A new polynomial-time algorithm for linear programming
Combinatorica
Learning linear threshold functions in the presence of classification noise
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
A new algorithm for minimizing convex functions over convex sets
Mathematical Programming: Series A and B
Solving convex programs by random walks
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Smoothed analysis of the perceptron algorithm for linear programming
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Perceptron, Winnow, and PAC Learning
SIAM Journal on Computing
Learning noisy perceptrons by a perceptron in polynomial time
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Perceptrons: An Introduction to Computational Geometry
Perceptrons: An Introduction to Computational Geometry
A randomized polynomial-time simplex algorithm for linear programming
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Boundedness Theorems for the Relaxation Method
Mathematics of Operations Research
Iteratively constructing preconditioners via the conjugate gradient method
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Evolvability from learning algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On exact learning halfspaces with random consistent hypothesis oracle
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Randomized relaxation methods for the maximum feasible subsystem problem
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
A complete characterization of statistical query learning with applications to evolvability
Journal of Computer and System Sciences
Sublinear optimization for machine learning
Journal of the ACM (JACM)
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The perceptron algorithm, developed mainly in the machine learning literature, is a simple greedy method for finding a feasible solution to a linear program (alternatively, for learning a threshold function. ). In spite of its exponential worst-case complexity, it is often quite useful, in part due to its noise-tolerance and also its overall simplicity. In this paper, we show that a randomized version of the perceptron algorithm with periodic rescaling runs in polynomial-time. The resulting algorithm for linear programming has an elementary description and analysis.