Probably Approximately Correct: Nature's Algorithms for Learning and Prospering in a Complex World
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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.
large prime numbers p and q, and the private key consists of the prime numbers p and q themselves. Anyone can encrypt a message intended for the recipient with the public key, but only the recipient with the aid of the retained secret private key will be able to decode it in polynomial time. To ensure that the number of potential private keys is so large that it is not practicable for the eavesdropper to simply try them all in turn, the key should be, say, a thousand-digit number, of which there
into existence as a result of concrete mechanisms operating in some environments. These mechanisms have been of two kinds, those that operate in individuals interacting with their environment, and those that operate via genetic changes over many generations. I then make two observations. First, ecorithms are defined broadly enough that they encompass any mechanistic process. This follows from the work of Turing and his contemporaries that established the principle, known as the Church-Turing
discussing thought experiments that invoke unusual or marginal situations. For example, some counterarguments to the possibility of artificial intelligence have the following form. A computer program with one instruction cannot possibly be considered conscious. But if we suppose that humans are each equivalent to a million-line program, say, and are conscious, then there must exist a minimum number of lines that qualifies for consciousness. Any specific such number is then argued to imply an
computation that is widely believed to encompass all information processing that one would think of as mechanistic. Acknowledgments As the text makes clear, this book is deeply rooted in the visionary ideas of Alan Turing. The synthesis offered here is within the framework of computational learning theory. Over the last three decades many have enriched this field, and I would particularly like to thank Dana Angluin, Avrim Blum, Andrzej Ehrenfeucht, Vitaly Feldman, Yoav Freund, David
one primary question of how complex mechanisms can arise at all within the limited time scale and resources in which they apparently have. The numerous other questions that are widely discussed by evolutionary theorists I regard as secondary to this one. The advantages offered by sex to evolution have been much debated, but evolution was far along when sex arrived on the scene. The intellectual challenge of understanding how peacocks could have acquired their elaborate plumage was much troubling