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Can learning algorithms find a Nash equilibrium? This is a natural question for several reasons. Learning algorithms resemble the behavior of players in many naturally arising games, and thus results on the convergence or non-convergence properties of such dynamics may inform our understanding of the applicability of Nash equilibria as a plausible solution concept in some settings. A second reason...
We consider the problem of verifying the identity of a distribution: Given the description of a distribution over a discrete support p = (p1, p2,, pn) how many samples (independent draws) must one obtain from an unknown distribution, q, to distinguish, with high probability, the case that p = q from the case that the total variation distance (L1 distance) ||p -- q|| 1≥ ε?...
We show that, if truth assignments on n variables reproduce through recombination so that satisfaction of a particular Boolean function confers a small evolutionary advantage, then a polynomially large population over polynomially many generations (polynomial in n and the inverse of the initial satisfaction probability) will end up almost certainly consisting exclusively of satisfying truth assignments...
Given a set of $d$-dimensional Boolean vectors with the promise that the vectors are chosen uniformly at random with the exception of two vectors that have Pearson -- correlation (Hamming distance $d\cdot \frac{1-\rho}{2}$), how quickly can one find the two correlated vectors? We present an algorithm which, for any constants and finds the correlated...
For a broad class of practically relevant distribution properties, which includes entropy and support size, nearly all of the proposed estimators have an especially simple form. Given a set of independent samples from a discrete distribution, these estimators tally the vector of summary statistics -- the number of domain elements seen once, twice, etc. in the sample -- and output the dot product between...
Braess's Paradox is the counterintuitive fact that removing edges from a network with “selfish routing” can decreasethe latency incurred by traffic in an equilibrium flow. We prove that Braess's Paradox is likely to occur in a natural random network model: with high probability, there is a traffic rate and a set of edges whose removal improves the latency of traffic in an equilibrium flow by a constant...
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