arXiv subjects

Yuejie Chi

Publications and source records attributed to Yuejie Chi.

At least 55 records · Page 3Linked to original sources

arXiv2024

Leveraging Multimodal Diffusion Models to Accelerate Imaging with Side Information

Diffusion models have found phenomenal success as expressive priors for solving inverse problems, but their extension beyond natural images to more structured scientific domains remains limited. Motivated by applications in materials science, we aim to reduce the number of measurements required from an expensive imaging modality of interest, by leveraging side information from an auxiliary modality that is much cheaper to obtain. To deal with the non-differentiable and black-box nature of the forward model, we propose a framework to train a multimodal diffusion model over the joint modalities, turning inverse problems with black-box forward models into simple linear inpainting problems. Numerically, we demonstrate the feasibility of training diffusion models over materials imagery data, and show that our approach achieves superior image reconstruction by leveraging the available side information, requiring significantly less amount of data from the expensive microscopy modality.

cs.CV↗

arXiv2024

In-Context Learning with Representations: Contextual Generalization of Trained Transformers

In-context learning (ICL) refers to a remarkable capability of pretrained large language models, which can learn a new task given a few examples during inference. However, theoretical understanding of ICL is largely under-explored, particularly whether transformers can be trained to generalize to unseen examples in a prompt, which will require the model to acquire contextual knowledge of the prompt for generalization. This paper investigates the training dynamics of transformers by gradient descent through the lens of non-linear regression tasks. The contextual generalization here can be attained via learning the template function for each task in-context, where all template functions lie in a linear space with $m$ basis functions. We analyze the training dynamics of one-layer multi-head transformers to in-contextly predict unlabeled inputs given partially labeled prompts, where the labels contain Gaussian noise and the number of examples in each prompt are not sufficient to determine the template. Under mild assumptions, we show that the training loss for a one-layer multi-head transformer converges linearly to a global minimum. Moreover, the transformer effectively learns to perform ridge regression over the basis functions. To our knowledge, this study is the first provable demonstration that transformers can learn contextual (i.e., template) information to generalize to both unseen examples and tasks when prompts contain only a small number of query-answer pairs.

cs.LG↗

arXiv2024

Federated Natural Policy Gradient and Actor Critic Methods for Multi-task Reinforcement Learning

Federated reinforcement learning (RL) enables collaborative decision making of multiple distributed agents without sharing local data trajectories. In this work, we consider a multi-task setting, in which each agent has its own private reward function corresponding to different tasks, while sharing the same transition kernel of the environment. Focusing on infinite-horizon Markov decision processes, the goal is to learn a globally optimal policy that maximizes the sum of the discounted total rewards of all the agents in a decentralized manner, where each agent only communicates with its neighbors over some prescribed graph topology. We develop federated vanilla and entropy-regularized natural policy gradient (NPG) methods in the tabular setting under softmax parameterization, where gradient tracking is applied to estimate the global Q-function to mitigate the impact of imperfect information sharing. We establish non-asymptotic global convergence guarantees under exact policy evaluation, where the rates are nearly independent of the size of the state-action space and illuminate the impacts of network size and connectivity. To the best of our knowledge, this is the first time that near dimension-free global convergence is established for federated multi-task RL using policy optimization. We further go beyond the tabular setting by proposing a federated natural actor critic (NAC) method for multi-task RL with function approximation, and establish its finite-time sample complexity taking the errors of function approximation into account.

cs.LG↗

arXiv2024

Prompt-prompted Adaptive Structured Pruning for Efficient LLM Generation

With the development of transformer-based large language models (LLMs), they have been applied to many fields due to their remarkable utility, but this comes at a considerable computational cost at deployment. Fortunately, some methods such as pruning or constructing a mixture of experts (MoE) aim at exploiting sparsity in transformer feedforward (FF) blocks to gain boosts in speed and reduction in memory requirements. However, these techniques can be very costly and inflexible in practice, as they often require training or are restricted to specific types of architectures. To address this, we introduce GRIFFIN, a novel training-free and calibration-free method that selects unique FF experts at the sequence level for efficient generation across a plethora of LLMs with different non-ReLU activation functions. This is possible due to a critical observation that many trained LLMs naturally produce highly structured FF activation patterns within a sequence, which we call flocking. Despite our method's simplicity, we show with 50% of the FF parameters, GRIFFIN maintains the original model's performance with little to no degradation on a variety of classification and generation tasks, all while improving latency (e.g. 1.29$\times$ and 1.25$\times$ speed-ups in Gemma 7B and Llama 2 13B, respectively, on an NVIDIA L40). Code is available at https://github.com/hdong920/GRIFFIN.

cs.LG↗

arXiv2024

A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a popular diffusion-based sampler (i.e., the probability flow ODE sampler) in discrete time, assuming access to $\ell_2$-accurate estimates of the (Stein) score functions. For distributions in $\mathbb{R}^d$, we prove that $d/\varepsilon$ iterations -- modulo some logarithmic and lower-order terms -- are sufficient to approximate the target distribution to within $\varepsilon$ total-variation distance. This is the first result establishing nearly linear dimension-dependency (in $d$) for the probability flow ODE sampler. Imposing only minimal assumptions on the target data distribution (e.g., no smoothness assumption is imposed), our results also characterize how $\ell_2$ score estimation errors affect the quality of the data generation processes. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach without the need of resorting to SDE and ODE toolboxes.

cs.LG↗

arXiv2024

Sample Complexity of Offline Distributionally Robust Linear Markov Decision Processes

In offline reinforcement learning (RL), the absence of active exploration calls for attention on the model robustness to tackle the sim-to-real gap, where the discrepancy between the simulated and deployed environments can significantly undermine the performance of the learned policy. To endow the learned policy with robustness in a sample-efficient manner in the presence of high-dimensional state-action space, this paper considers the sample complexity of distributionally robust linear Markov decision processes (MDPs) with an uncertainty set characterized by the total variation distance using offline data. We develop a pessimistic model-based algorithm and establish its sample complexity bound under minimal data coverage assumptions, which outperforms prior art by at least $\widetilde{O}(d)$, where $d$ is the feature dimension. We further improve the performance guarantee of the proposed algorithm by incorporating a carefully-designed variance estimator.

cs.LG↗

arXiv2024

Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $\varepsilon$ additive accuracy with runtime $\widetilde{O}( n^2/\varepsilon)$, where $n$ denotes the dimension of the probability distributions of interest. Our algorithm achieves the state-of-the-art computational guarantees among all first-order methods, while exhibiting favorable numerical performance compared to classical algorithms like Sinkhorn and Greenkhorn. Underlying our algorithm designs are two key elements: (a) converting the original problem into a bilinear minimax problem over probability distributions; (b) exploiting the extragradient idea -- in conjunction with entropy regularization and adaptive learning rates -- to accelerate convergence.

cs.LG↗

arXiv2024

Get More with LESS: Synthesizing Recurrence with KV Cache Compression for Efficient LLM Inference

Many computational factors limit broader deployment of large language models. In this paper, we focus on a memory bottleneck imposed by the key-value (KV) cache, a computational shortcut that requires storing previous KV pairs during decoding. While existing KV cache methods approach this problem by pruning or evicting large swaths of relatively less important KV pairs to dramatically reduce the memory footprint of the cache, they can have limited success in tasks that require recollecting a majority of previous tokens. To alleviate this issue, we propose LESS, a simple integration of a (nearly free) constant sized cache with eviction-based cache methods, such that all tokens can be queried at later decoding steps. Its ability to retain information throughout time shows merit on a variety of tasks where we demonstrate LESS can help reduce the performance gap from caching everything, sometimes even matching it, all while being efficient. Relevant code can be found at https://github.com/hdong920/LESS.

cs.LG↗

arXiv2024

Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction

In a great number of tasks in science and engineering, the goal is to infer an unknown image from a small number of measurements collected from a known forward model describing certain sensing or imaging modality. Due to resource constraints, this task is often extremely ill-posed, which necessitates the adoption of expressive prior information to regularize the solution space. Score-based diffusion models, due to its impressive empirical success, have emerged as an appealing candidate of an expressive prior in image reconstruction. In order to accommodate diverse tasks at once, it is of great interest to develop efficient, consistent and robust algorithms that incorporate unconditional score functions of an image prior distribution in conjunction with flexible choices of forward models. This work develops an algorithmic framework for employing score-based diffusion models as an expressive data prior in general nonlinear inverse problems. Motivated by the plug-and-play framework in the imaging community, we introduce a diffusion plug-and-play method (DPnP) that alternatively calls two samplers, a proximal consistency sampler based solely on the likelihood function of the forward model, and a denoising diffusion sampler based solely on the score functions of the image prior. The key insight is that denoising under white Gaussian noise can be solved rigorously via both stochastic (i.e., DDPM-type) and deterministic (i.e., DDIM-type) samplers using the unconditional score functions. We establish both asymptotic and non-asymptotic performance guarantees of DPnP, and provide numerical experiments to illustrate its promise in solving both linear and nonlinear image reconstruction tasks. To the best of our knowledge, DPnP is the first provably-robust posterior sampling method for nonlinear inverse problems using unconditional diffusion priors.

eess.IV↗

arXiv2024

Sample-Efficient Robust Multi-Agent Reinforcement Learning in the Face of Environmental Uncertainty

To overcome the sim-to-real gap in reinforcement learning (RL), learned policies must maintain robustness against environmental uncertainties. While robust RL has been widely studied in single-agent regimes, in multi-agent environments, the problem remains understudied -- despite the fact that the problems posed by environmental uncertainties are often exacerbated by strategic interactions. This work focuses on learning in distributionally robust Markov games (RMGs), a robust variant of standard Markov games, wherein each agent aims to learn a policy that maximizes its own worst-case performance when the deployed environment deviates within its own prescribed uncertainty set. This results in a set of robust equilibrium strategies for all agents that align with classic notions of game-theoretic equilibria. Assuming a non-adaptive sampling mechanism from a generative model, we propose a sample-efficient model-based algorithm (DRNVI) with finite-sample complexity guarantees for learning robust variants of various notions of game-theoretic equilibria. We also establish an information-theoretic lower bound for solving RMGs, which confirms the near-optimal sample complexity of DRNVI with respect to problem-dependent factors such as the size of the state space, the target accuracy, and the horizon length.

cs.LG↗

arXiv2024

High-probability sample complexities for policy evaluation with linear function approximation

This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation error of the best linear coefficients for two widely-used policy evaluation algorithms: the temporal difference (TD) learning algorithm and the two-timescale linear TD with gradient correction (TDC) algorithm. In both the on-policy setting, where observations are generated from the target policy, and the off-policy setting, where samples are drawn from a behavior policy potentially different from the target policy, we establish the first sample complexity bound with high-probability convergence guarantee that attains the optimal dependence on the tolerance level. We also exhihit an explicit dependence on problem-related quantities, and show in the on-policy setting that our upper bound matches the minimax lower bound on crucial problem parameters, including the choice of the feature maps and the problem dimension.

stat.ML↗

arXiv2024

Settling the Sample Complexity of Model-Based Offline Reinforcement Learning

This paper is concerned with offline reinforcement learning (RL), which learns using pre-collected data without further exploration. Effective offline RL would be able to accommodate distribution shift and limited data coverage. However, prior algorithms or analyses either suffer from suboptimal sample complexities or incur high burn-in cost to reach sample optimality, thus posing an impediment to efficient offline RL in sample-starved applications. We demonstrate that the model-based (or "plug-in") approach achieves minimax-optimal sample complexity without burn-in cost for tabular Markov decision processes (MDPs). Concretely, consider a finite-horizon (resp. $γ$-discounted infinite-horizon) MDP with $S$ states and horizon $H$ (resp. effective horizon $\frac{1}{1-γ}$), and suppose the distribution shift of data is reflected by some single-policy clipped concentrability coefficient $C^{\star}_{\text{clipped}}$. We prove that model-based offline RL yields $\varepsilon$-accuracy with a sample complexity of \[ \begin{cases} \frac{H^{4}SC_{\text{clipped}}^{\star}}{\varepsilon^{2}} & (\text{finite-horizon MDPs}) \frac{SC_{\text{clipped}}^{\star}}{(1-γ)^{3}\varepsilon^{2}} & (\text{infinite-horizon MDPs}) \end{cases} \] up to log factor, which is minimax optimal for the entire $\varepsilon$-range. The proposed algorithms are "pessimistic" variants of value iteration with Bernstein-style penalties, and do not require sophisticated variance reduction. Our analysis framework is established upon delicate leave-one-out decoupling arguments in conjunction with careful self-bounding techniques tailored to MDPs.

stat.ML↗

arXiv2024

Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the theoretical underpinnings remain far from mature. In this work, we develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models in discrete time, assuming access to $\ell_2$-accurate estimates of the (Stein) score functions. For a popular deterministic sampler (based on the probability flow ODE), we establish a convergence rate proportional to $1/T$ (with $T$ the total number of steps), improving upon past results; for another mainstream stochastic sampler (i.e., a type of the denoising diffusion probabilistic model), we derive a convergence rate proportional to $1/\sqrt{T}$, matching the state-of-the-art theory. Imposing only minimal assumptions on the target data distribution (e.g., no smoothness assumption is imposed), our results characterize how $\ell_2$ score estimation errors affect the quality of the data generation processes. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach without resorting to toolboxes for SDEs and ODEs. Further, we design two accelerated variants, improving the convergence to $1/T^2$ for the ODE-based sampler and $1/T$ for the DDPM-type sampler, which might be of independent theoretical and empirical interest.

stat.ML↗

arXiv2024

Accelerating Convergence of Score-Based Diffusion Models, Provably

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate $O(1/{T}^2)$ with $T$ the number of steps, improving upon the $O(1/T)$ rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate $O(1/T)$, outperforming the rate $O(1/\sqrt{T})$ for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates $\ell_2$-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.

cs.LG↗

arXiv2024

Counterfactual Generation with Identifiability Guarantees

Counterfactual generation lies at the core of various machine learning tasks, including image translation and controllable text generation. This generation process usually requires the identification of the disentangled latent representations, such as content and style, that underlie the observed data. However, it becomes more challenging when faced with a scarcity of paired data and labeling information. Existing disentangled methods crucially rely on oversimplified assumptions, such as assuming independent content and style variables, to identify the latent variables, even though such assumptions may not hold for complex data distributions. For instance, food reviews tend to involve words like tasty, whereas movie reviews commonly contain words such as thrilling for the same positive sentiment. This problem is exacerbated when data are sampled from multiple domains since the dependence between content and style may vary significantly over domains. In this work, we tackle the domain-varying dependence between the content and the style variables inherent in the counterfactual generation task. We provide identification guarantees for such latent-variable models by leveraging the relative sparsity of the influences from different latent variables. Our theoretical insights enable the development of a doMain AdapTive counTerfactual gEneration model, called (MATTE). Our theoretically grounded framework achieves state-of-the-art performance in unsupervised style transfer tasks, where neither paired data nor style labels are utilized, across four large-scale datasets. Code is available at https://github.com/hanqi-qi/Matte.git

cs.LG↗

arXiv2024

Federated Offline Reinforcement Learning: Collaborative Single-Policy Coverage Suffices

Offline reinforcement learning (RL), which seeks to learn an optimal policy using offline data, has garnered significant interest due to its potential in critical applications where online data collection is infeasible or expensive. This work explores the benefit of federated learning for offline RL, aiming at collaboratively leveraging offline datasets at multiple agents. Focusing on finite-horizon episodic tabular Markov decision processes (MDPs), we design FedLCB-Q, a variant of the popular model-free Q-learning algorithm tailored for federated offline RL. FedLCB-Q updates local Q-functions at agents with novel learning rate schedules and aggregates them at a central server using importance averaging and a carefully designed pessimistic penalty term. Our sample complexity analysis reveals that, with appropriately chosen parameters and synchronization schedules, FedLCB-Q achieves linear speedup in terms of the number of agents without requiring high-quality datasets at individual agents, as long as the local datasets collectively cover the state-action space visited by the optimal policy, highlighting the power of collaboration in the federated setting. In fact, the sample complexity almost matches that of the single-agent counterpart, as if all the data are stored at a central location, up to polynomial factors of the horizon length. Furthermore, FedLCB-Q is communication-efficient, where the number of communication rounds is only linear with respect to the horizon length up to logarithmic factors.

cs.LG↗

arXiv2023

Distributionally Robust Model-Based Offline Reinforcement Learning with Near-Optimal Sample Complexity

This paper concerns the central issues of model robustness and sample efficiency in offline reinforcement learning (RL), which aims to learn to perform decision making from history data without active exploration. Due to uncertainties and variabilities of the environment, it is critical to learn a robust policy -- with as few samples as possible -- that performs well even when the deployed environment deviates from the nominal one used to collect the history dataset. We consider a distributionally robust formulation of offline RL, focusing on tabular robust Markov decision processes with an uncertainty set specified by the Kullback-Leibler divergence in both finite-horizon and infinite-horizon settings. To combat with sample scarcity, a model-based algorithm that combines distributionally robust value iteration with the principle of pessimism in the face of uncertainty is proposed, by penalizing the robust value estimates with a carefully designed data-driven penalty term. Under a mild and tailored assumption of the history dataset that measures distribution shift without requiring full coverage of the state-action space, we establish the finite-sample complexity of the proposed algorithms. We further develop an information-theoretic lower bound, which suggests that learning RMDPs is at least as hard as the standard MDPs when the uncertainty level is sufficient small, and corroborates the tightness of our upper bound up to polynomial factors of the (effective) horizon length for a range of uncertainty levels. To the best our knowledge, this provides the first provably near-optimal robust offline RL algorithm that learns under model uncertainty and partial coverage.

cs.LG↗

arXiv2023

The Blessing of Heterogeneity in Federated Q-Learning: Linear Speedup and Beyond

When the data used for reinforcement learning (RL) are collected by multiple agents in a distributed manner, federated versions of RL algorithms allow collaborative learning without the need for agents to share their local data. In this paper, we consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. Focusing on infinite-horizon tabular Markov decision processes, we provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning. In both cases, our bounds exhibit a linear speedup with respect to the number of agents and near-optimal dependencies on other salient problem parameters. In the asynchronous setting, existing analyses of federated Q-learning, which adopt an equally weighted averaging of local Q-estimates, require that every agent covers the entire state-action space. In contrast, our improved sample complexity scales inverse proportionally to the minimum entry of the average stationary state-action occupancy distribution of all agents, thus only requiring the agents to collectively cover the entire state-action space, unveiling the blessing of heterogeneity in enabling collaborative learning by relaxing the coverage requirement of the single-agent case. However, its sample complexity still suffers when the local trajectories are highly heterogeneous. In response, we propose a novel federated Q-learning algorithm with importance averaging, giving larger weights to more frequently visited state-action pairs, which achieves a robust linear speedup as if all trajectories are centrally processed, regardless of the heterogeneity of local behavior policies.

cs.LG↗