Wenpin Tang

Hanyang Zhao, Haoxian Chen, Ji Zhang et al.

Reinforcement Learning from human feedback (RLHF) has been shown a promising direction for aligning generative models with human intent and has also been explored in recent works for alignment of diffusion generative models. In this work, we provide a rigorous treatment by formulating the task of fine-tuning diffusion models, with reward functions learned from human feedback, as an exploratory continuous-time stochastic control problem. Our key idea lies in treating the score-matching functions as controls/actions, and upon this, we develop a unified framework from a continuous-time perspective, to employ reinforcement learning (RL) algorithms in terms of improving the generation quality of diffusion models. We also develop the corresponding continuous-time RL theory for policy optimization and regularization under assumptions of stochastic different equations driven environment. Experiments on the text-to-image (T2I) generation will be reported in the accompanied paper.

Haoting Zhang, Haoxian Chen, Donglin Zhan et al.

The field of simulation optimization (SO) encompasses various methods developed to optimize complex, expensive-to-sample stochastic systems. Established methods include, but are not limited to, ranking-and-selection for finite alternatives and surrogate-based methods for continuous domains, with broad applications in engineering and operations management. The recent advent of large language models (LLMs) offers a new paradigm for exploiting system structure and automating the strategic selection and composition of these established SO methods into a tailored optimization procedure. This work introduces SOCRATES (Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations), a novel two-stage procedure that leverages LLMs to automate the design of tailored SO algorithms. The first stage constructs an ensemble of digital replicas of the real system. An LLM is employed to implement causal discovery from a textual description of the system, generating a structural `skeleton' that guides the sample-efficient learning of the replicas. In the second stage, this replica ensemble is used as an inexpensive testbed to evaluate a set of baseline SO algorithms. An LLM then acts as a meta-optimizer, analyzing the performance trajectories of these algorithms to iteratively revise and compose a final, hybrid optimization schedule. This schedule is designed to be adaptive, with the ability to be updated during the final execution on the real system when the optimization performance deviates from expectations. By integrating LLM-driven reasoning with LLM-assisted trajectory-aware meta-optimization, SOCRATES creates an effective and sample-efficient solution for complex SO optimization problems.

Hanyang Zhao, Dawen Liang, Wenpin Tang et al.

We propose DiFFPO, Diffusion Fast and Furious Policy Optimization, a unified framework for training masked diffusion large language models (dLLMs) to reason not only better (furious), but also faster via reinforcement learning (RL). We first unify the existing baseline approach such as d1 by proposing to train surrogate policies via off-policy RL, whose likelihood is much more tractable as an approximation to the true dLLM policy. This naturally motivates a more accurate and informative two-stage likelihood approximation combined with importance sampling correction, which leads to generalized RL algorithms with better sample efficiency and superior task performance. Second, we propose a new direction of joint training efficient samplers/controllers of dLLMs policy. Via RL, we incentivize dLLMs' natural multi-token prediction capabilities by letting the model learn to adaptively allocate an inference threshold for each prompt. By jointly training the sampler, we yield better accuracies with lower number of function evaluations (NFEs) compared to training the model only, obtaining the best performance in improving the Pareto frontier of the inference-time compute of dLLMs. We showcase the effectiveness of our pipeline by training open source large diffusion language models over benchmark math and planning tasks.

Wenpin Tang, Hanyang Zhao

This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling -- sampling and score matching, which encompass the SDE/ODE sampling, score matching efficiency, the consistency models, and reinforcement learning. Short proofs are given to illustrate the main idea of the stated results. The article is primarily a technical introduction to the field, and practitioners may also find some analysis useful in designing new models or algorithms.

Wenpin Tang, Fuzhong Zhou

This paper aims to develop and provide a rigorous treatment to the problem of entropy regularized fine-tuning in the context of continuous-time diffusion models, which was recently proposed by Uehara et al. (arXiv:2402.15194, 2024). The idea is to use stochastic control for sample generation, where the entropy regularizer is introduced to mitigate reward collapse. We also show how the analysis can be extended to fine-tuning with a general $f$-divergence regularizer. Numerical experiments on large-scale text-to-image models--Stable Diffusion v1.5 are conducted to validate our approach.

Wenpin Tang, Hanyang Zhao

Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed score matching, we propose a new criterion -- the contraction property of backward sampling in the design of DPMs, leading to a novel class of contractive DPMs (CDPMs). Our key insight is that, the contraction property can provably narrow score matching errors and discretization errors, thus our proposed CDPMs are robust to both sources of error. For practical use, we show that CDPM can leverage weights of pretrained DPMs by a simple transformation, and does not need retraining. We corroborated our approach by experiments on synthetic 1-dim examples, Swiss Roll, MNIST, CIFAR-10 32$\times$32 and AFHQ 64$\times$64 dataset. Notably, CDPM steadily improves the performance of baseline score-based diffusion models.

Hanyang Zhao, Haoxian Chen, Ji Zhang et al.

Reinforcement learning from human feedback (RLHF), which aligns a diffusion model with input prompt, has become a crucial step in building reliable generative AI models. Most works in this area use a discrete-time formulation, which is prone to induced discretization errors, and often not applicable to models with higher-order/black-box solvers. The objective of this study is to develop a disciplined approach to fine-tune diffusion models using continuous-time RL, formulated as a stochastic control problem with a reward function that aligns the end result (terminal state) with input prompt. The key idea is to treat score matching as controls or actions, and thereby making connections to policy optimization and regularization in continuous-time RL. To carry out this idea, we lay out a new policy optimization framework for continuous-time RL, and illustrate its potential in enhancing the value networks design space via leveraging the structural property of diffusion models. We validate the advantages of our method by experiments in downstream tasks of fine-tuning large-scale Text2Image models of Stable Diffusion v1.5.

Zhengyi Guo, Wenpin Tang, Renyuan Xu

We study conditional generation in diffusion models under hard constraints, where generated samples must satisfy prescribed events with probability one. Such constraints arise naturally in safety-critical applications and in rare-event simulation, where soft or reward-based guidance methods offer no guarantee of constraint satisfaction. Building on a probabilistic interpretation of diffusion models, we develop a principled conditional diffusion guidance framework based on Doob's h-transform, martingale representation and quadratic variation process. Specifically, the resulting guided dynamics augment a pretrained diffusion with an explicit drift correction involving the logarithmic gradient of a conditioning function, without modifying the pretrained score network. Leveraging martingale and quadratic-variation identities, we propose two novel off-policy learning algorithms based on a martingale loss and a martingale-covariation loss to estimate h and its gradient using only trajectories from the pretrained model. We provide non-asymptotic guarantees for the resulting conditional sampler in both total variation and Wasserstein distances, explicitly characterizing the impact of score approximation and guidance estimation errors. Numerical experiments demonstrate the effectiveness of the proposed methods in enforcing hard constraints and generating rare-event samples.

Hanyang Zhao, Wenpin Tang, David D. Yao

We study reinforcement learning (RL) in the setting of continuous time and space, for an infinite horizon with a discounted objective and the underlying dynamics driven by a stochastic differential equation. Built upon recent advances in the continuous approach to RL, we develop a notion of occupation time (specifically for a discounted objective), and show how it can be effectively used to derive performance-difference and local-approximation formulas. We further extend these results to illustrate their applications in the PG (policy gradient) and TRPO/PPO (trust region policy optimization/ proximal policy optimization) methods, which have been familiar and powerful tools in the discrete RL setting but under-developed in continuous RL. Through numerical experiments, we demonstrate the effectiveness and advantages of our approach.

Wenpin Tang, Xun Yu Zhou

We study the convergence rate of continuous-time simulated annealing $(X_t; \, t \ge 0)$ and its discretization $(x_k; \, k =0,1, \ldots)$ for approximating the global optimum of a given function $f$. We prove that the tail probability $\mathbb{P}(f(X_t) > \min f +δ)$ (resp. $\mathbb{P}(f(x_k) > \min f +δ)$) decays polynomial in time (resp. in cumulative step size), and provide an explicit rate as a function of the model parameters. Our argument applies the recent development on functional inequalities for the Gibbs measure at low temperatures -- the Eyring-Kramers law. In the discrete setting, we obtain a condition on the step size to ensure the convergence.

Wenpin Tang

In this paper, we consider mixtures of multinomial logistic models (MNL), which are known to $ε$-approximate any random utility model. Despite its long history and broad use, rigorous results are only available for learning a uniform mixture of two MNLs. Continuing this line of research, we study the problem of learning an arbitrary mixture of two MNLs. We show that the identifiability of the mixture models may only fail on an algebraic variety of a negligible measure. This is done by reducing the problem of learning a mixture of two MNLs to the problem of solving a system of univariate quartic equations. We also devise an algorithm to learn any mixture of two MNLs using a polynomial number of samples and a linear number of queries, provided that a mixture of two MNLs over some finite universe is identifiable. Several numerical experiments and conjectures are also presented.

Xin Guo, Jiequn Han, Mahan Tajrobehkar et al.

Motivated by the super-diffusivity of self-repelling random walk, which has roots in statistical physics, this paper develops a new perturbation mechanism for optimization algorithms. In this mechanism, perturbations are adapted to the history of states via the notion of occupation time. After integrating this mechanism into the framework of perturbed gradient descent (PGD) and perturbed accelerated gradient descent (PAGD), two new algorithms are proposed: perturbed gradient descent adapted to occupation time (PGDOT) and its accelerated version (PAGDOT). PGDOT and PAGDOT are shown to converge to second-order stationary points at least as fast as PGD and PAGD, respectively, and thus they are guaranteed to avoid getting stuck at non-degenerate saddle points. The theoretical analysis is corroborated by empirical studies in which the new algorithms consistently escape saddle points and outperform not only their counterparts, PGD and PAGD, but also other popular alternatives including stochastic gradient descent, Adam, AMSGrad, and RMSProp.