availability of storage space and CPU cycles may influence the selected algorithm. According to the No Free Lunch Theorem, while picking an algorithm, one must strike a balance between the program's processing power requirements and the data it loses.）

机器学习的实现（Implementation of Machine Learning）

“没有免费午餐定理”在机器学习中具有重要意义，因为它推翻了存在一种“万能”解决方案适用于所有情况的观点。在机器学习中，算法用于检测数据中的模式、做出决策或执行任务。然而，“没有免费午餐定理”表明，这些算法的有效性取决于具体情况和数据。某些方法在某些情况下比其他方法更有效。（The No Free Lunch Theorem is significant in machine learning because it refutes the notion that there is a "one-size-fits-all" solution that works in all cases. In machine learning, algorithms are used to detect patterns in data, make decisions, or accomplish things. On the other hand, the No Free Lunch Theorem says that these programs' value relies on the situation and the data. Some ways work better than others in some situations.）

机器学习方法，如决策树和基于规则的系统，在输入和输出之间存在明确关系时可能表现良好。当存在复杂的非线性关系时，其他方法，如深度神经网络，可能会表现得更好。“没有免费午餐定理”表明，实践者必须仔细考虑其具体情况和数据，才能选择合适的方法。（Methods for machine learning, like decision trees and rule-based systems, can work well when there are clear links between what goes in and what comes out. When complicated trades don't go in a straight line, other methods, like deep neural networks, work better. The No Free Lunch Theorem says that practitioners must think carefully about their situations and facts to choose the right way.）

对机器学习的影响（Implications for Machine Learning）

NFL 定理对机器学习具有重要影响。这表明，机器学习中的问题可能存在多种解决方法。但并非所有问题都能以多种方式解决。因此，存在多种机器学习算法，每种算法都有其优缺点。（Machine learning has a lot to do with the NFL Theorem. This shows that problems in machine learning can sometimes be fixed in multiple ways. But some problems can be solved in different ways. Because of this, there are many ways to teach a computer to learn, and each has its pros and cons.）

优化的重要性（Importance of Optimization）

努力才能获得回报。定理也有助于优化，即从一组选项中选择最佳答案。不同的优化问题需要使用不同的优化方法。尽管梯度下降法在解决凸优化问题方面非常有效，但进化算法在解决非凸优化问题方面往往优于其凸优化对应方法。在深入研究优化解决方案之前，请考虑问题的难度、适用的约束条件以及可用的计算资源。（It would help if you worked for your awards. Theorems also help with optimization, choosing the best answer from a set of options. Different optimization methods must be used when different optimization problems arise. Although gradient descent is effective in solving convex optimization issues, evolutionary approaches much outperform their convex optimization counterparts. Consider the problem's difficulty, the rules at play, and the computational resources at your disposal before diving into an optimization solution.）

对获得最佳结果的影响（Effects on Getting the Best Results）

优化是 NFL 定理影响的另一个领域。这表明，目前还没有一种优化方法能够适用于所有情况。但并非所有优化方法都是相同的。这导致了多种优化方法的出现，每种方法都有其优缺点。（Optimization is another area where the NFL Theorem has an effect. This shows that there isn't yet an optimization method that works everywhere. But not all methods for improvement are the same. This has led to the creation of many improvement methods, each with pros and cons.）

对决策的影响（Implications for Decision-Making）

NFL 定理在机器学习中具有重要意义。这表明，存在多种方法可以解决给定的机器学习问题。但是，可能存在其他方法来处理该问题。是的，存在多种教授机器新技能的方法，每种方法都有其自身的优缺点。（The NFL Theorem is important in machine learning. This exemplifies that various approaches exist for solving a given machine-learning issue. However, there may be alternative options for dealing with the matter. Yes, there are several methods for teaching machines new abilities, each with its own set of advantages and disadvantages.）

实际应用（Practical Applications）

“没有免费午餐定理”在许多领域都有用，例如机器学习、速度和决策制定。它突出了在机器学习中仔细选择算法并针对每个任务进行比较的重要性。它突出了针对特定任务选择合适优化方法的重要性。它表明，不存在一种通用的决策方法，并且不同的方法在不同的情况下可能表现得更好。（The No Free Lunch Theorem is useful in many areas, such as machine learning, speed, and decision-making. It shows how important it is in machine learning to choose algorithms carefully and compare them for each job. It shows how important it is to choose the right way to improvement for the job. It means there is no one way to make decisions and that different ways may work better in different situations.）

总的来说，“没有免费午餐定理”强调了仔细、认真地定义问题、选择方法和评估结果的重要性。（Overall, the No Free Lunch Theorem shows the importance of carefully and seriously describing problems, picking methods, and evaluating them.）

结论（Conclusion）

“没有免费午餐定理”对优化、机器学习和决策制定具有重大影响。没有一种算法能够同样有效地解决所有问题。相反，个人应该在做出决策之前全面考虑其具体情况和相关事实。这突出了清晰定义问题、选择合适的解决方案并分析结果的重要性。总之，“没有免费午餐定理”是一个强大的理论，它表明在追求理想解决方案的过程中，人们可以走多远。关键在于精确地制定问题、选择合适的解决方案并验证结果的准确性。诸如群体方法、超参数调整以及考虑问题解决的难度等方法可以帮助实践者跟踪其寻找特定问题最佳解决方案的过程。（The No Free Lunch Theorem has a big effect on efficiency, machine learning, and making decisions. No single program can give the same answer to all questions. Instead, individuals should thoroughly consider their circumstances and the facts at hand before making a decision. This demonstrates the significance of clearly describing the issue, selecting an appropriate solution, and analyzing the outcomes. In conclusion, the No Free Lunch Theorem is a powerful theory demonstrating how far one may go in pursuing an ideal solution. The key here is precision in issue formulation, appropriate solution selection, and verified accuracy of outcomes. Methods like group approaches, hyperparameter tweaking, and considering how difficult the issue is to solve may help practitioners maintain track of their search for the optimum solution to a problem.）

Someswar Pal

更新于: 2023年10月11日（Updated on: 11-Oct-2023）

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