Parallelized Acquisition for Active Learning using Monte Carlo Sampling

• URL: http://arxiv.org/abs/2305.19267v1
• Date: Tue, 30 May 2023 17:57:34 GMT
• Title: Parallelized Acquisition for Active Learning using Monte Carlo Sampling
• Authors: Jes\'us Torrado, Nils Sch\"oneberg, Jonas El Gammal
• Abstract summary: Recent attention has been directed towards the use of emulators of the posterior based on Gaussian Process (GP) regression. We show how to generate a Monte Carlo sample of the posterior using almost-embarrassingly parallel sequential samplers. The resulting nearly-sorted Monte Carlo sample is used to generate a batch of candidates ranked according to their sequentially conditioned acquisition function values.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian inference remains one of the most important tool-kits for any scientist, but increasingly expensive likelihood functions are required for ever-more complex experiments, raising the cost of generating a Monte Carlo sample of the posterior. Recent attention has been directed towards the use of emulators of the posterior based on Gaussian Process (GP) regression combined with active sampling to achieve comparable precision with far fewer costly likelihood evaluations. Key to this approach is the batched acquisition of proposals, so that the true posterior can be evaluated in parallel. This is usually achieved via sequential maximization of the highly multimodal acquisition function. Unfortunately, this approach parallelizes poorly and is prone to getting stuck in local maxima. Our approach addresses this issue by generating nearly-optimal batches of candidates using an almost-embarrassingly parallel Nested Sampler on the mean prediction of the GP. The resulting nearly-sorted Monte Carlo sample is used to generate a batch of candidates ranked according to their sequentially conditioned acquisition function values at little cost. The final sample can also be used for inferring marginal quantities. Our proposed implementation (NORA) demonstrates comparable accuracy to sequential conditioned acquisition optimization and efficient parallelization in various synthetic and cosmological inference problems.

Related papers

• Parallel simulation for sampling under isoperimetry and score-based diffusion models [56.39904484784127]
  As data size grows, reducing the iteration cost becomes an important goal. Inspired by the success of the parallel simulation of the initial value problem in scientific computation, we propose parallel Picard methods for sampling tasks. Our work highlights the potential advantages of simulation methods in scientific computation for dynamics-based sampling and diffusion models.
  arXiv  Detail & Related papers  (2024-12-10T11:50:46Z)
• Gaussian Processes Sampling with Sparse Grids under Additive Schwarz Preconditioner [6.408773096179187]
  We propose a scalable algorithm for sampling random realizations of the prior and posterior of GP models. The proposed algorithm leverages inducing points approximation with sparse grids, as well as additive Schwarz preconditioners.
  arXiv  Detail & Related papers  (2024-08-01T00:19:36Z)
• Langevin Monte Carlo for Contextual Bandits [72.00524614312002]
  Langevin Monte Carlo Thompson Sampling (LMC-TS) is proposed to directly sample from the posterior distribution in contextual bandits. We prove that the proposed algorithm achieves the same sublinear regret bound as the best Thompson sampling algorithms for a special case of contextual bandits.
  arXiv  Detail & Related papers  (2022-06-22T17:58:23Z)
• Surrogate modeling for Bayesian optimization beyond a single Gaussian process [62.294228304646516]
  We propose a novel Bayesian surrogate model to balance exploration with exploitation of the search space. To endow function sampling with scalability, random feature-based kernel approximation is leveraged per GP model. To further establish convergence of the proposed EGP-TS to the global optimum, analysis is conducted based on the notion of Bayesian regret.
  arXiv  Detail & Related papers  (2022-05-27T16:43:10Z)
• Low-variance estimation in the Plackett-Luce model via quasi-Monte Carlo sampling [58.14878401145309]
  We develop a novel approach to producing more sample-efficient estimators of expectations in the PL model. We illustrate our findings both theoretically and empirically using real-world recommendation data from Amazon Music and the Yahoo learning-to-rank challenge.
  arXiv  Detail & Related papers  (2022-05-12T11:15:47Z)
• Triangulation candidates for Bayesian optimization [0.3222802562733786]
  Bayesian optimization is a form of design to idealize input-output relationships with a suitably flexible regression model. Here we propose using candidates based a Delaunay triangulation, based on a simple conventional convex library.
  arXiv  Detail & Related papers  (2021-12-14T15:13:31Z)
• Local policy search with Bayesian optimization [73.0364959221845]
  Reinforcement learning aims to find an optimal policy by interaction with an environment. Policy gradients for local search are often obtained from random perturbations. We develop an algorithm utilizing a probabilistic model of the objective function and its gradient.
  arXiv  Detail & Related papers  (2021-06-22T16:07:02Z)
• Adaptive Sequential SAA for Solving Two-stage Stochastic Linear Programs [1.6181085766811525]
  We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage linear programs. The proposed algorithm can be stopped in finite-time to return a solution endowed with a probabilistic guarantee on quality.
  arXiv  Detail & Related papers  (2020-12-07T14:58:16Z)
• Pathwise Conditioning of Gaussian Processes [72.61885354624604]
  Conventional approaches for simulating Gaussian process posteriors view samples as draws from marginal distributions of process values at finite sets of input locations. This distribution-centric characterization leads to generative strategies that scale cubically in the size of the desired random vector. We show how this pathwise interpretation of conditioning gives rise to a general family of approximations that lend themselves to efficiently sampling Gaussian process posteriors.
  arXiv  Detail & Related papers  (2020-11-08T17:09:37Z)
• Efficiently Sampling Functions from Gaussian Process Posteriors [76.94808614373609]
  We propose an easy-to-use and general-purpose approach for fast posterior sampling. We demonstrate how decoupled sample paths accurately represent Gaussian process posteriors at a fraction of the usual cost.
  arXiv  Detail & Related papers  (2020-02-21T14:03:16Z)

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.