We study the problem of learning a series of tasks in a fully online Meta-Learning setting. The goal is to exploit similarities among the tasks to incrementally adapt an inner online algorithm in order to incur a low averaged cumulative error over the tasks. We focus on a family of inner algorithms based on a parametrized variant of online Mirror Descent. The inner algorithm is incrementally adapted by an online Mirror Descent meta-algorithm using the corresponding within-task minimum regularized empirical risk as the meta-loss. In order to keep the process fully online, we approximate the meta-subgradients by the online inner algorithm. An upper bound on the approximation error allows us to derive a cumulative error bound for the proposed method. Our analysis can also be converted to the statistical setting by online-to-batch arguments. We instantiate two examples of the framework in which the meta-parameter is either a common bias vector or feature map. Finally, preliminary numerical experiments confirm our theoretical findings.

Evaluation of machine learning models typically emphasizes final accuracy, overlooking the cost of adaptation: the cumulative errors incurred while learning from scratch. Guess-and- Learn (G&L) v1.0 addresses this gap by measuring cold-start adaptability - the total mistakes a model makes while sequentially labeling an unlabeled dataset. At each step, the learner selects an instance, predicts its label, receives the ground truth, and updates parameters under either online (per-sample) or batch (delayed) mode. The resulting error trajectory exposes adaptation speed, selection quality, and bias - dynamics invisible to endpoint metrics. G&L defines four tracks (Scratch/Pretrained $\times$ Online/Batch) to disentangle the effects of initialization and update frequency. We formalize the protocol, relate it to classical mistake-bound theory, and estimate a heuristic "oracle reference band" for MNIST as a plausibility reference. Baseline experiments on MNIST and AG News, spanning classical methods (Perceptron, k-NN), convolutional architectures (CNN, ResNet-50), and pretrained transformers (ViT-B/16, BERT-base), reveal systematic differences in early-phase efficiency: smaller models can adapt with fewer initial errors, while pretraining benefits vary by domain. Across settings, current models remain well above the oracle band, highlighting an adaptability gap. By quantifying the mistake cost of early learning, G&L complements conventional benchmarks and provides a reproducible framework for developing learners that are not only accurate in the limit but also reliable from the first examples.

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

We study the stochastic linear bandit problem with multiple arms over $T$ rounds, where the covariate dimension $d$ may exceed $T$, but each arm-specific parameter vector is $s$-sparse. We begin by analyzing the sequential estimation problem in the single-arm setting, focusing on cumulative mean-squared error. We show that Lasso estimators are provably suboptimal in the sequential setting, exhibiting suboptimal dependence on $d$ and $T$, whereas thresholded Lasso estimators -- obtained by applying least squares to the support selected by thresholding an initial Lasso estimator -- achieve the minimax rate. Building on these insights, we consider the full linear contextual bandit problem and propose a three-stage arm selection algorithm that uses thresholded Lasso as the main estimation method. We derive an upper bound on the cumulative regret of order $s(\log s)(\log d + \log T)$, and establish a matching lower bound up to a $\log s$ factor, thereby characterizing the minimax regret rate up to a logarithmic term in $s$. Moreover, when a short initial period is excluded from the regret, the proposed algorithm achieves exact minimax optimality.

Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like Chain-of-Thought, debating, and self-refinement have been applied to auto-regressive LLMs, achieving significant successes in tasks such as mathematical reasoning, commonsense reasoning, and multi-hop question answering. Despite these successes, the theoretical basis for how multi-round reasoning enhances problem-solving abilities remains underexplored. In this work, we investigate the approximation, learnability, and generalization properties of multi-round auto-regressive models. We show that Transformers with finite context windows are universal approximators for steps of Turing-computable functions and can approximate any Turing-computable sequence-to-sequence function through multi-round reasoning. We extend PAC learning to sequence generation and demonstrate that multi-round generation is learnable even when the sequence length exceeds the model's context window. Finally, we examine how generalization error propagates across rounds, and show how the aforementioned approaches can help constrain this error, ensuring outputs stay within an expectation boundary. This work sheds light on the systemic theoretical foundations of multi-round sequence learning and reasoning, emphasizing its role in inference complexity.

We study the problem of learning a series of tasks in a fully online Meta-Learning setting. The goal is to exploit similarities among the tasks to incrementally adapt an inner online algorithm in order to incur a low averaged cumulative error over the tasks. We focus on a family of inner algorithms based on a parametrized variant of online Mirror Descent. The inner algorithm is incrementally adapted by an online Mirror Descent meta-algorithm using the corresponding within-task minimum regularized empirical risk as the meta-loss. In order to keep the process fully online, we approximate the meta-subgradients by the online inner algorithm.

Autoregressive next-token prediction is a standard pretraining method for large-scale language models, but its application to vision tasks is hindered by the non-sequential nature of image data, leading to cumulative errors. Most vision models employ masked autoencoder (MAE) based pretraining, which faces scalability issues. To address these challenges, we introduce \textbf{TokenUnify}, a novel pretraining method that integrates random token prediction, next-token prediction, and next-all token prediction. We provide theoretical evidence demonstrating that TokenUnify mitigates cumulative errors in visual autoregression. Cooperated with TokenUnify, we have assembled a large-scale electron microscopy (EM) image dataset with ultra-high resolution, ideal for creating spatially correlated long sequences. This dataset includes over 120 million annotated voxels, making it the largest neuron segmentation dataset to date and providing a unified benchmark for experimental validation. Leveraging the Mamba network inherently suited for long-sequence modeling on this dataset, TokenUnify not only reduces the computational complexity but also leads to a significant 45\% improvement in segmentation performance on downstream EM neuron segmentation tasks compared to existing methods. Furthermore, TokenUnify demonstrates superior scalability over MAE and traditional autoregressive methods, effectively bridging the gap between pretraining strategies for language and vision models. Code is available at \url{https://github.com/ydchen0806/TokenUnify}.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

The average reward criterion is relatively less studied as most existing works in the Reinforcement Learning literature consider the discounted reward criterion. There are few recent works that present on-policy average reward actor-critic algorithms, but average reward off-policy actor-critic is relatively less explored. In this work, we present both on-policy and off-policy deterministic policy gradient theorems for the average reward performance criterion. Using these theorems, we also present an Average Reward Off-Policy Deep Deterministic Policy Gradient (ARO-DDPG) Algorithm. We first show asymptotic convergence analysis using the ODE-based method. Subsequently, we provide a finite time analysis of the resulting stochastic approximation scheme with linear function approximator and obtain an $\epsilon$-optimal stationary policy with a sample complexity of $\Omega(\epsilon^{-2.5})$. We compare the average reward performance of our proposed ARO-DDPG algorithm and observe better empirical performance compared to state-of-the-art on-policy average reward actor-critic algorithms over MuJoCo-based environments.