arXiv subjects

Wenhao Yang

Publications and source records attributed to Wenhao Yang.

At least 55 records · Page 3Linked to original sources

arXiv2024

Integrated Multi-Level Knowledge Distillation for Enhanced Speaker Verification

Knowledge distillation (KD) is widely used in audio tasks, such as speaker verification (SV), by transferring knowledge from a well-trained large model (the teacher) to a smaller, more compact model (the student) for efficiency and portability. Existing KD methods for SV often mirror those used in image processing, focusing on approximating predicted probabilities and hidden representations. However, these methods fail to account for the multi-level temporal properties of speech audio. In this paper, we propose a novel KD method, i.e., Integrated Multi-level Knowledge Distillation (IML-KD), to transfer knowledge of various temporal-scale features of speech from a teacher model to a student model. In the IML-KD, temporal context information from the teacher model is integrated into novel Integrated Gradient-based input-sensitive representations from speech segments with various durations, and the student model is trained to infer these representations with multi-level alignment for the output. We conduct SV experiments on the VoxCeleb1 dataset to evaluate the proposed method. Experimental results demonstrate that IML-KD significantly enhances KD performance, reducing the Equal Error Rate (EER) by 5%.

eess.AS↗

arXiv2024

Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions

The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions built from spatial Poisson point processes. While powerful, these models are only asymptotically valid for large samples. However, since extreme data is by definition scarce, the potential for model misspecification error is inherent to these applications, thus DRO estimators are natural. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. We study both tractable convex formulations for some problems of interest (e.g. CVaR) and more general neural network based estimators. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques. Additionally, the proposed method is applied to a real data set of financial returns for comparison to a previous analysis. We established the proposed model as a novel formulation in the multivariate EVT domain, and innovative with respect to performance when compared to relevant alternate proposals.

stat.ML↗

arXiv2024

Robust Channel Learning for Large-Scale Radio Speaker Verification

Recent research in speaker verification has increasingly focused on achieving robust and reliable recognition under challenging channel conditions and noisy environments. Identifying speakers in radio communications is particularly difficult due to inherent limitations such as constrained bandwidth and pervasive noise interference. To address this issue, we present a Channel Robust Speaker Learning (CRSL) framework that enhances the robustness of the current speaker verification pipeline, considering data source, data augmentation, and the efficiency of model transfer processes. Our framework introduces an augmentation module that mitigates bandwidth variations in radio speech datasets by manipulating the bandwidth of training inputs. It also addresses unknown noise by introducing noise within the manifold space. Additionally, we propose an efficient fine-tuning method that reduces the need for extensive additional training time and large amounts of data. Moreover, we develop a toolkit for assembling a large-scale radio speech corpus and establish a benchmark specifically tailored for radio scenario speaker verification studies. Experimental results demonstrate that our proposed methodology effectively enhances performance and mitigates degradation caused by radio transmission in speaker verification tasks. The code will be available on Github.

cs.SD↗

arXiv2024

Projection-Free Variance Reduction Methods for Stochastic Constrained Multi-Level Compositional Optimization

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex. Existing projection-free algorithms for solving this problem suffer from two limitations: 1) they solely focus on the gradient mapping criterion and fail to match the optimal sample complexities in unconstrained settings; 2) their analysis is exclusively applicable to non-convex functions, without considering convex and strongly convex objectives. To address these issues, we introduce novel projection-free variance reduction algorithms and analyze their complexities under different criteria. For gradient mapping, our complexities improve existing results and match the optimal rates for unconstrained problems. For the widely-used Frank-Wolfe gap criterion, we provide theoretical guarantees that align with those for single-level problems. Additionally, by using a stage-wise adaptation, we further obtain complexities for convex and strongly convex functions. Finally, numerical experiments on different tasks demonstrate the effectiveness of our methods.

math.OC↗

arXiv2024

Universal Online Convex Optimization with $1$ Projection per Round

To address the uncertainty in function types, recent progress in online convex optimization (OCO) has spurred the development of universal algorithms that simultaneously attain minimax rates for multiple types of convex functions. However, for a $T$-round online problem, state-of-the-art methods typically conduct $O(\log T)$ projections onto the domain in each round, a process potentially time-consuming with complicated feasible sets. In this paper, inspired by the black-box reduction of Cutkosky and Orabona (2018), we employ a surrogate loss defined over simpler domains to develop universal OCO algorithms that only require $1$ projection. Embracing the framework of prediction with expert advice, we maintain a set of experts for each type of functions and aggregate their predictions via a meta-algorithm. The crux of our approach lies in a uniquely designed expert-loss for strongly convex functions, stemming from an innovative decomposition of the regret into the meta-regret and the expert-regret. Our analysis sheds new light on the surrogate loss, facilitating a rigorous examination of the discrepancy between the regret of the original loss and that of the surrogate loss, and carefully controlling meta-regret under the strong convexity condition. In this way, with only $1$ projection per round, we establish optimal regret bounds for general convex, exponentially concave, and strongly convex functions simultaneously. Furthermore, we enhance the expert-loss to exploit the smoothness property, and demonstrate that our algorithm can attain small-loss regret for multiple types of convex and smooth functions.

cs.LG↗

arXiv2024

PyRadar: Towards Automatically Retrieving and Validating Source Code Repository Information for PyPI Packages

A package's source code repository records the development history of the package, providing indispensable information for the use and risk monitoring of the package. However, a package release often misses its source code repository due to the separation of the package's development platform from its distribution platform. Existing tools retrieve the release's repository information from its metadata, which suffers from two limitations: the metadata may not contain or contain wrong information. Our analysis shows that existing tools can only retrieve repository information for up to 70.5% of PyPI releases. To address the limitations, this paper proposes PyRadar, a novel framework that utilizes the metadata and source distribution to retrieve and validate the repository information for PyPI releases. We start with an empirical study to compare four existing tools on 4,227,425 PyPI releases and analyze phantom files (files appearing in the release's distribution but not in the release's repository) in 14,375 correct package-repository links and 2,064 incorrect links. Based on the findings, we design PyRadar with three components, i.e., Metadata-based Retriever, Source Code Repository Validator, and Source Code-based Retriever. In particular, the Metadata-based Retriever combines best practices of existing tools and successfully retrieves repository information from the metadata for 72.1% of PyPI releases. The Source Code Repository Validator applies common machine learning algorithms on six crafted features and achieves an AUC of up to 0.995. The Source Code-based Retriever queries World of Code with the SHA-1 hashes of all Python files in the release's source distribution and retrieves repository information for 90.2% of packages in our dataset with an accuracy of 0.970. Both practitioners and researchers can employ the PyRadar to better use PyPI packages.

cs.SE↗

arXiv2023

Liouville theorems for ancient solutions of subexponential growth to the heat equation on graphs

Mosconi proved Liouville theorems for ancient solutions of subexponential growth to the heat equation on a manifold with Ricci curvature bounded below. We extend these results to graphs with bounded geometry: for a graph with bounded geometry, any nonnegative ancient solution of subexponential growth in space and time to the heat equation is stationary, and thus is a harmonic solution.

math.DG↗

arXiv2023

Robust Markov Decision Processes without Model Estimation

Robust Markov Decision Processes (MDPs) are receiving much attention in learning a robust policy which is less sensitive to environment changes. There are an increasing number of works analyzing sample-efficiency of robust MDPs. However, there are two major barriers to applying robust MDPs in practice. First, most works study robust MDPs in a model-based regime, where the transition probability needs to be estimated and requires a large amount of memories $\mathcal{O}(|\mathcal{S}|^2|\mathcal{A}|)$. Second, prior work typically assumes a strong oracle to obtain the optimal solution as an intermediate step to solve robust MDPs. However, in practice, such an oracle does not exist usually. To remove the oracle, we transform the original robust MDPs into an alternative form, which allows us to use stochastic gradient methods to solve the robust MDPs. Moreover, we prove the alternative form still plays a similar role as the original form. With this new formulation, we devise a sample-efficient algorithm to solve the robust MDPs in a model-free regime, which does not require an oracle and trades off a lower storage requirement $\mathcal{O}(|\mathcal{S}||\mathcal{A}|)$ with being able to generate samples from a generative model or Markovian chain. Finally, we validate our theoretical findings via numerical experiments, showing the efficiency with the alternative form of robust MDPs.

stat.ML↗

arXiv2023

Regularization and Variance-Weighted Regression Achieves Minimax Optimality in Linear MDPs: Theory and Practice

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an $\varepsilon$-optimal policy with probability $1-δ$ under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

cs.LG↗

arXiv2023

Non-stationary Projection-free Online Learning with Dynamic and Adaptive Regret Guarantees

Projection-free online learning has drawn increasing interest due to its efficiency in solving high-dimensional problems with complicated constraints. However, most existing projection-free online methods focus on minimizing the static regret, which unfortunately fails to capture the challenge of changing environments. In this paper, we investigate non-stationary projection-free online learning, and choose dynamic regret and adaptive regret to measure the performance. Specifically, we first provide a novel dynamic regret analysis for an existing projection-free method named $\text{BOGD}_\text{IP}$, and establish an $\mathcal{O}(T^{3/4}(1+P_T))$ dynamic regret bound, where $P_T$ denotes the path-length of the comparator sequence. Then, we improve the upper bound to $\mathcal{O}(T^{3/4}(1+P_T)^{1/4})$ by running multiple $\text{BOGD}_\text{IP}$ algorithms with different step sizes in parallel, and tracking the best one on the fly. Our results are the first general-case dynamic regret bounds for projection-free online learning, and can recover the existing $\mathcal{O}(T^{3/4})$ static regret by setting $P_T = 0$. Furthermore, we propose a projection-free method to attain an $\tilde{\mathcal{O}}(τ^{3/4})$ adaptive regret bound for any interval with length $τ$, which nearly matches the static regret over that interval. The essential idea is to maintain a set of $\text{BOGD}_\text{IP}$ algorithms dynamically, and combine them by a meta algorithm. Moreover, we demonstrate that it is also equipped with an $\mathcal{O}(T^{3/4}(1+P_T)^{1/4})$ dynamic regret bound. Finally, empirical studies verify our theoretical findings.

cs.LG↗

arXiv2023

Semi-Infinitely Constrained Markov Decision Processes and Efficient Reinforcement Learning

We propose a novel generalization of constrained Markov decision processes (CMDPs) that we call the \emph{semi-infinitely constrained Markov decision process} (SICMDP). Particularly, we consider a continuum of constraints instead of a finite number of constraints as in the case of ordinary CMDPs. We also devise two reinforcement learning algorithms for SICMDPs that we call SI-CRL and SI-CPO. SI-CRL is a model-based reinforcement learning algorithm. Given an estimate of the transition model, we first transform the reinforcement learning problem into a linear semi-infinitely programming (LSIP) problem and then use the dual exchange method in the LSIP literature to solve it. SI-CPO is a policy optimization algorithm. Borrowing the ideas from the cooperative stochastic approximation approach, we make alternative updates to the policy parameters to maximize the reward or minimize the cost. To the best of our knowledge, we are the first to apply tools from semi-infinitely programming (SIP) to solve constrained reinforcement learning problems. We present theoretical analysis for SI-CRL and SI-CPO, identifying their iteration complexity and sample complexity. We also conduct extensive numerical examples to illustrate the SICMDP model and demonstrate that our proposed algorithms are able to solve complex sequential decision-making tasks leveraging modern deep reinforcement learning techniques.

cs.LG↗

arXiv2023

A Statistical Analysis of Polyak-Ruppert Averaged Q-learning

We study Q-learning with Polyak-Ruppert averaging in a discounted Markov decision process in synchronous and tabular settings. Under a Lipschitz condition, we establish a functional central limit theorem for the averaged iteration $\bar{\boldsymbol{Q}}_T$ and show that its standardized partial-sum process converges weakly to a rescaled Brownian motion. The functional central limit theorem implies a fully online inference method for reinforcement learning. Furthermore, we show that $\bar{\boldsymbol{Q}}_T$ is the regular asymptotically linear (RAL) estimator for the optimal Q-value function $\boldsymbol{Q}^*$ that has the most efficient influence function. We present a nonasymptotic analysis for the $\ell_{\infty}$ error, $\mathbb{E}\|\bar{\boldsymbol{Q}}_T-\boldsymbol{Q}^*\|_{\infty}$, showing that it matches the instance-dependent lower bound for polynomial step sizes. Similar results are provided for entropy-regularized Q-learning without the Lipschitz condition.

stat.ML↗

arXiv2022

Statistical Estimation of Confounded Linear MDPs: An Instrumental Variable Approach

In an Markov decision process (MDP), unobservable confounders may exist and have impacts on the data generating process, so that the classic off-policy evaluation (OPE) estimators may fail to identify the true value function of the target policy. In this paper, we study the statistical properties of OPE in confounded MDPs with observable instrumental variables. Specifically, we propose a two-stage estimator based on the instrumental variables and establish its statistical properties in the confounded MDPs with a linear structure. For non-asymptotic analysis, we prove a $\mathcal{O}(n^{-1/2})$-error bound where $n$ is the number of samples. For asymptotic analysis, we prove that the two-stage estimator is asymptotically normal with a typical rate of $n^{1/2}$. To the best of our knowledge, we are the first to show such statistical results of the two-stage estimator for confounded linear MDPs via instrumental variables.

stat.ML↗

arXiv2022

Towards Theoretical Understandings of Robust Markov Decision Processes: Sample Complexity and Asymptotics

In this paper, we study the non-asymptotic and asymptotic performances of the optimal robust policy and value function of robust Markov Decision Processes(MDPs), where the optimal robust policy and value function are solved only from a generative model. While prior work focusing on non-asymptotic performances of robust MDPs is restricted in the setting of the KL uncertainty set and $(s,a)$-rectangular assumption, we improve their results and also consider other uncertainty sets, including $L_1$ and $χ^2$ balls. Our results show that when we assume $(s,a)$-rectangular on uncertainty sets, the sample complexity is about $\widetilde{O}\left(\frac{|\mathcal{S}|^2|\mathcal{A}|}{\varepsilon^2ρ^2(1-γ)^4}\right)$. In addition, we extend our results from $(s,a)$-rectangular assumption to $s$-rectangular assumption. In this scenario, the sample complexity varies with the choice of uncertainty sets and is generally larger than the case under $(s,a)$-rectangular assumption. Moreover, we also show that the optimal robust value function is asymptotic normal with a typical rate $\sqrt{n}$ under $(s,a)$ and $s$-rectangular assumptions from both theoretical and empirical perspectives.

stat.ML↗

arXiv2022

KL-Entropy-Regularized RL with a Generative Model is Minimax Optimal

In this work, we consider and analyze the sample complexity of model-free reinforcement learning with a generative model. Particularly, we analyze mirror descent value iteration (MDVI) by Geist et al. (2019) and Vieillard et al. (2020a), which uses the Kullback-Leibler divergence and entropy regularization in its value and policy updates. Our analysis shows that it is nearly minimax-optimal for finding an $\varepsilon$-optimal policy when $\varepsilon$ is sufficiently small. This is the first theoretical result that demonstrates that a simple model-free algorithm without variance-reduction can be nearly minimax-optimal under the considered setting.

cs.LG↗

arXiv2022

Pluralistic Image Completion with Probabilistic Mixture-of-Experts

Pluralistic image completion focuses on generating both visually realistic and diverse results for image completion. Prior methods enjoy the empirical successes of this task. However, their used constraints for pluralistic image completion are argued to be not well interpretable and unsatisfactory from two aspects. First, the constraints for visual reality can be weakly correlated to the objective of image completion or even redundant. Second, the constraints for diversity are designed to be task-agnostic, which causes the constraints to not work well. In this paper, to address the issues, we propose an end-to-end probabilistic method. Specifically, we introduce a unified probabilistic graph model that represents the complex interactions in image completion. The entire procedure of image completion is then mathematically divided into several sub-procedures, which helps efficient enforcement of constraints. The sub-procedure directly related to pluralistic results is identified, where the interaction is established by a Gaussian mixture model (GMM). The inherent parameters of GMM are task-related, which are optimized adaptively during training, while the number of its primitives can control the diversity of results conveniently. We formally establish the effectiveness of our method and demonstrate it with comprehensive experiments.

cs.CV↗

arXiv2022

Federated Reinforcement Learning with Environment Heterogeneity

We study a Federated Reinforcement Learning (FedRL) problem in which $n$ agents collaboratively learn a single policy without sharing the trajectories they collected during agent-environment interaction. We stress the constraint of environment heterogeneity, which means $n$ environments corresponding to these $n$ agents have different state transitions. To obtain a value function or a policy function which optimizes the overall performance in all environments, we propose two federated RL algorithms, \texttt{QAvg} and \texttt{PAvg}. We theoretically prove that these algorithms converge to suboptimal solutions, while such suboptimality depends on how heterogeneous these $n$ environments are. Moreover, we propose a heuristic that achieves personalization by embedding the $n$ environments into $n$ vectors. The personalization heuristic not only improves the training but also allows for better generalization to new environments.

cs.LG↗

arXiv2021

Communication-Efficient Local Decentralized SGD Methods

Recently, the technique of local updates is a powerful tool in centralized settings to improve communication efficiency via periodical communication. For decentralized settings, it is still unclear how to efficiently combine local updates and decentralized communication. In this work, we propose an algorithm named as LD-SGD, which incorporates arbitrary update schemes that alternate between multiple Local updates and multiple Decentralized SGDs, and provide an analytical framework for LD-SGD. Under the framework, we present a sufficient condition to guarantee the convergence. We show that LD-SGD converges to a critical point for a wide range of update schemes when the objective is non-convex and the training data are non-identically independent distributed. Moreover, our framework brings many insights into the design of update schemes for decentralized optimization. As examples, we specify two update schemes and show how they help improve communication efficiency. Specifically, the first scheme alternates the number of local and global update steps. From our analysis, the ratio of the number of local updates to that of decentralized SGD trades off communication and computation. The second scheme is to periodically shrink the length of local updates. We show that the decaying strategy helps improve communication efficiency both theoretically and empirically.

stat.ML↗