Yifan Hu

Xin Chen, Yifan Hu, Minda Zhao

Policy gradient methods are widely used in reinforcement learning. Yet, the nonconvexity of policy optimization imposes significant challenges in understanding the global convergence of policy gradient methods. For a class of finite-horizon Markov Decision Processes (MDPs) with general state and action spaces, we develop a framework that provides a set of easily verifiable assumptions to ensure the Kurdyka-Lojasiewicz (KL) condition of the policy optimization. Leveraging the KL condition, policy gradient methods converge to the globally optimal policy with a non-asymptomatic rate despite nonconvexity. Our results find applications in various control and operations models, including entropy-regularized tabular MDPs, Linear Quadratic Regulator (LQR) problems, stochastic inventory models, and stochastic cash balance problems, for which we show an $ε$-optimal policy can be obtained using a sample size in $\tilde{\mathcal{O}}(ε^{-1})$ and polynomial in terms of the planning horizon by stochastic policy gradient methods. Our result establishes the first sample complexity for multi-period inventory systems with Markov-modulated demands and stochastic cash balance problems in the literature.

Cai Zhou, Chenxiao Yang, Yi Hu et al.

Diffusion language models, especially masked discrete diffusion models, have achieved great success recently. While there are some theoretical and primary empirical results showing the advantages of latent reasoning with looped transformers or continuous chain-of-thoughts, continuous diffusion models typically underperform their discrete counterparts. In this paper, we argue that diffusion language models do not necessarily need to be in the discrete space. In particular, we prove that continuous diffusion models have stronger expressivity than discrete diffusions and looped transformers. We attribute the contradiction between the theoretical expressiveness and empirical performance to their practical trainability: while continuous diffusion provides intermediate supervision that looped transformers lack, they introduce additional difficulty decoding tokens into the discrete token space from the continuous representation space. We therefore propose Coevolutionary Continuous Discrete Diffusion (CCDD), which defines a joint multimodal diffusion process on the union of a continuous representation space and a discrete token space, leveraging a single model to simultaneously denoise in the joint space. By combining two modalities, CCDD is expressive with rich semantics in the latent space, as well as good trainability and sample quality with the help of explicit discrete tokens. We also propose effective architectures and advanced training/sampling techniques for CCDD, which reveals strong empirical performance in extensive language modeling experiments on real-world tasks.