Combinatorial Black-Box Optimization with Expert Advice

• URL: http://arxiv.org/abs/2006.03963v2
• Date: Tue, 13 Oct 2020 20:00:44 GMT
• Title: Combinatorial Black-Box Optimization with Expert Advice
• Authors: Hamid Dadkhahi, Karthikeyan Shanmugam, Jesus Rios, Payel Das, Samuel Hoffman, Troy David Loeffler, Subramanian Sankaranarayanan
• Abstract summary: We consider the problem of black-box function optimization over the hypercube. We propose a computationally efficient model learning algorithm based on multilinears and exponential weight updates.
• Score: 28.45580493454314
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of black-box function optimization over the boolean hypercube. Despite the vast literature on black-box function optimization over continuous domains, not much attention has been paid to learning models for optimization over combinatorial domains until recently. However, the computational complexity of the recently devised algorithms are prohibitive even for moderate numbers of variables; drawing one sample using the existing algorithms is more expensive than a function evaluation for many black-box functions of interest. To address this problem, we propose a computationally efficient model learning algorithm based on multilinear polynomials and exponential weight updates. In the proposed algorithm, we alternate between simulated annealing with respect to the current polynomial representation and updating the weights using monomial experts' advice. Numerical experiments on various datasets in both unconstrained and sum-constrained boolean optimization indicate the competitive performance of the proposed algorithm, while improving the computational time up to several orders of magnitude compared to state-of-the-art algorithms in the literature.

Related papers

• Approximating Metric Magnitude of Point Sets [4.522729058300309]
  Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization algorithms. In this paper, we study the magnitude problem, and show efficient ways of approximating it. We show that it can be cast as a convex optimization problem, but not as a submodular optimization. The paper describes two new algorithms - an iterative approximation algorithm that converges fast and is accurate, and a subset selection method that makes the computation even faster.
  arXiv  Detail & Related papers  (2024-09-06T17:15:28Z)
• An Efficient Algorithm for Clustered Multi-Task Compressive Sensing [60.70532293880842]
  Clustered multi-task compressive sensing is a hierarchical model that solves multiple compressive sensing tasks. The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions. We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices.
  arXiv  Detail & Related papers  (2023-09-30T15:57:14Z)
• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Neural-BO: A Black-box Optimization Algorithm using Deep Neural Networks [12.218039144209017]
  We propose a novel black-box optimization algorithm where the black-box function is modeled using a neural network. Our algorithm does not need a Bayesian neural network to estimate predictive uncertainty and is therefore computationally favorable.
  arXiv  Detail & Related papers  (2023-03-03T02:53:56Z)
• Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces [54.58348769621782]
  Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.
  arXiv  Detail & Related papers  (2022-07-02T16:59:37Z)
• Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms [9.245687221460654]
  Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrixing based on a noisy monotone Toeplitz matrix model. We establish fundamental statistical limit for this problem in a decision-theoretic framework and demonstrate that a constrained least squares rate. To address this, we propose a novel-time adaptive sorting algorithm with guaranteed performance improvement.
  arXiv  Detail & Related papers  (2022-01-17T14:53:52Z)
• Minimax Optimization with Smooth Algorithmic Adversaries [59.47122537182611]
  We propose a new algorithm for the min-player against smooth algorithms deployed by an adversary. Our algorithm is guaranteed to make monotonic progress having no limit cycles, and to find an appropriate number of gradient ascents.
  arXiv  Detail & Related papers  (2021-06-02T22:03:36Z)
• Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks [0.0]
  We present a new class of Langevin based algorithms, which overcomes many of the known shortcomings of popular adaptive vanishing algorithms. In particular, we provide a nonasymptotic analysis and full theoretical guarantees for the convergence properties of an algorithm of this novel class, which we named TH$varepsilon$O POULA (or, simply, TheoPouLa)
  arXiv  Detail & Related papers  (2021-05-28T15:58:48Z)
• Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information [78.78486761923855]
  In many real world problems, we want to infer some property of an expensive black-box function f, given a budget of T function evaluations. We present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm's output. On these problems, InfoBAX uses up to 500 times fewer queries to f than required by the original algorithm.
  arXiv  Detail & Related papers  (2021-04-19T17:22:11Z)
• Meta Learning Black-Box Population-Based Optimizers [0.0]
  We propose the use of meta-learning to infer population-based blackbox generalizations. We show that the meta-loss function encourages a learned algorithm to alter its search behavior so that it can easily fit into a new context.
  arXiv  Detail & Related papers  (2021-03-05T08:13:25Z)
• Divide and Learn: A Divide and Conquer Approach for Predict+Optimize [50.03608569227359]
  The predict+optimize problem combines machine learning ofproblem coefficients with a optimization prob-lem that uses the predicted coefficients. We show how to directlyexpress the loss of the optimization problem in terms of thepredicted coefficients as a piece-wise linear function. We propose a novel divide and algorithm to tackle optimization problems without this restriction and predict itscoefficients using the optimization loss.
  arXiv  Detail & Related papers  (2020-12-04T00:26:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.