Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation
The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood that identifies a probability measure which lies in the neighborhood of the nominal measure and that maximizes the probability of observing the given sample point. We show that when the neighborhood is constructed by the Kullback-Leibler divergence, by moment conditions or by the Wasserstein distance, then our \textit{optimistic likelihood} can be determined through the solution of a convex optimization problem, and it admits an analytical expression in particular cases. We also show that the posterior inference problem with our optimistic likelihood approximation enjoys strong theoretical performance guarantees, and it performs competitively in a probabilistic classification task.
Code (1)
Similar Papers 제목 키워드 기반
Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotical…
Stochastic OptimizationA data-driven approach to beating SAA out-of-sample
While solutions of Distributionally Robust Optimization (DRO) problems can sometimes have a higher out-of-sample expected reward than the Sample Average Approximation (SAA), there is no guarantee. In this paper, we intro…
Optimistic Distributionally Robust Policy Optimization
Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), as the widely employed policy based reinforcement learning (RL) methods, are prone to converge to a sub-optimal solution as they limit the p…
reinforcement-learningReinforcement Learning (RL)Optimistic Policy Optimization with General Function Approximations
Although policy optimization with neural networks has a track record of achieving state-of-the-art results in reinforcement learning on various domains, the theoretical understanding of the computational and sample effic…
reinforcement-learningReinforcement Learning (RL)Distributionally Robust Chance Constrained Programming with Generative Adversarial Networks (GANs)
This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed…
Generative Adversarial Network