More Like this

1. Object-Oriented Implementation and Parallelization of the Rapid Gaussian Markov Improvement Algorithm.

   Semelhago, Mark ; Nelson, Barry L. ; Song, Eunhye ; Waechter, Andreas ( December 2022 , Proceedings of the 2022 Winter Simulation Conference)

   Feng, B. ; Pedrielli, G ; Peng, Y. ; Shashaani, S. ; Song, E. ; Corlu, C. ; Lee, L. ; Chew, E. ; Roeder, T. ; Lendermann, P. (Ed.)

   The Rapid Gaussian Markov Improvement Algorithm (rGMIA) solves discrete optimization via simulation problems by using a Gaussian Markov random field and complete expected improvement as the sampling and stopping criterion. rGMIA has been created as a sequential sampling procedure run on a single processor. In this paper, we extend rGMIA to a parallel computing environment when q+1 solutions can be simulated in parallel. To this end, we introduce the q-point complete expected improvement criterion to determine a batch of q+1 solutions to simulate. This new criterion is implemented in a new object-oriented rGMIA package. 

   more » « less
2. The Swendsen-Wang Dynamics on Trees.

   Blanca, Antonio ; Chen, Zongchen ; Stefankovic, Daniel ; Vigoda, Eric ( September 2021 , Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021))

   Wootters, Mary ; Sanita, Laura (Ed.)

   The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models. This chain has proved difficult to analyze, due in part to the global nature of its updates. We present optimal bounds on the convergence rate of the Swendsen-Wang algorithm for the complete d-ary tree. Our bounds extend to the non-uniqueness region and apply to all boundary conditions. We show that the spatial mixing conditions known as Variance Mixing and Entropy Mixing, introduced in the study of local Markov chains by Martinelli et al. (2003), imply Ω(1) spectral gap and O(log n) mixing time, respectively, for the Swendsen-Wang dynamics on the d-ary tree. We also show that these bounds are asymptotically optimal. As a consequence, we establish Θ(log n) mixing for the Swendsen-Wang dynamics for all boundary conditions throughout the tree uniqueness region; in fact, our bounds hold beyond the uniqueness threshold for the Ising model, and for the q-state Potts model when q is small with respect to d. Our proofs feature a novel spectral view of the Variance Mixing condition inspired by several recent rapid mixing results on high-dimensional expanders and utilize recent work on block factorization of entropy under spatial mixing conditions. 

   more » « less
3. SMART LINEAR ALGEBRAIC OPERATIONS FOR EFFICIENT GAUSSIAN MARKOV IMPROVEMENT ALGORITHM

   Li, X ; Song, S ( December 2020 , Proceedings of the Winter Simulation Conference)

   Bae, K-H ; Feng, B ; Kim, S ; Lazarova-Molnar, S ; Zheng, Z ; Roeder, T ; Thiesing, R (Ed.)

   This paper studies computational improvement of the Gaussian Markov improvement algorithm (GMIA) whose underlying response surface model is a Gaussian Markov random field (GMRF). GMIA’s computational bottleneck lies in the sampling decision, which requires factorizing and inverting a sparse, but large precision matrix of the GMRF at every iteration. We propose smart GMIA (sGMIA) that performs expensive linear algebraic operations intermittently, while recursively updating the vectors and matrices necessary to make sampling decisions for several iterations in between. The latter iterations are much cheaper than the former at the beginning, but their costs increase as the recursion continues and ultimately surpass the cost of the former. sGMIA adaptively decides how long to continue the recursion by minimizing the average per-iteration cost. We perform a floating-point operation analysis to demonstrate the computational benefit of sGMIA. Experiment results show that sGMIA enjoys computational efficiency while achieving the same search effectiveness as GMIA. 

   more » « less
4. On Mixing of Markov Chains: Coupling, Spectral Independence, and Entropy Factorization.

   Antonio Blanca, Pietro Caputo ( January 2022 , SODA 2022)

   For general spin systems, we prove that a contractive coupling for an arbitrary local Markov chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a large class of Markov chains including the Glauber dynamics, arbitrary heat-bath block dynamics, and the Swendsen-Wang dynamics. This reveals a novel connection between probabilistic techniques for bounding the convergence to stationarity and analytic tools for analyzing the decay of relative entropy. As a corollary of our general results, we obtain O(n log n) mixing time and Ω(1/n) modified log-Sobolev constant of the Glauber dynamics for sampling random q-colorings of an n-vertex graph with constant maximum degree Δ when q > (11/6–∊0)Δ for some fixed ∊0 > 0. We also obtain O(log n) mixing time and Ω(1) modified log-Sobolev constant of the Swendsen-Wang dynamics for the ferromagnetic Ising model on an n-vertex graph of constant maximum degree when the parameters of the system lie in the tree uniqueness region. At the heart of our results are new techniques for establishing spectral independence of the spin system and block factorization of the relative entropy. On one hand we prove that a contractive coupling of any local Markov chain implies spectral independence of the Gibbs distribution. On the other hand we show that spectral independence implies factorization of entropy for arbitrary blocks, establishing optimal bounds on the modified log-Sobolev constant of the corresponding block dynamics. 

   more » « less
5. Bayesian Optimization with Ensemble Learning Models and Adaptive Expected Improvement

   https://doi.org/10.1109/ICASSP49357.2023.10095008  

   Polyzos, Konstantinos D. ; Lu, Qin ; Giannakis, Georgios B. ( June 2023 , IEEE International Conference on Acoustics, Speech, and Signal Processing)

   Optimizing a black-box function that is expensive to evaluate emerges in a gamut of machine learning and artifcial intelligence applications including drug discovery, policy optimization in robotics, and hyperparameter tuning of learning models to list a few. Bayesian optimization (BO) provides a principled framework to fnd the global optimum of such functions using a limited number of function evaluations. BO relies on a statistical surrogate model to actively select new query points, that is typically captured by a Gaussian process (GP). Unlike most existing approaches that hinge on a single GP surrogate model with a pre-selected kernel function that may confne the expressiveness of the sought function especially under the limited evaluation budget, the present work puts forth a weighted ensemble of GPs as a surrogate model. Building on the advocated Gaussian mixture (GM) posterior, the EGP framework adapts to the most ftted surrogate model as data arrive on-the-fy, offering a richer function space. For the acquisition of next evaluation points, the EGP-based posterior is coupled with an adaptive expected improvement (EI) criterion to balance exploration and exploitation of the search space. Numerical tests on a set of benchmark synthetic functions and two robotic tasks, demonstrate the impressive benefts of the proposed approach. 

   more » « less