Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds

• URL: http://arxiv.org/abs/2311.03760v3
• Date: Tue, 4 Jun 2024 12:56:46 GMT
• Title: Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds
• Authors: Shion Takeno, Yu Inatsu, Masayuki Karasuyama, Ichiro Takeuchi,
• Abstract summary: Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR) We show that PIMS achieves the tighter BCR bound and avoids the hyper parameter tuning, unlike GP-UCB. We demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.
• Score: 22.752728853701083
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR). Recently, it has been shown that a randomized variant of GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the tighter BCR bound for brevity. Inspired by this study, this paper first shows that TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often practically suffer from manual hyperparameter tuning and over-exploration issues, respectively. Therefore, we analyze yet another AF called a probability of improvement from the maximum of a sample path (PIMS). We show that PIMS achieves the tighter BCR bound and avoids the hyperparameter tuning, unlike GP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.

Related papers

• Regret Analysis for Randomized Gaussian Process Upper Confidence Bound [9.967062483758632]
  This paper analyzes the randomized variant of GP-UCB called improved randomized GP-UCB. In both regret analyses, IRGP-UCB achieves a sub-linear regret upper bound without increasing the confidence parameter if the input domain is finite.
  arXiv  Detail & Related papers  (2024-09-02T06:49:29Z)
• Poisson Process for Bayesian Optimization [126.51200593377739]
  We propose a ranking-based surrogate model based on the Poisson process and introduce an efficient BO framework, namely Poisson Process Bayesian Optimization (PoPBO) Compared to the classic GP-BO method, our PoPBO has lower costs and better robustness to noise, which is verified by abundant experiments.
  arXiv  Detail & Related papers  (2024-02-05T02:54:50Z)
• Bayesian Analysis of Combinatorial Gaussian Process Bandits [6.594362025904486]
  We provide novel cumulative regret bounds for three GP-based algorithms: GP-UCB, GP-BayesUCB and GP-TS. We employ our framework to address the challenging real-world problem of online energy-efficient navigation.
  arXiv  Detail & Related papers  (2023-12-20T00:31:43Z)
• Regret Optimality of GP-UCB [12.323109084902228]
  Gaussian Process Upper Confidence Bound (GP-UCB) is one of the most popular methods for optimizing black-box functions with noisy observations. We establish new upper bounds on both the simple and cumulative regret of GP-UCB when the objective function to optimize admits certain smoothness property. With the same level of exploration, GP-UCB can simultaneously achieve optimality in both simple and cumulative regret.
  arXiv  Detail & Related papers  (2023-12-03T13:20:08Z)
• On the Sublinear Regret of GP-UCB [58.25014663727544]
  We show that the Gaussian Process Upper Confidence Bound (GP-UCB) algorithm enjoys nearly optimal regret rates. Our improvements rely on a key technical contribution -- regularizing kernel ridge estimators in proportion to the smoothness of the underlying kernel.
  arXiv  Detail & Related papers  (2023-07-14T13:56:11Z)
• Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds [9.89553853547974]
  This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. We propose improved RGP-UCB based on a two- parameter exponential distribution, which achieves tighter Bayesian regret bounds. We demonstrate the effectiveness of IRGP-UCB through extensive experiments.
  arXiv  Detail & Related papers  (2023-02-03T02:48:48Z)
• Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processes [48.09817971375995]
  We introduce DPP-Batch Bayesian Optimization (DPP-BBO), a universal framework for inducing batch diversity in sampling based BO. We illustrate this framework by formulating DPP-Thompson Sampling (DPP-TS) as a variant of the popular Thompson Sampling (TS) algorithm and introducing a Markov Chain Monte Carlo procedure to sample.
  arXiv  Detail & Related papers  (2021-10-22T08:51:28Z)
• Likelihood-Free Inference with Deep Gaussian Processes [70.74203794847344]
  Surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. We propose a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. Our experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases.
  arXiv  Detail & Related papers  (2020-06-18T14:24:05Z)
• Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisation [60.93091603232817]
  We develop a modified Gaussian process upper confidence bound (GP-UCB) acquisition function. This is done by sampling the exploration-exploitation trade-off parameter from a distribution. We prove that this allows the expected trade-off parameter to be altered to better suit the problem without compromising a bound on the function's Bayesian regret.
  arXiv  Detail & Related papers  (2020-06-08T00:28:41Z)
• Near-linear Time Gaussian Process Optimization with Adaptive Batching and Resparsification [119.41129787351092]
  We introduce BBKB, the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. We show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation, achieving a near-constant per-step amortized cost.
  arXiv  Detail & Related papers  (2020-02-23T17:43:29Z)

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.