Reinforcement learning (RL) for large language models (LLMs) is dominated by the cost of rollout generation, which has motivated the use of low-precision rollouts (e.g., FP8) paired with a BF16 trainer to improve throughput and reduce memory pressure. This introduces a rollout-training mismatch that biases the policy gradient and can cause training to collapse outright on reasoning benchmarks. We show that the mismatch is non-stationary and acts as a double-edged sword: early in training it provides a stochastic exploration bonus, exposing the gradient to trajectories the trainer would otherwise under-sample, but the same perturbation transitions into a destabilizing source of bias as the policy concentrates. To solve this, we propose Adaptive Importance Sampling (AIS), a correction framework that adjusts the strength of its intervention on a per-batch basis. AIS combines three real-time diagnostics, namely weight reliability, divergence severity, and variance amplification, into a single mixing coefficient that interpolates between the uncorrected and fully importance-weighted gradients, suppressing the destabilizing component of the mismatch while preserving its exploratory benefit. We integrate AIS into GRPO and evaluate it on the diffusion-based LLaDA-8B-Instruct and the autoregressive Qwen3-8B and Qwen3.5-9B across mathematical reasoning and planning benchmarks. AIS matches the BF16 baseline on most tasks while retaining the 1.5 to 2.76x rollout speedup of FP8.

We draw the data points by random sampling from the full data according to their gradient values.

Neural Information Processing Systems http://nips.cc/

Weaknesses: (W1) - The contributions of the paper are very close from the one of [12]. Indeed, it takes ideas from [12] to restrict the analysis on a simplex that we can control. Moreover, it doesn't clearly put forward the novelty of the bound on dynamic regret compared to the one of [18]. For instance, the following sentence serves to define a key quantity in the authors development: ''For each i [N ], denote by hti the last observed gradient of fi at time t, with h1i initialized arbitrarily'' Unfortunately, it is quite unclear as two readers might understand something different. In the same line of comments, the proof of Lemma 3 is very confusing.

In the era of big data, researchers and practitioners across various domains are grappling with datasets of unprecedented scale and complexity. These high-dimensional datasets, characterized by a large number of features relative to the sample size, pose significant challenges to traditional statistical methods. Simultaneously, the increasing prevalence of non-standard data environments, such as those with heavy-tailed distributions or complex dependence structures, further complicates the landscape of data analysis. Subsampling techniques have emerged as a promising approach to address the computational challenges associated with large-scale data analysis. By working with a carefully chosen subset of the data, these methods aim to achieve a balance between statistical accuracy and computational efficiency. However, the theoretical foundations of subsampling in high-dimensional, nonstandard environments remain inadequately explored, leaving a critical gap in our understanding of their statistical properties and practical applicability.

Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies. Recently, the problem of designing such schemes was formulated as an online learning problem with bandit feedback, and algorithms with sub-linear static regret were designed. In this work, we build on this framework and propose a simple and efficient algorithm for adaptive importance sampling for finite-sum optimization and sampling with decreasing step-sizes. Under standard technical conditions, we show that our proposed algorithm achieves O(T {2/3}) and O(T {5/6}) dynamic regret for SGD and SGLD respectively when run with O(1/t) step sizes.

Importance sampling has become an indispensable strategy to speed up optimization algorithms for large-scale applications. Improved adaptive variants--using importance values defined by the complete gradient information which changes during optimization--enjoy favorable theoretical properties, but are typically computationally infeasible. In this paper we propose an efficient approximation of gradient-based sampling, which is based on safe bounds on the gradient. The proposed sampling distribution is (i) provably the best sampling with respect to the given bounds, (ii) always better than uniform sampling and fixed importance sampling and (iii) can efficiently be computed--in many applications at negligible extra cost. The proposed sampling scheme is generic and can easily be integrated into existing algorithms. In particular, we show that coordinate-descent (CD) and stochastic gradient descent (SGD) can enjoy significant a speed-up under the novel scheme. The proven efficiency of the proposed sampling is verified by extensive numerical testing.

In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the input data but independent on the response variable, however the response variable may also be informative for sampling. In this paper we propose an adaptive sampling called the gradient-based sampling which is dependent on both the input data and the output for fast solving of least-square (LS) problems. We draw the data points by random sampling from the full data according to their gradient values. This sampling is computationally saving, since the running time of computing the sampling probabilities is reduced to O(nd) where n is the full sample size and d is the dimension of the input. Theoretically, we establish an error bound analysis of the general importance sampling with respect to LS solution from full data. The result establishes an improved performance of the use of our gradientbased sampling. Synthetic and real data sets are used to empirically argue that the gradient-based sampling has an obvious advantage over existing sampling methods from two aspects of statistical efficiency and computational saving.

We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS. We build on Optimised Adaptive Importance Samplers (OAIS), a class of techniques that adapt proposals to improve the mean-squared error of the importance sampling estimators by parameterising the proposal and optimising the $\chi^2$-divergence between the target and the proposal. We show that a naive implementation of OAIS using stochastic gradient descent may lead to unstable estimators despite its convergence guarantees. To remedy this shortcoming, we instead propose to use adaptive optimisers (such as AdaGrad and Adam) to improve the stability of the OAIS. We provide convergence results for AdaOAIS in a similar manner to OAIS. We also provide empirical demonstration on a variety of examples and show that AdaOAIS lead to stable importance sampling estimators in practice.

Importance sampling has become an indispensable strategy to speed up optimization algorithms for large-scale applications. Improved adaptive variants -- using importance values defined by the complete gradient information which changes during optimization -- enjoy favorable theoretical properties, but are typically computationally infeasible. In this paper we propose an efficient approximation of gradient-based sampling, which is based on safe bounds on the gradient. The proposed sampling distribution is (i) provably the \emph{best sampling} with respect to the given bounds, (ii) always better than uniform sampling and fixed importance sampling and (iii) can efficiently be computed -- in many applications at negligible extra cost. The proposed sampling scheme is generic and can easily be integrated into existing algorithms. In particular, we show that coordinate-descent (CD) and stochastic gradient descent (SGD) can enjoy significant a speed-up under the novel scheme. The proven efficiency of the proposed sampling is verified by extensive numerical testing.