arXiv subjects

Mengdi Wang

Publications and source records attributed to Mengdi Wang.

At least 181 records · Page 10Linked to original sources

arXiv2024

Provable Statistical Rates for Consistency Diffusion Models

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive number of steps involved. In response, consistency models have been developed to merge multiple steps in the sampling process, thereby significantly boosting the speed of sample generation without compromising quality. This paper contributes towards the first statistical theory for consistency models, formulating their training as a distribution discrepancy minimization problem. Our analysis yields statistical estimation rates based on the Wasserstein distance for consistency models, matching those of vanilla diffusion models. Additionally, our results encompass the training of consistency models through both distillation and isolation methods, demystifying their underlying advantage.

cs.LG↗

arXiv2024

SAIL: Self-Improving Efficient Online Alignment of Large Language Models

Reinforcement Learning from Human Feedback (RLHF) is a key method for aligning large language models (LLMs) with human preferences. However, current offline alignment approaches like DPO, IPO, and SLiC rely heavily on fixed preference datasets, which can lead to sub-optimal performance. On the other hand, recent literature has focused on designing online RLHF methods but still lacks a unified conceptual formulation and suffers from distribution shift issues. To address this, we establish that online LLM alignment is underpinned by bilevel optimization. By reducing this formulation to an efficient single-level first-order method (using the reward-policy equivalence), our approach generates new samples and iteratively refines model alignment by exploring responses and regulating preference labels. In doing so, we permit alignment methods to operate in an online and self-improving manner, as well as generalize prior online RLHF methods as special cases. Compared to state-of-the-art iterative RLHF methods, our approach significantly improves alignment performance on open-sourced datasets with minimal computational overhead.

cs.LG↗

arXiv2024

Embedding Large Language Models into Extended Reality: Opportunities and Challenges for Inclusion, Engagement, and Privacy

Advances in artificial intelligence and human-computer interaction will likely lead to extended reality (XR) becoming pervasive. While XR can provide users with interactive, engaging, and immersive experiences, non-player characters are often utilized in pre-scripted and conventional ways. This paper argues for using large language models (LLMs) in XR by embedding them in avatars or as narratives to facilitate inclusion through prompt engineering and fine-tuning the LLMs. We argue that this inclusion will promote diversity for XR use. Furthermore, the versatile conversational capabilities of LLMs will likely increase engagement in XR, helping XR become ubiquitous. Lastly, we speculate that combining the information provided to LLM-powered spaces by users and the biometric data obtained might lead to novel privacy invasions. While exploring potential privacy breaches, examining user privacy concerns and preferences is also essential. Therefore, despite challenges, LLM-powered XR is a promising area with several opportunities.

cs.HC↗

arXiv2024

Self-Play with Adversarial Critic: Provable and Scalable Offline Alignment for Language Models

This work studies the challenge of aligning large language models (LLMs) with offline preference data. We focus on alignment by Reinforcement Learning from Human Feedback (RLHF) in particular. While popular preference optimization methods exhibit good empirical performance in practice, they are not theoretically guaranteed to converge to the optimal policy and can provably fail when the data coverage is sparse by classical offline reinforcement learning (RL) results. On the other hand, a recent line of work has focused on theoretically motivated preference optimization methods with provable guarantees, but these are not computationally efficient for large-scale applications like LLM alignment. To bridge this gap, we propose SPAC, a new offline preference optimization method with self-play, inspired by the on-average pessimism technique from the offline RL literature, to be the first provable and scalable approach to LLM alignment. We both provide theoretical analysis for its convergence under single-policy concentrability for the general function approximation setting and demonstrate its competitive empirical performance for LLM alignment on a 7B Mistral model with Open LLM Leaderboard evaluations.

cs.LG↗

arXiv2024

Transfer Q Star: Principled Decoding for LLM Alignment

Aligning foundation models is essential for their safe and trustworthy deployment. However, traditional fine-tuning methods are computationally intensive and require updating billions of model parameters. A promising alternative, alignment via decoding, adjusts the response distribution directly without model updates to maximize a target reward $r$, thus providing a lightweight and adaptable framework for alignment. However, principled decoding methods rely on oracle access to an optimal Q-function ($Q^*$), which is often unavailable in practice. Hence, prior SoTA methods either approximate this $Q^*$ using $Q^{π_{\texttt{sft}}}$ (derived from the reference $\texttt{SFT}$ model) or rely on short-term rewards, resulting in sub-optimal decoding performance. In this work, we propose Transfer $Q^*$, which implicitly estimates the optimal value function for a target reward $r$ through a baseline model $ρ_{\texttt{BL}}$ aligned with a baseline reward $ρ_{\texttt{BL}}$ (which can be different from the target reward $r$). Theoretical analyses of Transfer $Q^*$ provide a rigorous characterization of its optimality, deriving an upper bound on the sub-optimality gap and identifying a hyperparameter to control the deviation from the pre-trained reference $\texttt{SFT}$ model based on user needs. Our approach significantly reduces the sub-optimality gap observed in prior SoTA methods and demonstrates superior empirical performance across key metrics such as coherence, diversity, and quality in extensive tests on several synthetic and real datasets.

cs.CL↗

arXiv2024

AI Risk Management Should Incorporate Both Safety and Security

The exposure of security vulnerabilities in safety-aligned language models, e.g., susceptibility to adversarial attacks, has shed light on the intricate interplay between AI safety and AI security. Although the two disciplines now come together under the overarching goal of AI risk management, they have historically evolved separately, giving rise to differing perspectives. Therefore, in this paper, we advocate that stakeholders in AI risk management should be aware of the nuances, synergies, and interplay between safety and security, and unambiguously take into account the perspectives of both disciplines in order to devise mostly effective and holistic risk mitigation approaches. Unfortunately, this vision is often obfuscated, as the definitions of the basic concepts of "safety" and "security" themselves are often inconsistent and lack consensus across communities. With AI risk management being increasingly cross-disciplinary, this issue is particularly salient. In light of this conceptual challenge, we introduce a unified reference framework to clarify the differences and interplay between AI safety and AI security, aiming to facilitate a shared understanding and effective collaboration across communities.

cs.CR↗

arXiv2024

Embodied LLM Agents Learn to Cooperate in Organized Teams

Large Language Models (LLMs) have emerged as integral tools for reasoning, planning, and decision-making, drawing upon their extensive world knowledge and proficiency in language-related tasks. LLMs thus hold tremendous potential for natural language interaction within multi-agent systems to foster cooperation. However, LLM agents tend to over-report and comply with any instruction, which may result in information redundancy and confusion in multi-agent cooperation. Inspired by human organizations, this paper introduces a framework that imposes prompt-based organization structures on LLM agents to mitigate these problems. Through a series of experiments with embodied LLM agents and human-agent collaboration, our results highlight the impact of designated leadership on team efficiency, shedding light on the leadership qualities displayed by LLM agents and their spontaneous cooperative behaviors. Further, we harness the potential of LLMs to propose enhanced organizational prompts, via a Criticize-Reflect process, resulting in novel organization structures that reduce communication costs and enhance team efficiency.

cs.AI↗

arXiv2024

PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedback

We present a novel unified bilevel optimization-based framework, \textsf{PARL}, formulated to address the recently highlighted critical issue of policy alignment in reinforcement learning using utility or preference-based feedback. We identify a major gap within current algorithmic designs for solving policy alignment due to a lack of precise characterization of the dependence of the alignment objective on the data generated by policy trajectories. This shortfall contributes to the sub-optimal performance observed in contemporary algorithms. Our framework addressed these concerns by explicitly parameterizing the distribution of the upper alignment objective (reward design) by the lower optimal variable (optimal policy for the designed reward). Interestingly, from an optimization perspective, our formulation leads to a new class of stochastic bilevel problems where the stochasticity at the upper objective depends upon the lower-level variable. {True to our best knowledge, this work presents the first formulation of the RLHF as a bilevel optimization problem which generalizes the existing RLHF formulations and addresses the existing distribution shift issues in RLHF formulations.} To demonstrate the efficacy of our formulation in resolving alignment issues in RL, we devised an algorithm named \textsf{A-PARL} to solve PARL problem, establishing sample complexity bounds of order $\mathcal{O}(1/T)$. Our empirical results substantiate that the proposed \textsf{PARL} can address the alignment concerns in RL by showing significant improvements (up to 63\% in terms of required samples) for policy alignment in large-scale environments of the Deepmind control suite and Meta world tasks.

cs.LG↗

arXiv2024

An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

cs.LG↗

arXiv2024

Diffusion Model for Data-Driven Black-Box Optimization

Generative AI has redefined artificial intelligence, enabling the creation of innovative content and customized solutions that drive business practices into a new era of efficiency and creativity. In this paper, we focus on diffusion models, a powerful generative AI technology, and investigate their potential for black-box optimization over complex structured variables. Consider the practical scenario where one wants to optimize some structured design in a high-dimensional space, based on massive unlabeled data (representing design variables) and a small labeled dataset. We study two practical types of labels: 1) noisy measurements of a real-valued reward function and 2) human preference based on pairwise comparisons. The goal is to generate new designs that are near-optimal and preserve the designed latent structures. Our proposed method reformulates the design optimization problem into a conditional sampling problem, which allows us to leverage the power of diffusion models for modeling complex distributions. In particular, we propose a reward-directed conditional diffusion model, to be trained on the mixed data, for sampling a near-optimal solution conditioned on high predicted rewards. Theoretically, we establish sub-optimality error bounds for the generated designs. The sub-optimality gap nearly matches the optimal guarantee in off-policy bandits, demonstrating the efficiency of reward-directed diffusion models for black-box optimization. Moreover, when the data admits a low-dimensional latent subspace structure, our model efficiently generates high-fidelity designs that closely respect the latent structure. We provide empirical experiments validating our model in decision-making and content-creation tasks.

cs.LG↗

arXiv2024

Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate various conditional information, such as prompt input, to guide the sample generation towards desired properties. Despite the empirical success, theory of conditional diffusion models is largely missing. This paper bridges this gap by presenting a sharp statistical theory of distribution estimation using conditional diffusion models. Our analysis yields a sample complexity bound that adapts to the smoothness of the data distribution and matches the minimax lower bound. The key to our theoretical development lies in an approximation result for the conditional score function, which relies on a novel diffused Taylor approximation technique. Moreover, we demonstrate the utility of our statistical theory in elucidating the performance of conditional diffusion models across diverse applications, including model-based transition kernel estimation in reinforcement learning, solving inverse problems, and reward conditioned sample generation.

cs.LG↗

arXiv2024

Regularized DeepIV with Model Selection

In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. While recent advancements in machine learning have introduced flexible methods for IV estimation, they often encounter one or more of the following limitations: (1) restricting the IV regression to be uniquely identified; (2) requiring minimax computation oracle, which is highly unstable in practice; (3) absence of model selection procedure. In this paper, we present the first method and analysis that can avoid all three limitations, while still enabling general function approximation. Specifically, we propose a minimax-oracle-free method called Regularized DeepIV (RDIV) regression that can converge to the least-norm IV solution. Our method consists of two stages: first, we learn the conditional distribution of covariates, and by utilizing the learned distribution, we learn the estimator by minimizing a Tikhonov-regularized loss function. We further show that our method allows model selection procedures that can achieve the oracle rates in the misspecified regime. When extended to an iterative estimator, our method matches the current state-of-the-art convergence rate. Our method is a Tikhonov regularized variant of the popular DeepIV method with a non-parametric MLE first-stage estimator, and our results provide the first rigorous guarantees for this empirically used method, showcasing the importance of regularization which was absent from the original work.

cs.LG↗

arXiv2024

Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models

Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. Such information is coined as guidance. For example, in text-to-image synthesis, text input is encoded as guidance to generate semantically aligned images. Proper guidance inputs are closely tied to the performance of diffusion models. A common observation is that strong guidance promotes a tight alignment to the task-specific information, while reducing the diversity of the generated samples. In this paper, we provide the first theoretical study towards understanding the influence of guidance on diffusion models in the context of Gaussian mixture models. Under mild conditions, we prove that incorporating diffusion guidance not only boosts classification confidence but also diminishes distribution diversity, leading to a reduction in the differential entropy of the output distribution. Our analysis covers the widely adopted sampling schemes including DDPM and DDIM, and leverages comparison inequalities for differential equations as well as the Fokker-Planck equation that characterizes the evolution of probability density function, which may be of independent theoretical interest.

cs.LG↗

arXiv2024

Sample Complexity of Preference-Based Nonparametric Off-Policy Evaluation with Deep Networks

A recently popular approach to solving reinforcement learning is with data from human preferences. In fact, human preference data are now used with classic reinforcement learning algorithms such as actor-critic methods, which involve evaluating an intermediate policy over a reward learned from human preference data with distribution shift, known as off-policy evaluation (OPE). Such algorithm includes (i) learning reward function from human preference dataset, and (ii) learning expected cumulative reward of a target policy. Despite the huge empirical success, existing OPE methods with preference data often lack theoretical understanding and rely heavily on heuristics. In this paper, we study the sample efficiency of OPE with human preference and establish a statistical guarantee for it. Specifically, we approach OPE by learning the value function by fitted-Q-evaluation with a deep neural network. By appropriately selecting the size of a ReLU network, we show that one can leverage any low-dimensional manifold structure in the Markov decision process and obtain a sample-efficient estimator without suffering from the curse of high data ambient dimensionality. Under the assumption of high reward smoothness, our results \textit{almost align with the classical OPE results with observable reward data}. To the best of our knowledge, this is the first result that establishes a \textit{provably efficient} guarantee for off-policy evaluation with RLHF.

cs.LG↗

arXiv2024

Double Duality: Variational Primal-Dual Policy Optimization for Constrained Reinforcement Learning

We study the Constrained Convex Markov Decision Process (MDP), where the goal is to minimize a convex functional of the visitation measure, subject to a convex constraint. Designing algorithms for a constrained convex MDP faces several challenges, including (1) handling the large state space, (2) managing the exploration/exploitation tradeoff, and (3) solving the constrained optimization where the objective and the constraint are both nonlinear functions of the visitation measure. In this work, we present a model-based algorithm, Variational Primal-Dual Policy Optimization (VPDPO), in which Lagrangian and Fenchel duality are implemented to reformulate the original constrained problem into an unconstrained primal-dual optimization. Moreover, the primal variables are updated by model-based value iteration following the principle of Optimism in the Face of Uncertainty (OFU), while the dual variables are updated by gradient ascent. Moreover, by embedding the visitation measure into a finite-dimensional space, we can handle large state spaces by incorporating function approximation. Two notable examples are (1) Kernelized Nonlinear Regulators and (2) Low-rank MDPs. We prove that with an optimistic planning oracle, our algorithm achieves sublinear regret and constraint violation in both cases and can attain the globally optimal policy of the original constrained problem.

cs.LG↗

arXiv2024

Is Inverse Reinforcement Learning Harder than Standard Reinforcement Learning? A Theoretical Perspective

Inverse Reinforcement Learning (IRL) -- the problem of learning reward functions from demonstrations of an \emph{expert policy} -- plays a critical role in developing intelligent systems. While widely used in applications, theoretical understandings of IRL present unique challenges and remain less developed compared with standard RL. For example, it remains open how to do IRL efficiently in standard \emph{offline} settings with pre-collected data, where states are obtained from a \emph{behavior policy} (which could be the expert policy itself), and actions are sampled from the expert policy. This paper provides the first line of results for efficient IRL in vanilla offline and online settings using polynomial samples and runtime. Our algorithms and analyses seamlessly adapt the pessimism principle commonly used in offline RL, and achieve IRL guarantees in stronger metrics than considered in existing work. We provide lower bounds showing that our sample complexities are nearly optimal. As an application, we also show that the learned rewards can \emph{transfer} to another target MDP with suitable guarantees when the target MDP satisfies certain similarity assumptions with the original (source) MDP.

stat.ML↗

arXiv2024

Sample Complexity of Neural Policy Mirror Descent for Policy Optimization on Low-Dimensional Manifolds

Policy gradient methods equipped with deep neural networks have achieved great success in solving high-dimensional reinforcement learning (RL) problems. However, current analyses cannot explain why they are resistant to the curse of dimensionality. In this work, we study the sample complexity of the neural policy mirror descent (NPMD) algorithm with deep convolutional neural networks (CNN). Motivated by the empirical observation that many high-dimensional environments have state spaces possessing low-dimensional structures, such as those taking images as states, we consider the state space to be a $d$-dimensional manifold embedded in the $D$-dimensional Euclidean space with intrinsic dimension $d\ll D$. We show that in each iteration of NPMD, both the value function and the policy can be well approximated by CNNs. The approximation errors are controlled by the size of the networks, and the smoothness of the previous networks can be inherited. As a result, by properly choosing the network size and hyperparameters, NPMD can find an $ε$-optimal policy with $\widetilde{O}(ε^{-\frac{d}α-2})$ samples in expectation, where $α\in(0,1]$ indicates the smoothness of environment. Compared to previous work, our result exhibits that NPMD can leverage the low-dimensional structure of state space to escape from the curse of dimensionality, explaining the efficacy of deep policy gradient algorithms.

cs.LG↗

arXiv2024

Scalable Normalizing Flows Enable Boltzmann Generators for Macromolecules

The Boltzmann distribution of a protein provides a roadmap to all of its functional states. Normalizing flows are a promising tool for modeling this distribution, but current methods are intractable for typical pharmacological targets; they become computationally intractable due to the size of the system, heterogeneity of intra-molecular potential energy, and long-range interactions. To remedy these issues, we present a novel flow architecture that utilizes split channels and gated attention to efficiently learn the conformational distribution of proteins defined by internal coordinates. We show that by utilizing a 2-Wasserstein loss, one can smooth the transition from maximum likelihood training to energy-based training, enabling the training of Boltzmann Generators for macromolecules. We evaluate our model and training strategy on villin headpiece HP35(nle-nle), a 35-residue subdomain, and protein G, a 56-residue protein. We demonstrate that standard architectures and training strategies, such as maximum likelihood alone, fail while our novel architecture and multi-stage training strategy are able to model the conformational distributions of protein G and HP35.

cs.LG↗