Black-Box Methods for Restoring Monotonicity

Jul 12, 2020



In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties expected to hold in the optimum. In this work we develop algorithms that are able to restore monotonicity in the parameters of interest. Specifically, given oracle access to a possibly non monotone function, we provide an algorithm that restores monotonicity while degrading the expected value of the function by at most ϵ. The number of queries required is at most logarithmic in 1/ϵ and exponential in the number of parameters. We also give a lower bound showing that this exponential dependence is necessary. Finally, we obtain improved query complexity bounds for restoring the weaker property of k-marginal monotonicity. Under this property, every k-dimensional projection of the function is required to be monotone. The query complexity we obtain only scales exponentially with k and is polynomial in the number of parameters.



About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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