Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBayesian Posterior Sampling via Stochastic Gradient Fisher Scoring
147
0
0.0
(
0
)
Authors
Sungjin Ahn
Ask ChatGPT about the research
No Arabic abstract
In this paper we address the following question: Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?. An algorithm based on the Langevin equation with stochastic gradients (SGLD) was previously proposed to solve this, but its mixing rate was slow. By leveraging the Bayesian Central Limit Theorem, we extend the SGLD algorithm so that at high mixing rates it will sample from a normal approximation of the posterior, while for slow mixing rates it will mimic the behavior of SGLD with a pre-conditioner matrix. As a bonus, the proposed algorithm is reminiscent of Fisher scoring (with stochastic gradients) and as such an efficient optimizer during burn-in.
rate research
Read More
We consider the problem of online reinforcement learning for the Stochastic Shortest Path (SSP) problem modeled as an unknown MDP with an absorbing state. We propose PSRL-SSP, a simple posterior sampling-based reinforcement learning algorithm for the SSP problem. The algorithm operates in epochs. At the beginning of each epoch, a sample is drawn from the posterior distribution on the unknown model dynamics, and the optimal policy with respect to the drawn sample is followed during that epoch. An epoch completes if either the number of visits to the goal state in the current epoch exceeds that of the previous epoch, or the number of visits to any of the state-action pairs is doubled. We establish a Bayesian regret bound of $O(B_star Ssqrt{AK})$, where $B_star$ is an upper bound on the expected cost of the optimal policy, $S$ is the size of the state space, $A$ is the size of the action space, and $K$ is the number of episodes. The algorithm only requires the knowledge of the prior distribution, and has no hyper-parameters to tune. It is the first such posterior sampling algorithm and outperforms numerically previously proposed optimism-based algorithms.
Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.
In this paper, we propose Posterior Sampling Reinforcement Learning for Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that achieves Bayesian regret bound of $O(HSsqrt{AT})$ in the infinite-horizon zero-sum stochastic games with average-reward criterion. Here $H$ is an upper bound on the span of the bias function, $S$ is the number of states, $A$ is the number of joint actions and $T$ is the horizon. We consider the online setting where the opponent can not be controlled and can take any arbitrary time-adaptive history-dependent strategy. This improves the best existing regret bound of $O(sqrt[3]{DS^2AT^2})$ by Wei et. al., 2017 under the same assumption and matches the theoretical lower bound in $A$ and $T$.
We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements and emph{any} prior distribution on the signal, that the posterior sampling estimator achieves near-optimal recovery guarantees. Moreover, this result is robust to model mismatch, as long as the distribution estimate (e.g., from an invertible generative model) is close to the true distribution in Wasserstein distance. We implement the posterior sampling estimator for deep generative priors using Langevin dynamics, and empirically find that it produces accurate estimates with more diversity than MAP.
Thompson sampling is a heuristic algorithm for the multi-armed bandit problem which has a long tradition in machine learning. The algorithm has a Bayesian spirit in the sense that it selects arms based on posterior samples of reward probabilities of each arm. By forging a connection between combinatorial binary bandits and spike-and-slab variable selection, we propose a stochastic optimization approach to subset selection called Thompson Variable Selection (TVS). TVS is a framework for interpretable machine learning which does not rely on the underlying model to be linear. TVS brings together Bayesian reinforcement and machine learning in order to extend the reach of Bayesian subset selection to non-parametric models and large datasets with very many predictors and/or very many observations. Depending on the choice of a reward, TVS can be deployed in offline as well as online setups with streaming data batches. Tailoring multiplay bandits to variable selection, we provide regret bounds without necessarily assuming that the arm mean rewards be unrelated. We show a very strong empirical performance on both simulated and real data. Unlike deterministic optimization methods for spike-and-slab variable selection, the stochastic nature makes TVS less prone to local convergence and thereby more robust.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
