Despite the development of numerous adaptive optimizers, tuning the learning rate of stochastic gradient methods remains a major roadblock to obtaining good practical performance in machine learning. Rather than changing the learning rate at each iteration, we propose an approach that automates the most common hand-tuning heuristic: use a constant learning rate until "progress stops", then drop. We design an explicit statistical test that determines when the dynamics of stochastic gradient descent reach a stationary distribution. This test can be performed easily during training, and when it fires, we decrease the learning rate by a constant multiplicative factor. Our experiments on several deep learning tasks demonstrate that this statistical adaptive stochastic approximation (SASA) method can automatically find good learning rate schedules and match the performance of hand-tuned methods using default settings of its parameters. The statistical testing helps to control the variance of this procedure and improves its robustness.

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.

Large language models have demonstrated impressive capabilities across various natural language processing tasks, especially in solving mathematical problems. However, large language models are not good at math theorem proving using formal languages like Lean. A significant challenge in this area is the scarcity of training data available in these formal languages. To address this issue, we propose a novel pipeline that iteratively generates and filters synthetic data to translate natural language mathematical problems into Lean 4 statements, and vice versa. Our results indicate that the synthetic data pipeline can provide useful training data and improve the performance of LLMs in translating and understanding complex mathematical problems and proofs. Our final dataset contains about 57K formal-informal question pairs along with searched proof from the math contest forum and 21 new IMO questions.

Consider a player that in each of T rounds chooses one of K arms.

Conformal Prediction (CP) is a distribution-free uncertainty estimation framework that constructs prediction sets guaranteed to contain the true answer with a userspecified probability. Intuitively, the size of the prediction set encodes a general notion of uncertainty, with larger sets associated with higher degrees of uncertainty. In this work, we leverage information theory to connect conformal prediction to other notions of uncertainty. More precisely, we prove three different ways to upper bound the intrinsic uncertainty, as described by the conditional entropy of the target variable given the inputs, by combining CP with information theoretical inequalities. Moreover, we demonstrate two direct and useful applications of such connection between conformal prediction and information theory: (i) more principled and effective conformal training objectives that generalize previous approaches and enable end-to-end training of machine learning models from scratch, and (ii) a natural mechanism to incorporate side information into conformal prediction. We empirically validate both applications in centralized and federated learning settings, showing our theoretical results translate to lower inefficiency (average prediction set size) for popular CP methods.

Recent advancements in multimodal foundation models have showcased impressive capabilities in understanding and reasoning with visual and textual information. Adapting these foundation models trained for general usage to specialized domains like biomedicine requires large-scale domain-specific instruction datasets. While existing works have explored curating such datasets automatically, the resultant datasets are not explicitly aligned with domain expertise. In this work, we propose a data-centric framework, Biomedical Visual Instruction Tuning with Clinician Preference Alignment (BioMed-VITAL), that incorporates clinician preferences into both stages of generating and selecting instruction data for tuning biomedical multimodal foundation models. First, during the generation stage, we prompt the GPT-4V generator with a diverse set of clinician-selected demonstrations for preference-aligned data candidate generation. Then, during the selection phase, we train a separate selection model, which explicitly distills clinician and policy-guided model preferences into a rating function to select high-quality data for medical instruction tuning. Results show that the model tuned with the instruction data from our method demonstrates a significant improvement in open visual chat (18.5% relatively) and medical VQA (win rate up to 81.73%). Our instruction-following data, models, and code are available at https://BioMed-VITAL.github.io.

Artificial general intelligence on graphs has shown significant advancements across various applications, yet the traditional'Pre-train & Fine-tune' paradigm faces inefficiencies and negative transfer issues, particularly in complex and few-shot settings. Graph prompt learning emerges as a promising alternative, leveraging lightweight prompts to manipulate data and fill the task gap by reformulating downstream tasks to the pretext. However, several critical challenges still remain: how to unify diverse graph prompt models, how to evaluate the quality of graph prompts, and to improve their usability for practical comparisons and selection. In response to these challenges, we introduce the first comprehensive benchmark for graph prompt learning. Our benchmark integrates SIX pre-training methods and FIVE state-of-the-art graph prompt techniques, evaluated across FIFTEEN diverse datasets to assess performance, flexibility, and efficiency. We also present'ProG', an easy-to-use open-source library that streamlines the execution of various graph prompt models, facilitating objective evaluations. Additionally, we propose a unified framework that categorizes existing graph prompt methods into two main approaches: prompts as graphs and prompts as tokens. This framework enhances the applicability and comparison of graph prompt techniques.

Alon et al. [4] and Bun et al. [10] recently showed that online learnability and private PAC learnability are equivalent in binary classification. We investigate whether this equivalence extends to multi-class classification and regression. First, we show that private learnability implies online learnability in both settings. Our extension involves studying a novel variant of the Littlestone dimension that depends on a tolerance parameter and on an appropriate generalization of the concept of threshold functions beyond binary classification. Second, we show that while online learnability continues to imply private learnability in multi-class classification, current proof techniques encounter significant hurdles in the regression setting. While the equivalence for regression remains open, we provide non-trivial sufficient conditions for an online learnable class to also be privately learnable.

Imitation learning enables an agent to learn from expert demonstrations when the performance measure is unknown and the reward signal is not specified. Standard imitation methods do not generally apply when the learner and the expert's sensory capabilities mismatch and demonstrations are contaminated with unobserved confounding bias. To address these challenges, recent advancements in causal imitation learning have been pursued. However, these methods often require access to underlying causal structures that might not always be available, posing practical challenges. In this paper, we investigate robust imitation learning within the framework of canonical Markov Decision Processes (MDPs) using partial identification, allowing the agent to achieve expert performance even when the system dynamics are not uniquely determined from the confounded expert demonstrations. Specifically, first, we theoretically demonstrate that when unobserved confounders (UCs) exist in an MDP, the learner is generally unable to imitate expert performance. We then explore imitation learning in partially identifiable settings -- either transition distribution or reward function is non-identifiable from the available data and knowledge. Augmenting the celebrated GAIL method (Ho & Ermon, 2016), our analysis leads to two novel causal imitation algorithms that can obtain effective policies guaranteed to achieve expert performance.

Language models trained on diverse datasets unlock generalization by in-context learning. Reinforcement Learning (RL) policies can achieve a similar effect by meta-learning within the memory of a sequence model. However, meta-RL research primarily focuses on adapting to minor variations of a single task. It is difficult to scale towards more general behavior without confronting challenges in multi-task optimization, and few solutions are compatible with meta-RL's goal of learning from large training sets of unlabeled tasks. To address this challenge, we revisit the idea that multi-task RL is bottlenecked by imbalanced training losses created by uneven return scales across different tasks. We build upon recent advancements in Transformer-based (in-context) meta-RL and evaluate a simple yet scalable solution where both an agent's actor and critic objectives are converted to classification terms that decouple optimization from the current scale of returns. Large-scale comparisons in Meta-World ML45, Multi-Game Procgen, Multi-Task POPGym, Multi-Game Atari, and BabyAI find that this design unlocks significant progress in online multi-task adaptation and memory problems without explicit task labels.