Langevin Monte Carlo for Contextual Bandits

• URL: http://arxiv.org/abs/2206.11254v1
• Date: Wed, 22 Jun 2022 17:58:23 GMT
• Title: Langevin Monte Carlo for Contextual Bandits
• Authors: Pan Xu, Hongkai Zheng, Eric Mazumdar, Kamyar Azizzadenesheli, Anima Anandkumar
• Abstract summary: 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.
• Score: 72.00524614312002
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, which is inefficient to sample in high dimensional applications for general covariance matrices. Moreover, the Gaussian approximation may not be a good surrogate for the posterior distribution for general reward generating functions. We propose an efficient posterior sampling algorithm, viz., Langevin Monte Carlo Thompson Sampling (LMC-TS), that uses Markov Chain Monte Carlo (MCMC) methods to directly sample from the posterior distribution in contextual bandits. Our method is computationally efficient since it only needs to perform noisy gradient descent updates without constructing the Laplace approximation of the posterior distribution. 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, viz., linear contextual bandits. We conduct experiments on both synthetic data and real-world datasets on different contextual bandit models, which demonstrates that directly sampling from the posterior is both computationally efficient and competitive in performance.

Related papers

• Online Posterior Sampling with a Diffusion Prior [20.24212000441531]
  Posterior sampling in contextual bandits with a Gaussian prior can be implemented exactly or approximately using the Laplace approximation. In this work, we propose approximate posterior sampling algorithms for contextual bandits with a diffusion model prior.
  arXiv  Detail & Related papers  (2024-10-04T20:47:16Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• VITS : Variational Inference Thompson Sampling for contextual bandits [10.028119153832346]
  We introduce and analyze a variant of the Thompson sampling (TS) algorithm for contextual bandits. We propose a new algorithm, Varational Inference Thompson sampling VITS, based on Gaussian Variational Inference. We show that VITS achieves a sub-linear regret bound of the same order in the dimension and number of round as traditional TS for linear contextual bandit.
  arXiv  Detail & Related papers  (2023-07-19T17:53:22Z)
• Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo [104.9535542833054]
  We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL) We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.
  arXiv  Detail & Related papers  (2023-05-29T17:11:28Z)
• Thompson Sampling for High-Dimensional Sparse Linear Contextual Bandits [17.11922027966447]
  This work provides theoretical guarantees of Thompson sampling in high dimensional and sparse contextual bandits. For faster computation, we use spike-and-slab prior to model the unknown parameter and variational inference instead of MCMC.
  arXiv  Detail & Related papers  (2022-11-11T02:23:39Z)
• Thompson Sampling for Unimodal Bandits [21.514495320038712]
  We propose a Thompson Sampling algorithm for emphunimodal bandits, where the expected reward is unimodal over the partially ordered arms. For Gaussian rewards, the regret of our algorithm is $mathcalO(log T)$, which is far better than standard Thompson Sampling algorithms.
  arXiv  Detail & Related papers  (2021-06-15T14:40:34Z)
• Plug-And-Play Learned Gaussian-mixture Approximate Message Passing [71.74028918819046]
  We propose a plug-and-play compressed sensing (CS) recovery algorithm suitable for any i.i.d. source prior. Our algorithm builds upon Borgerding's learned AMP (LAMP), yet significantly improves it by adopting a universal denoising function within the algorithm. Numerical evaluation shows that the L-GM-AMP algorithm achieves state-of-the-art performance without any knowledge of the source prior.
  arXiv  Detail & Related papers  (2020-11-18T16:40:45Z)
• Analysis and Design of Thompson Sampling for Stochastic Partial Monitoring [91.22679787578438]
  We present a novel Thompson-sampling-based algorithm for partial monitoring. We prove that the new algorithm achieves the logarithmic problem-dependent expected pseudo-regret $mathrmO(log T)$ for a linearized variant of the problem with local observability.
  arXiv  Detail & Related papers  (2020-06-17T05:48:33Z)
• On Thompson Sampling with Langevin Algorithms [106.78254564840844]
  Thompson sampling for multi-armed bandit problems enjoys favorable performance in both theory and practice. It suffers from a significant limitation computationally, arising from the need for samples from posterior distributions at every iteration. We propose two Markov Chain Monte Carlo (MCMC) methods tailored to Thompson sampling to address this issue.
  arXiv  Detail & Related papers  (2020-02-23T22:35:29Z)

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.