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A central issue lying at the heart of online reinforcement learning (RL) is data efficiency. While a number of recent works achieved asymptotically minimal regret in online RL, the optimality of these results is only guaranteed in a “large-sample” regime, imposing enormous burn-in cost in order for their algorithms to operate optimally. How to achieve minimax-optimal regret without incurring any burn-in cost has been an open problem in RL theory. We settle this problem for finite-horizon inhomogeneous Markov decision processes. Specifically, we prove that a modified version ofMVP(Monotonic Value Propagation), an optimistic model-based algorithm proposed by Zhang et al. [82], achieves a regret on the order of (modulo log factors)\begin{equation*} \min \big \lbrace \sqrt {SAH^3K}, \,HK \big \rbrace,\end{equation*}whereSis the number of states,Ais the number of actions,His the horizon length, andKis the total number of episodes. This regret matches the minimax lower bound for the entire range of sample sizeK≥ 1, essentially eliminating any burn-in requirement. It also translates to a PAC sample complexity (i.e., the number of episodes needed to yield ε-accuracy) of\(\frac{SAH^3}{\varepsilon ^2} \)up to log factor, which is minimax-optimal for the full ε-range. Further, we extend our theory to unveil the influences of problem-dependent quantities like the optimal value/cost and certain variances. The key technical innovation lies in a novel analysis paradigm (based on a new concept called “profiles”) to decouple complicated statistical dependency across the sample trajectories — a long-standing challenge facing the analysis of online RL in the sample-starved regime. 

This paper is associated with a poster winner of a 2023 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, . Published by the American Physical Society2024 

The gradual nature of a diffusion process that synthesizes samples in small increments constitutes a key ingredient of Denoising Diffusion Probabilistic Models (DDPM), which have presented unprecedented quality in image synthesis and been recently explored in the motion domain. In this work, we propose to adapt the gradual diffusion concept (operating along a diffusion time-axis) into the temporal-axis of the motion sequence. Our key idea is to extend the DDPM framework to support temporally varying denoising, thereby entangling the two axes. Using our special formulation, we iteratively denoise a motion buffer that contains a set of increasingly-noised poses, which auto-regressively produces an arbitrarily long stream of frames. With a stationary diffusion time-axis, in each diffusion step we increment only the temporal-axis of the motion such that the framework produces a new, clean frame which is removed from the beginning of the buffer, followed by a newly drawn noise vector that is appended to it. This new mechanism paves the way towards a new framework for long-term motion synthesis with applications to character animation and other domains.