arXiv subjects

Yijie Peng

Publications and source records attributed to Yijie Peng.

53 records · Page 3Linked to original sources

arXiv2023

Top-Two Thompson Sampling for Contextual Top-mc Selection Problems

We aim to efficiently allocate a fixed simulation budget to identify the top-mc designs for each context among a finite number of contexts. The performance of each design under a context is measured by an identifiable statistical characteristic, possibly with the existence of nuisance parameters. Under a Bayesian framework, we extend the top-two Thompson sampling method designed for selecting the best design in a single context to the contextual top-mc selection problems, leading to an efficient sampling policy that simultaneously allocates simulation samples to both contexts and designs. To demonstrate the asymptotic optimality of the proposed sampling policy, we characterize the exponential convergence rate of the posterior distribution for a wide range of identifiable sampling distribution families. The proposed sampling policy is proved to be consistent, and asymptotically satisfies a necessary condition for optimality. In particular, when selecting contextual best designs (i.e., mc = 1), the proposed sampling policy is proved to be asymptotically optimal. Numerical experiments demonstrate the good finite sample performance of the proposed sampling policy.

stat.ME↗

arXiv2023

Efficient Learning for Selecting Top-m Context-Dependent Designs

We consider a simulation optimization problem for a context-dependent decision-making, which aims to determine the top-m designs for all contexts. Under a Bayesian framework, we formulate the optimal dynamic sampling decision as a stochastic dynamic programming problem, and develop a sequential sampling policy to efficiently learn the performance of each design under each context. The asymptotically optimal sampling ratios are derived to attain the optimal large deviations rate of the worst-case of probability of false selection. The proposed sampling policy is proved to be consistent and its asymptotic sampling ratios are asymptotically optimal. Numerical experiments demonstrate that the proposed method improves the efficiency for selection of top-m context-dependent designs.

stat.ML↗

arXiv2023

A Novel Noise Injection-based Training Scheme for Better Model Robustness

Noise injection-based method has been shown to be able to improve the robustness of artificial neural networks in previous work. In this work, we propose a novel noise injection-based training scheme for better model robustness. Specifically, we first develop a likelihood ratio method to estimate the gradient with respect to both synaptic weights and noise levels for stochastic gradient descent training. Then, we design an approximation for the vanilla noise injection-based training method to reduce memory and improve computational efficiency. Next, we apply our proposed scheme to spiking neural networks and evaluate the performance of classification accuracy and robustness on MNIST and Fashion-MNIST datasets. Experiment results show that our proposed method achieves a much better performance on adversarial robustness and slightly better performance on original accuracy, compared with the conventional gradient-based training method.

cs.LG↗

arXiv2023

Quantile-Based Deep Reinforcement Learning using Two-Timescale Policy Gradient Algorithms

Classical reinforcement learning (RL) aims to optimize the expected cumulative reward. In this work, we consider the RL setting where the goal is to optimize the quantile of the cumulative reward. We parameterize the policy controlling actions by neural networks, and propose a novel policy gradient algorithm called Quantile-Based Policy Optimization (QPO) and its variant Quantile-Based Proximal Policy Optimization (QPPO) for solving deep RL problems with quantile objectives. QPO uses two coupled iterations running at different timescales for simultaneously updating quantiles and policy parameters, whereas QPPO is an off-policy version of QPO that allows multiple updates of parameters during one simulation episode, leading to improved algorithm efficiency. Our numerical results indicate that the proposed algorithms outperform the existing baseline algorithms under the quantile criterion.

cs.LG↗

arXiv2022

An Efficient Dynamic Sampling Policy For Monte Carlo Tree Search

We consider the popular tree-based search strategy within the framework of reinforcement learning, the Monte Carlo Tree Search (MCTS), in the context of finite-horizon Markov decision process. We propose a dynamic sampling tree policy that efficiently allocates limited computational budget to maximize the probability of correct selection of the best action at the root node of the tree. Experimental results on Tic-Tac-Toe and Gomoku show that the proposed tree policy is more efficient than other competing methods.

cs.AI↗

arXiv2022

Quantile-Based Policy Optimization for Reinforcement Learning

Classical reinforcement learning (RL) aims to optimize the expected cumulative rewards. In this work, we consider the RL setting where the goal is to optimize the quantile of the cumulative rewards. We parameterize the policy controlling actions by neural networks and propose a novel policy gradient algorithm called Quantile-Based Policy Optimization (QPO) and its variant Quantile-Based Proximal Policy Optimization (QPPO) to solve deep RL problems with quantile objectives. QPO uses two coupled iterations running at different time scales for simultaneously estimating quantiles and policy parameters and is shown to converge to the global optimal policy under certain conditions. Our numerical results demonstrate that the proposed algorithms outperform the existing baseline algorithms under the quantile criterion.

cs.LG↗

arXiv2022

Efficient Distributed Learning in Stochastic Non-cooperative Games without Information Exchange

In this work, we study stochastic non-cooperative games, where only noisy black-box function evaluations are available to estimate the cost function for each player. Since each player's cost function depends on both its own decision variables and its rivals' decision variables, local information needs to be exchanged through a center/network in most existing work for seeking the Nash equilibrium. We propose a new stochastic distributed learning algorithm that does not require communications among players. The proposed algorithm uses simultaneous perturbation method to estimate the gradient of each cost function, and uses mirror descent method to search for the Nash equilibrium. We provide asymptotic analysis for the bias and variance of gradient estimates, and show the proposed algorithm converges to the Nash equilibrium in mean square for the class of strictly monotone games at a rate faster than the existing algorithms. The effectiveness of the proposed method is buttressed in a numerical experiment.

cs.GT↗

arXiv2021

Asymptotically Optimal Sampling Policy for Selecting Top-m Alternatives

We consider selecting the top-$m$ alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a sequential sampling policy that maximizes a value function approximation one-step look ahead. To show the asymptotic optimality of the proposed procedure, the asymptotically optimal sampling ratios which optimize large deviations rate of the probability of false selection for selecting top-$m$ alternatives has been rigorously defined. The proposed sampling policy is not only proved to be consistent but also achieves the asymptotically optimal sampling ratios. Numerical experiments demonstrate superiority of the proposed allocation procedure over existing ones.

math.OC↗

arXiv2021

Efficient Sampling Policy for Selecting a Good Enough Subset

The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good subset. We formulate the dynamic sampling decision as a stochastic control problem in a Bayesian setting. In an approximate dynamic programming paradigm, we propose a sequential sampling policy based on value function approximation. We analyze the asymptotic property of the proposed sampling policy. Numerical experiments demonstrate the efficiency of the proposed procedure.

math.OC↗

arXiv2021

Pathological Image Segmentation with Noisy Labels

Segmentation of pathological images is essential for accurate disease diagnosis. The quality of manual labels plays a critical role in segmentation accuracy; yet, in practice, the labels between pathologists could be inconsistent, thus confusing the training process. In this work, we propose a novel label re-weighting framework to account for the reliability of different experts' labels on each pixel according to its surrounding features. We further devise a new attention heatmap, which takes roughness as prior knowledge to guide the model to focus on important regions. Our approach is evaluated on the public Gleason 2019 datasets. The results show that our approach effectively improves the model's robustness against noisy labels and outperforms state-of-the-art approaches.

eess.IV↗

arXiv2021

Noise Optimization for Artificial Neural Networks

Adding noises to artificial neural network(ANN) has been shown to be able to improve robustness in previous work. In this work, we propose a new technique to compute the pathwise stochastic gradient estimate with respect to the standard deviation of the Gaussian noise added to each neuron of the ANN. By our proposed technique, the gradient estimate with respect to noise levels is a byproduct of the backpropagation algorithm for estimating gradient with respect to synaptic weights in ANN. Thus, the noise level for each neuron can be optimized simultaneously in the processing of training the synaptic weights at nearly no extra computational cost. In numerical experiments, our proposed method can achieve significant performance improvement on robustness of several popular ANN structures under both black box and white box attacks tested in various computer vision datasets.

cs.LG↗

arXiv2020

Context-dependent Ranking and Selection under a Bayesian Framework

We consider a context-dependent ranking and selection problem. The best design is not universal but depends on the contexts. Under a Bayesian framework, we develop a dynamic sampling scheme for context-dependent optimization (DSCO) to efficiently learn and select the best designs in all contexts. The proposed sampling scheme is proved to be consistent. Numerical experiments show that the proposed sampling scheme significantly improves the efficiency in context-dependent ranking and selection.

stat.ME↗

arXiv2020

Efficient Learning for Clustering and Optimizing Context-Dependent Designs

We consider a simulation optimization problem for a context-dependent decision-making. A Gaussian mixture model is proposed to capture the performance clustering phenomena of context-dependent designs. Under a Bayesian framework, we develop a dynamic sampling policy to efficiently learn both the global information of each cluster and local information of each design for selecting the best designs in all contexts. The proposed sampling policy is proved to be consistent and achieve the asymptotically optimal sampling ratio. Numerical experiments show that the proposed sampling policy significantly improves the efficiency in context-dependent simulation optimization.

stat.ME↗

arXiv2020

Optimal Unbiased Estimation for Expected Cumulative Cost

We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the random horizon are given, and explicit expressions for the optimal random truncation level are obtained, leading to a full analysis of the bias-variance tradeoff when comparing this new class of randomized estimators with traditional fixed truncation estimators. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. This comparison provides guidance on when to choose randomized estimators over fixed truncation estimators in practice. Numerical experiments substantiate the theoretical results.

math.NA↗

arXiv2019

Training Artificial Neural Networks by Generalized Likelihood Ratio Method: Exploring Brain-like Learning to Improve Robustness

In this work, we propose a generalized likelihood ratio method capable of training the artificial neural networks with some biological brain-like mechanisms,.e.g., (a) learning by the loss value, (b) learning via neurons with discontinuous activation and loss functions. The traditional back propagation method cannot train the artificial neural networks with aforementioned brain-like learning mechanisms. Numerical results show that the robustness of various artificial neural networks trained by the new method is significantly improved when the input data is affected by both the natural noises and adversarial attacks. Code is available: \url{https://github.com/LX-doctorAI/GLR_ADV} .

cs.LG↗

arXiv2019

Efficient Sampling for Selecting Important Nodes in Random Network

We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the corresponding nodes in a Markov chain defined over the network, as in Google's PageRank. Unlike deterministic network, the transition probabilities in random network are unknown but can be estimated by sampling. Under a Bayesian learning framework, we apply the first-order Taylor expansion and normal approximation to provide a computationally efficient posterior approximation of the stationary probabilities. In order to maximize the probability of correct selection, we propose a dynamic sampling procedure which uses not only posterior means and variances of certain interaction parameters between different nodes, but also the sensitivities of the stationary probabilities with respect to each interaction parameter. Numerical experiment results demonstrate the superiority of the proposed sampling procedure.

stat.ME↗

arXiv2017

Ranking and Selection as Stochastic Control

Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this policy is not only computationally efficient but also possesses both one-step-ahead and asymptotic optimality for independent normal sampling distributions. Moreover, the proposed allocation policy is easily generalizable in the approximate dynamic programming paradigm.

cs.LG↗