Consistency Models (CMs) have shown promise for efficient one-step generation. However, most existing CMs rely on manually designed discretization schemes, which can cause repeated adjustments for different noise schedules and datasets. To address this, we propose a unified framework for the automatic and adaptive discretization of CMs, formulating it as an optimization problem with respect to the discretization step. Concretely, during the consistency training process, we propose using local consistency as the optimization objective to ensure trainability by avoiding excessive discretization, and taking global consistency as a constraint to ensure stability by controlling the denoising error in the training target. We establish the trade-off between local and global consistency with a Lagrange multiplier. Building on this framework, we achieve adaptive discretization for CMs using the Gauss-Newton method. We refer to our approach as ADCMs. Experiments demonstrate that ADCMs significantly improve the training efficiency of CMs, achieving superior generative performance with minimal training overhead on both CIFAR-10 and ImageNet. Moreover, ADCMs exhibit strong adaptability to more advanced DM variants.

Ouralgorithm isbasedonoptimistic one-stepvalueiteration extended to maintain an adaptive discretization of the space. From atheoretical perspective we provide worst-case regret bounds for our algorithm which are competitivecompared tothestate-of-the-art model-based algorithms.

We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space. From a theoretical perspective we provide worst-case regret bounds for our algorithm which are competitive compared to the state-of-the-art model-based algorithms. Moreover, our bounds are obtained via a modular proof technique which can potentially extend to incorporate additional structure on the problem. From an implementation standpoint, our algorithm has much lower storage and computational requirements due to maintaining a more efficient partition of the state and action spaces. We illustrate this via experiments on several canonical control problems, which shows that our algorithm empirically performs significantly better than fixed discretization in terms of both faster convergence and lower memory usage. Interestingly, we observe empirically that while fixed discretization model-based algorithms vastly outperform their model-free counterparts, the two achieve comparable performance with adaptive discretization.

We provide storage, time, and regret guarantees for our algorithm. Our regret bound is novel vs. prior work with MB has minimal tuning, and needs much less storage. Also, by using a simpler basis (step functions) we get lower storage, runtime. MB under resource constraints (i.e., on-policy settings) would be unfair. (Table 1).

Additional Feedback: medium points: table 1: the "Lower Bounds" method doesn't have "Time complexity" or "Space complexity" entries? Also why is it separated from the other prior work? Is this assuming something the others baselines in Table 1 aren't? If so, is this a fair comparison then? Everything except red (epsilonQL) seems to perform the same.

The work has clear positives: paper presents a novel algorithm that achieves low regret novel consideration of adaptive discretization for model-based RL (prior work focuses on the model-free case) important practical focus on computational resources novel theory However, there are significant issues as well: - the experiments are not were presented or discussed within the context of the rest of the paper: they appear to contradict the main messages of the paper - there is confusion over how the experiments were implemented and evaluated (e.g., proper averaging over independent runs, fair treatment of hyperparameters etc). See R1 for more details - the proposed algorithm exhibits space complexity that monotonically increases; the authors suggested to just cap it - poor discussion of model-based RL with function approximation (linear dyna, recent deep learning approaches etc) - related no clear argument why we would explore adaptive discretization approaches compared to other approaches. The paper is doing something different than the majority of the community---that can be good but it should be directly addressed Summary of the discussion. The reviewers thought the experiments considerably weakened the paper, and it would be best if they were removed from the paper. The strongest advocate of the paper had low confidence and not much to say much during discussion.

We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space. From a theoretical perspective we provide worst-case regret bounds for our algorithm which are competitive compared to the state-of-the-art model-based algorithms. Moreover, our bounds are obtained via a modular proof technique which can potentially extend to incorporate additional structure on the problem. From an implementation standpoint, our algorithm has much lower storage and computational requirements due to maintaining a more efficient partition of the state and action spaces.

We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space. From a theoretical perspective we provide worst-case regret bounds for our algorithm which are competitive compared to the state-of-the-art model-based algorithms. Moreover, our bounds are obtained via a modular proof technique which can potentially extend to incorporate additional structure on the problem. From an implementation standpoint, our algorithm has much lower storage and computational requirements due to maintaining a more efficient partition of the state and action spaces. We illustrate this via experiments on several canonical control problems, which shows that our algorithm empirically performs significantly better than fixed discretization in terms of both faster convergence and lower memory usage. Interestingly, we observe empirically that while fixed-discretization model-based algorithms vastly outperform their model-free counterparts, the two achieve comparable performance with adaptive discretization.