# Probably Approximately Correct: Nature's Algorithms for Learning and Prospering in a Complex World

# Probably Approximately Correct: Nature's Algorithms for Learning and Prospering in a Complex World

## Leslie Valiant

Language: English

Pages: 208

ISBN: 0465060722

Format: PDF / Kindle (mobi) / ePub

**From a leading computer scientist, a unifying theory that will revolutionize our understanding of how life evolves and learns.**

How does life prosper in a complex and erratic world? While we know that nature follows patterns—such as the law of gravity—our everyday lives are beyond what known science can predict. We nevertheless muddle through even in the absence of theories of how to act. But how do we do it?

In *Probably Approximately Correct*, computer scientist Leslie Valiant presents a masterful synthesis of learning and evolution to show how both individually and collectively we not only survive, but prosper in a world as complex as our own. The key is “probably approximately correct” algorithms, a concept Valiant developed to explain how effective behavior can be learned. The model shows that pragmatically coping with a problem can provide a satisfactory solution in the absence of any theory of the problem. After all, finding a mate does not require a theory of mating. Valiant’s theory reveals the shared computational nature of evolution and learning, and sheds light on perennial questions such as nature versus nurture and the limits of artificial intelligence.

Offering a powerful and elegant model that encompasses life’s complexity, *Probably Approximately Correct* has profound implications for how we think about behavior, cognition, biological evolution, and the possibilities and limits of human and machine intelligence.

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or for oil in the ground. Given a particular problem, one can characterize a set of potential solutions large enough that any true solution must be in that set of candidates. For the problem of determining whether some n-digit number x can be factored, one may specify the potential solutions as the integers {2, 3,…, x − 1}. Finding the solution is simply a matter of testing each number, one by one, to see whether it divides x. Such exhaustive searches are not feasible for large values of n, for

to the patrons of the Eagle pub in Cambridge, England, that he and James Watson had discovered the “secret of life.” What they had discovered was the double-stranded helical structure of DNA, the molecule that by then was suspected to be the carrier of heredity. This structure, with the two strands containing identical information, was suggestive of the process by which cells might copy their DNA during replication. The two strands simply separate, each strand carrying all the information it

the start. Starting from an arbitrary starting point, we want convergence toward f to take place with only a modest-size population and within a modest number of generations, where by modest I mean that they are polynomially, rather than exponentially, bounded in terms of the relevant numerical parameters, such as the number of variables (e.g., proteins). Further, we want the computational cost of the algorithm A that computes the variants from the current genome to be polynomial also. The

Problems,” Annual Eugenics 7, part II (1936): 179–188. 20. Without loss of generality we can make the right-hand side of any perceptron 0 by adding an extra variable to the left-hand side and extending each example to have the fixed value 1 for this last variable. Figure 3.7 implements this idea to find the separator 3x − 6y > 1 for the six points listed in the rubric of Figure 3.6. Note that the inequality 2x − 3y > 2 illustrated there also satisfies these six examples. Chapter 4 1. Eddington

Cover, “Capacity Problems for Linear Machines,” in L. Kanal (ed.), Pattern Recognition (Washington, DC: Thompson Book Co., 1968). 11. Such a general lower bound on the number of examples needed for learning is given in A. Ehrenfeucht, D. Haussler, M. Kearns, and L. G. Valiant, “A General Lower Bound on the Number of Examples Needed for Learning,” Information and Computation 82, no. 2 (1989): 247–261. 12. The first publication of the notion of public-key cryptosystems was W. Diffie and M. E.