arXiv subjects

Yudong Chen

Publications and source records attributed to Yudong Chen.

At least 55 records · Page 3Linked to original sources

arXiv2024

The Collusion of Memory and Nonlinearity in Stochastic Approximation With Constant Stepsize

In this work, we investigate stochastic approximation (SA) with Markovian data and nonlinear updates under constant stepsize $α>0$. Existing work has primarily focused on either i.i.d. data or linear update rules. We take a new perspective and carefully examine the simultaneous presence of Markovian dependency of data and nonlinear update rules, delineating how the interplay between these two structures leads to complications that are not captured by prior techniques. By leveraging the smoothness and recurrence properties of the SA updates, we develop a fine-grained analysis of the correlation between the SA iterates $θ_k$ and Markovian data $x_k$. This enables us to overcome the obstacles in existing analysis and establish for the first time the weak convergence of the joint process $(x_k, θ_k)_{k\geq0}$. Furthermore, we present a precise characterization of the asymptotic bias of the SA iterates, given by $\mathbb{E}[θ_\infty]-θ^\ast=α(b_\text{m}+b_\text{n}+b_\text{c})+O(α^{3/2})$. Here, $b_\text{m}$ is associated with the Markovian noise, $b_\text{n}$ is tied to the nonlinearity, and notably, $b_\text{c}$ represents a multiplicative interaction between the Markovian noise and nonlinearity, which is absent in previous works. As a by-product of our analysis, we derive finite-time bounds on higher moment $\mathbb{E}[\|θ_k-θ^\ast\|^{2p}]$ and present non-asymptotic geometric convergence rates for the iterates, along with a Central Limit Theorem.

stat.ML↗

arXiv2024

Learning to Stabilize Online Reinforcement Learning in Unbounded State Spaces

In many reinforcement learning (RL) applications, we want policies that reach desired states and then keep the controlled system within an acceptable region around the desired states over an indefinite period of time. This latter objective is called stability and is especially important when the state space is unbounded, such that the states can be arbitrarily far from each other and the agent can drift far away from the desired states. For example, in stochastic queuing networks, where queues of waiting jobs can grow without bound, the desired state is all-zero queue lengths. Here, a stable policy ensures queue lengths are finite while an optimal policy minimizes queue lengths. Since an optimal policy is also stable, one would expect that RL algorithms would implicitly give us stable policies. However, in this work, we find that deep RL algorithms that directly minimize the distance to the desired state during online training often result in unstable policies, i.e., policies that drift far away from the desired state. We attribute this instability to poor credit-assignment for destabilizing actions. We then introduce an approach based on two ideas: 1) a Lyapunov-based cost-shaping technique and 2) state transformations to the unbounded state space. We conduct an empirical study on various queueing networks and traffic signal control problems and find that our approach performs competitively against strong baselines with knowledge of the transition dynamics. Our code is available here: https://github.com/Badger-RL/STOP.

cs.LG↗

arXiv2024

Span-Based Optimal Sample Complexity for Average Reward MDPs

We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. We establish the complexity bound $\widetilde{O}\left(SA\frac{H}{\varepsilon^2} \right)$, where $H$ is the span of the bias function of the optimal policy and $SA$ is the cardinality of the state-action space. Our result is the first that is minimax optimal (up to log factors) in all parameters $S,A,H$ and $\varepsilon$, improving on existing work that either assumes uniformly bounded mixing times for all policies or has suboptimal dependence on the parameters. Our result is based on reducing the average-reward MDP to a discounted MDP. To establish the optimality of this reduction, we develop improved bounds for $γ$-discounted MDPs, showing that $\widetilde{O}\left(SA\frac{H}{(1-γ)^2\varepsilon^2} \right)$ samples suffice to learn a $\varepsilon$-optimal policy in weakly communicating MDPs under the regime that $γ\geq 1 - \frac{1}{H}$, circumventing the well-known lower bound of $\widetildeΩ\left(SA\frac{1}{(1-γ)^3\varepsilon^2} \right)$ for general $γ$-discounted MDPs. Our analysis develops upper bounds on certain instance-dependent variance parameters in terms of the span parameter. These bounds are tighter than those based on the mixing time or diameter of the MDP and may be of broader use.

cs.LG↗

arXiv2024

Local Minima Structures in Gaussian Mixture Models

We investigate the landscape of the negative log-likelihood function of Gaussian Mixture Models (GMMs) with a general number of components in the population limit. As the objective function is non-convex, there can be multiple local minima that are not globally optimal, even for well-separated mixture models. Our study reveals that all local minima share a common structure that partially identifies the cluster centers (i.e., means of the Gaussian components) of the true location mixture. Specifically, each local minimum can be represented as a non-overlapping combination of two types of sub-configurations: fitting a single mean estimate to multiple Gaussian components or fitting multiple estimates to a single true component. These results apply to settings where the true mixture components satisfy a certain separation condition, and are valid even when the number of components is over- or under-specified. We also present a more fine-grained analysis for the setting of one-dimensional GMMs with three components, which provide sharper approximation error bounds with improved dependence on the separation.

stat.ML↗

arXiv2024

Entry-Specific Bounds for Low-Rank Matrix Completion under Highly Non-Uniform Sampling

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying probabilities, potentially with different asymptotic scalings. We show that under structured sampling probabilities, it is often better and sometimes optimal to run estimation algorithms on a smaller submatrix rather than the entire matrix. In particular, we prove error upper bounds customized to each entry, which match the minimax lower bounds under certain conditions. Our bounds characterize the hardness of estimating each entry as a function of the localized sampling probabilities. We provide numerical experiments that confirm our theoretical findings.

stat.ML↗

arXiv2024

Restless Bandits with Average Reward: Breaking the Uniform Global Attractor Assumption

We study the infinite-horizon restless bandit problem with the average reward criterion, in both discrete-time and continuous-time settings. A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as the number of arms, $N$, grows large. Existing results on asymptotic optimality all rely on the uniform global attractor property (UGAP), a complex and challenging-to-verify assumption. In this paper, we propose a general, simulation-based framework, Follow-the-Virtual-Advice, that converts any single-armed policy into a policy for the original $N$-armed problem. This is done by simulating the single-armed policy on each arm and carefully steering the real state towards the simulated state. Our framework can be instantiated to produce a policy with an $O(1/\sqrt{N})$ optimality gap. In the discrete-time setting, our result holds under a simpler synchronization assumption, which covers some problem instances that violate UGAP. More notably, in the continuous-time setting, we do not require \emph{any} additional assumptions beyond the standard unichain condition. In both settings, our work is the first asymptotic optimality result that does not require UGAP.

cs.LG↗

arXiv2024

GTP-ViT: Efficient Vision Transformers via Graph-based Token Propagation

Vision Transformers (ViTs) have revolutionized the field of computer vision, yet their deployments on resource-constrained devices remain challenging due to high computational demands. To expedite pre-trained ViTs, token pruning and token merging approaches have been developed, which aim at reducing the number of tokens involved in the computation. However, these methods still have some limitations, such as image information loss from pruned tokens and inefficiency in the token-matching process. In this paper, we introduce a novel Graph-based Token Propagation (GTP) method to resolve the challenge of balancing model efficiency and information preservation for efficient ViTs. Inspired by graph summarization algorithms, GTP meticulously propagates less significant tokens' information to spatially and semantically connected tokens that are of greater importance. Consequently, the remaining few tokens serve as a summarization of the entire token graph, allowing the method to reduce computational complexity while preserving essential information of eliminated tokens. Combined with an innovative token selection strategy, GTP can efficiently identify image tokens to be propagated. Extensive experiments have validated GTP's effectiveness, demonstrating both efficiency and performance improvements. Specifically, GTP decreases the computational complexity of both DeiT-S and DeiT-B by up to 26% with only a minimal 0.3% accuracy drop on ImageNet-1K without finetuning, and remarkably surpasses the state-of-the-art token merging method on various backbones at an even faster inference speed. The source code is available at https://github.com/Ackesnal/GTP-ViT.

cs.CV↗

arXiv2023

Effectiveness of Constant Stepsize in Markovian LSA and Statistical Inference

In this paper, we study the effectiveness of using a constant stepsize in statistical inference via linear stochastic approximation (LSA) algorithms with Markovian data. After establishing a Central Limit Theorem (CLT), we outline an inference procedure that uses averaged LSA iterates to construct confidence intervals (CIs). Our procedure leverages the fast mixing property of constant-stepsize LSA for better covariance estimation and employs Richardson-Romberg (RR) extrapolation to reduce the bias induced by constant stepsize and Markovian data. We develop theoretical results for guiding stepsize selection in RR extrapolation, and identify several important settings where the bias provably vanishes even without extrapolation. We conduct extensive numerical experiments and compare against classical inference approaches. Our results show that using a constant stepsize enjoys easy hyperparameter tuning, fast convergence, and consistently better CI coverage, especially when data is limited.

stat.ML↗

arXiv2023

No Token Left Behind: Efficient Vision Transformer via Dynamic Token Idling

Vision Transformers (ViTs) have demonstrated outstanding performance in computer vision tasks, yet their high computational complexity prevents their deployment in computing resource-constrained environments. Various token pruning techniques have been introduced to alleviate the high computational burden of ViTs by dynamically dropping image tokens. However, some undesirable pruning at early stages may result in permanent loss of image information in subsequent layers, consequently hindering model performance. To address this problem, we propose IdleViT, a dynamic token-idle-based method that achieves an excellent trade-off between performance and efficiency. Specifically, in each layer, IdleViT selects a subset of the image tokens to participate in computations while keeping the rest of the tokens idle and directly passing them to this layer's output. By allowing the idle tokens to be re-selected in the following layers, IdleViT mitigates the negative impact of improper pruning in the early stages. Furthermore, inspired by the normalized graph cut, we devise a token cut loss on the attention map as regularization to improve IdleViT's token selection ability. Our method is simple yet effective and can be extended to pyramid ViTs since no token is completely dropped. Extensive experimental results on various ViT architectures have shown that IdleViT can diminish the complexity of pretrained ViTs by up to 33\% with no more than 0.2\% accuracy decrease on ImageNet, after finetuning for only 30 epochs. Notably, when the keep ratio is 0.5, IdleViT outperforms the state-of-the-art EViT on DeiT-S by 0.5\% higher accuracy and even faster inference speed. The source code is available in the supplementary material.

cs.CV↗

arXiv2023

Understanding the Effects of Projectors in Knowledge Distillation

Conventionally, during the knowledge distillation process (e.g. feature distillation), an additional projector is often required to perform feature transformation due to the dimension mismatch between the teacher and the student networks. Interestingly, we discovered that even if the student and the teacher have the same feature dimensions, adding a projector still helps to improve the distillation performance. In addition, projectors even improve logit distillation if we add them to the architecture too. Inspired by these surprising findings and the general lack of understanding of the projectors in the knowledge distillation process from existing literature, this paper investigates the implicit role that projectors play but so far have been overlooked. Our empirical study shows that the student with a projector (1) obtains a better trade-off between the training accuracy and the testing accuracy compared to the student without a projector when it has the same feature dimensions as the teacher, (2) better preserves its similarity to the teacher beyond shallow and numeric resemblance, from the view of Centered Kernel Alignment (CKA), and (3) avoids being over-confident as the teacher does at the testing phase. Motivated by the positive effects of projectors, we propose a projector ensemble-based feature distillation method to further improve distillation performance. Despite the simplicity of the proposed strategy, empirical results from the evaluation of classification tasks on benchmark datasets demonstrate the superior classification performance of our method on a broad range of teacher-student pairs and verify from the aspects of CKA and model calibration that the student's features are of improved quality with the projector ensemble design.

cs.CV↗

arXiv2023

Plug n' Play: Channel Shuffle Module for Enhancing Tiny Vision Transformers

Vision Transformers (ViTs) have demonstrated remarkable performance in various computer vision tasks. However, the high computational complexity hinders ViTs' applicability on devices with limited memory and computing resources. Although certain investigations have delved into the fusion of convolutional layers with self-attention mechanisms to enhance the efficiency of ViTs, there remains a knowledge gap in constructing tiny yet effective ViTs solely based on the self-attention mechanism. Furthermore, the straightforward strategy of reducing the feature channels in a large but outperforming ViT often results in significant performance degradation despite improved efficiency. To address these challenges, we propose a novel channel shuffle module to improve tiny-size ViTs, showing the potential of pure self-attention models in environments with constrained computing resources. Inspired by the channel shuffle design in ShuffleNetV2 \cite{ma2018shufflenet}, our module expands the feature channels of a tiny ViT and partitions the channels into two groups: the \textit{Attended} and \textit{Idle} groups. Self-attention computations are exclusively employed on the designated \textit{Attended} group, followed by a channel shuffle operation that facilitates information exchange between the two groups. By incorporating our module into a tiny ViT, we can achieve superior performance while maintaining a comparable computational complexity to the vanilla model. Specifically, our proposed channel shuffle module consistently improves the top-1 accuracy on the ImageNet-1K dataset for various tiny ViT models by up to 2.8\%, with the changes in model complexity being less than 0.03 GMACs.

cs.CV↗

arXiv2023

Towards Joint Modeling of Dialogue Response and Speech Synthesis based on Large Language Model

This paper explores the potential of constructing an AI spoken dialogue system that "thinks how to respond" and "thinks how to speak" simultaneously, which more closely aligns with the human speech production process compared to the current cascade pipeline of independent chatbot and Text-to-Speech (TTS) modules. We hypothesize that Large Language Models (LLMs) with billions of parameters possess significant speech understanding capabilities and can jointly model dialogue responses and linguistic features. We conduct two sets of experiments: 1) Prosodic structure prediction, a typical front-end task in TTS, demonstrating the speech understanding ability of LLMs, and 2) Further integrating dialogue response and a wide array of linguistic features using a unified encoding format. Our results indicate that the LLM-based approach is a promising direction for building unified spoken dialogue systems.

cs.CL↗

arXiv2023

Bias and Extrapolation in Markovian Linear Stochastic Approximation with Constant Stepsizes

We consider Linear Stochastic Approximation (LSA) with a constant stepsize and Markovian data. Viewing the joint process of the data and LSA iterate as a time-homogeneous Markov chain, we prove its convergence to a unique limiting and stationary distribution in Wasserstein distance and establish non-asymptotic, geometric convergence rates. Furthermore, we show that the bias vector of this limit admits an infinite series expansion with respect to the stepsize. Consequently, the bias is proportional to the stepsize up to higher order terms. This result stands in contrast with LSA under i.i.d. data, for which the bias vanishes. In the reversible chain setting, we provide a general characterization of the relationship between the bias and the mixing time of the Markovian data, establishing that they are roughly proportional to each other. While Polyak-Ruppert tail-averaging reduces the variance of the LSA iterates, it does not affect the bias. The above characterization allows us to show that the bias can be reduced using Richardson-Romberg extrapolation with $m\ge 2$ stepsizes, which eliminates the $m-1$ leading terms in the bias expansion. This extrapolation scheme leads to an exponentially smaller bias and an improved mean squared error, both in theory and empirically. Our results immediately apply to the Temporal Difference learning algorithm with linear function approximation, Markovian data, and constant stepsizes.

stat.ML↗

arXiv2023

VISER: A Tractable Solution Concept for Games with Information Asymmetry

Many real-world games suffer from information asymmetry: one player is only aware of their own payoffs while the other player has the full game information. Examples include the critical domain of security games and adversarial multi-agent reinforcement learning. Information asymmetry renders traditional solution concepts such as Strong Stackelberg Equilibrium (SSE) and Robust-Optimization Equilibrium (ROE) inoperative. We propose a novel solution concept called VISER (Victim Is Secure, Exploiter best-Responds). VISER enables an external observer to predict the outcome of such games. In particular, for security applications, VISER allows the victim to better defend itself while characterizing the most damaging attacks available to the attacker. We show that each player's VISER strategy can be computed independently in polynomial time using linear programming (LP). We also extend VISER to its Markov-perfect counterpart for Markov games, which can be solved efficiently using a series of LPs.

cs.GT↗

arXiv2023

Stochastic Methods in Variational Inequalities: Ergodicity, Bias and Refinements

For min-max optimization and variational inequalities problems (VIP) encountered in diverse machine learning tasks, Stochastic Extragradient (SEG) and Stochastic Gradient Descent Ascent (SGDA) have emerged as preeminent algorithms. Constant step-size variants of SEG/SGDA have gained popularity, with appealing benefits such as easy tuning and rapid forgiveness of initial conditions, but their convergence behaviors are more complicated even in rudimentary bilinear models. Our work endeavors to elucidate and quantify the probabilistic structures intrinsic to these algorithms. By recasting the constant step-size SEG/SGDA as time-homogeneous Markov Chains, we establish a first-of-its-kind Law of Large Numbers and a Central Limit Theorem, demonstrating that the average iterate is asymptotically normal with a unique invariant distribution for an extensive range of monotone and non-monotone VIPs. Specializing to convex-concave min-max optimization, we characterize the relationship between the step-size and the induced bias with respect to the Von-Neumann's value. Finally, we establish that Richardson-Romberg extrapolation can improve proximity of the average iterate to the global solution for VIPs. Our probabilistic analysis, underpinned by experiments corroborating our theoretical discoveries, harnesses techniques from optimization, Markov chains, and operator theory.

stat.ML↗

arXiv2023

Overcoming the Long Horizon Barrier for Sample-Efficient Reinforcement Learning with Latent Low-Rank Structure

The practicality of reinforcement learning algorithms has been limited due to poor scaling with respect to the problem size, as the sample complexity of learning an $ε$-optimal policy is $\tildeΩ\left(|S||A|H^3 / ε^2\right)$ over worst case instances of an MDP with state space $S$, action space $A$, and horizon $H$. We consider a class of MDPs for which the associated optimal $Q^*$ function is low rank, where the latent features are unknown. While one would hope to achieve linear sample complexity in $|S|$ and $|A|$ due to the low rank structure, we show that without imposing further assumptions beyond low rank of $Q^*$, if one is constrained to estimate the $Q$ function using only observations from a subset of entries, there is a worst case instance in which one must incur a sample complexity exponential in the horizon $H$ to learn a near optimal policy. We subsequently show that under stronger low rank structural assumptions, given access to a generative model, Low Rank Monte Carlo Policy Iteration (LR-MCPI) and Low Rank Empirical Value Iteration (LR-EVI) achieve the desired sample complexity of $\tilde{O}\left((|S|+|A|)\mathrm{poly}(d,H)/ε^2\right)$ for a rank $d$ setting, which is minimax optimal with respect to the scaling of $|S|, |A|$, and $ε$. In contrast to literature on linear and low-rank MDPs, we do not require a known feature mapping, our algorithm is computationally simple, and our results hold for long time horizons. Our results provide insights on the minimal low-rank structural assumptions required on the MDP with respect to the transition kernel versus the optimal action-value function.

cs.LG↗

arXiv2023

Matrix Estimation for Offline Reinforcement Learning with Low-Rank Structure

We consider offline Reinforcement Learning (RL), where the agent does not interact with the environment and must rely on offline data collected using a behavior policy. Previous works provide policy evaluation guarantees when the target policy to be evaluated is covered by the behavior policy, that is, state-action pairs visited by the target policy must also be visited by the behavior policy. We show that when the MDP has a latent low-rank structure, this coverage condition can be relaxed. Building on the connection to weighted matrix completion with non-uniform observations, we propose an offline policy evaluation algorithm that leverages the low-rank structure to estimate the values of uncovered state-action pairs. Our algorithm does not require a known feature representation, and our finite-sample error bound involves a novel discrepancy measure quantifying the discrepancy between the behavior and target policies in the spectral space. We provide concrete examples where our algorithm achieves accurate estimation while existing coverage conditions are not satisfied. Building on the above evaluation algorithm, we further design an offline policy optimization algorithm and provide non-asymptotic performance guarantees.

cs.LG↗

arXiv2023

Inference in high-dimensional online changepoint detection

We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulations confirm the effectiveness of our methodology, and we also illustrate its applicability on the US excess deaths data from 2017--2020.

stat.ME↗