Author name cluster

Enlu Zhou

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

9 papers

2 author rows

AAAI Conference 2025 Conference Paper

Approximate Bilevel Difference Convex Programming for Bayesian Risk Markov Decision Processes

Yifan Lin
Enlu Zhou

We consider infinite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes be overly conservative. In this paper, we utilize the recently proposed formulation, Bayesian risk Markov Decision Process (BR-MDP), to address parameter (or epistemic) uncertainty in MDPs. To solve the infinite-horizon BR-MDP with a class of convex risk measures, we propose a computationally efficient approach called approximate bilevel difference convex programming (ABDCP). The optimization is performed offline and produces the optimal policy that is represented as a finite state controller with desirable performance guarantees. We also demonstrate the empirical performance of the BR-MDP formulation and the proposed algorithm.

PDF Details DOI

NeurIPS Conference 2023 Conference Paper

Bayesian Risk-Averse Q-Learning with Streaming Observations

Yuhao Wang
Enlu Zhou

We consider a robust reinforcement learning problem, where a learning agent learns from a simulated training environment. To account for the model mis-specification between this training environment and the true environment due to lack of data, we adopt a formulation of Bayesian risk MDP (BRMDP) with infinite horizon, which uses Bayesian posterior to estimate the transition model and impose a risk functional to account for the model uncertainty. Observations from the real environment that is out of the agent's control arrive periodically and are utilized by the agent to update the Bayesian posterior to reduce model uncertainty. We theoretically demonstrate that BRMDP balances the trade-off between robustness and conservativeness, and we further develop a multi-stage Bayesian risk-averse Q-learning algorithm to solve BRMDP with streaming observations from real environment. The proposed algorithm learns a risk-averse yet optimal policy that depends on the availability of real-world observations. We provide a theoretical guarantee of strong convergence for the proposed algorithm.

PDF Details

IROS Conference 2023 Conference Paper

Cognition Difference-Based Dynamic Trust Network for Distributed Bayesian Data Fusion

Yingke Li
Ziqiao Zhang
Junkai Wang
Huibo Zhang
Enlu Zhou
Fumin Zhang 0001

Distributed Data Fusion (DDF), as a prevalent technique that empowers scalable, flexible, and robust information fusing, has been employed in various multi-sensor networks operating in uncertain and dynamic environments. This paper proposes a cognition difference-based mechanism to construct a dynamic trust network for real-time DDF, where the cognition difference is defined as the statistical difference between the sensors' estimated probability distributions. Distinguished by the mutual correlation between trust and cognition difference, two principles of determining trust are investigated, and their performances are analyzed by conducting simulations in the scenarios of source seeking. Our simulation and experiment results show that the proposed approach is effective in providing comprehensive and robust performance in general and unstructured environments.

Details

NeurIPS Conference 2022 Conference Paper

Bayesian Risk Markov Decision Processes

Yifan Lin
Yuxuan Ren
Enlu Zhou

We consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes be overly conservative. In this paper, we propose a new formulation, Bayesian risk Markov decision process (BR-MDP), to address parameter uncertainty in MDPs, where a risk functional is applied in nested form to the expected total cost with respect to the Bayesian posterior distributions of the unknown parameters. The proposed formulation provides more flexible risk attitudes towards parameter uncertainty and takes into account the availability of data in future time stages. To solve the proposed formulation with the conditional value-at-risk (CVaR) risk functional, we propose an efficient approximation algorithm by deriving an analytical approximation of the value function and utilizing the convexity of CVaR. We demonstrate the empirical performance of the BR-MDP formulation and proposed algorithms on a gambler’s betting problem and an inventory control problem.

PDF Details

ICML Conference 2022 Conference Paper

Robust Multi-Objective Bayesian Optimization Under Input Noise

Samuel Daulton
Sait Cakmak
Maximilian Balandat
Michael A. Osborne
Enlu Zhou
Eytan Bakshy

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability.

Details

NeurIPS Conference 2020 Conference Paper

Bayesian Optimization of Risk Measures

Sait Cakmak
Raul Astudillo Marban
Peter Frazier
Enlu Zhou

We consider Bayesian optimization of objective functions of the form $\rho[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function and $\rho$ denotes either the VaR or CVaR risk measure, computed with respect to the randomness induced by the environmental random variable $W$. Such problems arise in decision making under uncertainty, such as in portfolio optimization and robust systems design. We propose a family of novel Bayesian optimization algorithms that exploit the structure of the objective function to substantially improve sampling efficiency. Instead of modeling the objective function directly as is typical in Bayesian optimization, these algorithms model $F$ as a Gaussian process, and use the implied posterior on the objective function to decide which points to evaluate. We demonstrate the effectiveness of our approach in a variety of numerical experiments.

PDF Details

ICML Conference 2019 Conference Paper

Toward Understanding the Importance of Noise in Training Neural Networks

Mo Zhou
Tianyi Liu
Yan Li 0074
Dachao Lin
Enlu Zhou
Tuo Zhao

Numerous empirical evidence has corroborated that the noise plays a crucial rule in effective and efficient training of deep neural networks. The theory behind, however, is still largely unknown. This paper studies this fundamental problem through training a simple two-layer convolutional neural network model. Although training such a network requires to solve a non-convex optimization problem with a spurious local optimum and a global optimum, we prove that a perturbed gradient descent algorithm in conjunction with noise annealing is guaranteed to converge to a global optimum in polynomial time with arbitrary initialization. This implies that the noise enables the algorithm to efficiently escape from the spurious local optimum. Numerical experiments are provided to support our theory.

Details

NeurIPS Conference 2019 Conference Paper

Towards Understanding the Importance of Shortcut Connections in Residual Networks

Tianyi Liu
Minshuo Chen
Mo Zhou
Simon Du
Enlu Zhou
Tuo Zhao

Residual Network (ResNet) is undoubtedly a milestone in deep learning. ResNet is equipped with shortcut connections between layers, and exhibits efficient training using simple first order algorithms. Despite of the great empirical success, the reason behind is far from being well understood. In this paper, we study a two-layer non-overlapping convolutional ResNet. Training such a network requires solving a non-convex optimization problem with a spurious local optimum. We show, however, that gradient descent combined with proper normalization, avoids being trapped by the spurious local optimum, and converges to a global optimum in polynomial time, when the weight of the first layer is initialized at 0, and that of the second layer is initialized arbitrarily in a ball. Numerical experiments are provided to support our theory.

PDF Details

NeurIPS Conference 2018 Conference Paper

Towards Understanding Acceleration Tradeoff between Momentum and Asynchrony in Nonconvex Stochastic Optimization

Tianyi Liu
Shiyang Li
Jianping Shi
Enlu Zhou
Tuo Zhao

Asynchronous momentum stochastic gradient descent algorithms (Async-MSGD) have been widely used in distributed machine learning, e. g. , training large collaborative filtering systems and deep neural networks. Due to current technical limit, however, establishing convergence properties of Async-MSGD for these highly complicated nonoconvex problems is generally infeasible. Therefore, we propose to analyze the algorithm through a simpler but nontrivial nonconvex problems --- streaming PCA. This allows us to make progress toward understanding Aync-MSGD and gaining new insights for more general problems. Specifically, by exploiting the diffusion approximation of stochastic optimization, we establish the asymptotic rate of convergence of Async-MSGD for streaming PCA. Our results indicate a fundamental tradeoff between asynchrony and momentum: To ensure convergence and acceleration through asynchrony, we have to reduce the momentum (compared with Sync-MSGD). To the best of our knowledge, this is the first theoretical attempt on understanding Async-MSGD for distributed nonconvex stochastic optimization. Numerical experiments on both streaming PCA and training deep neural networks are provided to support our findings for Async-MSGD.

PDF Details