We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. For weakly communicating MDPs, we establish the complexity bound $\widetilde{O}\left(SA\frac{\mathsf{H}}{\varepsilon^2} \right)$, where $\mathsf{H}$ 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 $S,A,\mathsf{H}$, and $\varepsilon$, improving on existing work that either assumes uniformly bounded mixing times for all policies or has suboptimal dependence on the parameters. We also initiate the study of sample complexity in general (multichain) average-reward MDPs. We argue a new transient time parameter $\mathsf{B}$ is necessary, establish an $\widetilde{O}\left(SA\frac{\mathsf{B} + \mathsf{H}}{\varepsilon^2} \right)$ complexity bound, and prove a matching (up to log factors) minimax lower bound. Both results are based on reducing the average-reward MDP to a discounted MDP, which requires new ideas in the general setting. To optimally analyze this reduction, we develop improved bounds for $\gamma$-discounted MDPs, showing that $\widetilde{O}\left(SA\frac{\mathsf{H}}{(1-\gamma)^2\varepsilon^2} \right)$ and $\widetilde{O}\left(SA\frac{\mathsf{B} + \mathsf{H}}{(1-\gamma)^2\varepsilon^2} \right)$ samples suffice to learn $\varepsilon$-optimal policies in weakly communicating and in general MDPs, respectively. Both these results circumvent the well-known minimax lower bound of $\widetilde{\Omega}\left(SA\frac{1}{(1-\gamma)^3\varepsilon^2} \right)$ for $\gamma$-discounted MDPs, and establish a quadratic rather than cubic horizon dependence for a fixed MDP instance.

We introduce VASA, a framework for generating lifelike talking faces with appealing visual affective skills (VAS) given a single static image and a speech audio clip. Our premiere model, VASA-1, is capable of not only generating lip movements that are exquisitely synchronized with the audio, but also producing a large spectrum of facial nuances and natural head motions that contribute to the perception of authenticity and liveliness. The core innovations include a diffusion-based holistic facial dynamics and head movement generation model that works in a face latent space, and the development of such an expressive and disentangled face latent space using videos.Through extensive experiments including evaluation on a set of new metrics, we show that our method significantly outperforms previous methods along various dimensions comprehensively. Our method delivers high video quality with realistic facial and head dynamics and also supports the online generation of 512$\times$512 videos at up to 40 FPS with negligible starting latency.It paves the way for real-time engagements with lifelike avatars that emulate human conversational behaviors.

We present Visual AutoRegressive modeling (VAR), a new generation paradigm that redefines the autoregressive learning on images as coarse-to-fine "next-scale prediction" or "next-resolution prediction", diverging from the standard raster-scan "next-token prediction". This simple, intuitive methodology allows autoregressive (AR) transformers to learn visual distributions fast and generalize well: VAR, for the first time, makes GPT-style AR models surpass diffusion transformers in image generation. On ImageNet 256x256 benchmark, VAR significantly improve AR baseline by improving Frechet inception distance (FID) from 18.65 to 1.73, inception score (IS) from 80.4 to 350.2, with around 20x faster inference speed. It is also empirically verified that VAR outperforms the Diffusion Transformer (DiT) in multiple dimensions including image quality, inference speed, data efficiency, and scalability. Scaling up VAR models exhibits clear power-law scaling laws similar to those observed in LLMs, with linear correlation coefficients near -0.998 as solid evidence. VAR further showcases zero-shot generalization ability in downstream tasks including image in-painting, out-painting, and editing. These results suggest VAR has initially emulated the two important properties of LLMs: Scaling Laws and zero-shot task generalization. We have released all models and codes to promote the exploration of AR/VAR models for visual generation and unified learning.