This paper proposes a hierarchical Bayesian multitask learning model that is applicable to the general multi-task binary classification learning problem where the model assumes a shared sparsity structure across different tasks. We derive a computationally efficient inference algorithm based on variational inference to approximate the posterior distribution. We demonstrate the potential of the new approach on various synthetic datasets and for predicting human health status based on microbiome profile. Our analysis incorporates data pooled from multiple microbiome studies, along with a comprehensive comparison with other benchmark methods. Results in synthetic datasets show that the proposed approach has superior support recovery property when the underlying regression coefficients share a common sparsity structure across different tasks. Our experiments on microbiome classification demonstrate the utility of the method in extracting informative taxa while providing well-calibrated predictions with uncertainty quantification and achieving competitive performance in terms of prediction metrics. Notably, despite the heterogeneity of the pooled datasets (e.g., different experimental objectives, laboratory setups, sequencing equipment, patient demographics), our method delivers robust results.

Prediction-powered inference (PPI) enables valid statistical inference by combining experimental data with machine learning predictions. When a sufficient number of high-quality predictions is available, PPI results in more accurate estimates and tighter confidence intervals than traditional methods. In this paper, we propose to inform the PPI framework with prior knowledge on the quality of the predictions. The resulting method, which we call frequentist, assisted by Bayes, PPI (FAB-PPI), improves over PPI when the observed prediction quality is likely under the prior, while maintaining its frequentist guarantees. Furthermore, when using heavy-tailed priors, FAB-PPI adaptively reverts to standard PPI in low prior probability regions. We demonstrate the benefits of FAB-PPI in real and synthetic examples.

Self-Explainable Graph Neural Networks (SE-GNNs) are popular explainable-by-design GNNs, but the properties and the limitations of their explanations are not well understood. Our first contribution fills this gap by formalizing the explanations extracted by SE-GNNs, referred to as Trivial Explanations (TEs), and comparing them to established notions of explanations, namely Prime Implicant (PI) and faithful explanations. Our analysis reveals that TEs match PI explanations for a restricted but significant family of tasks. In general, however, they can be less informative than PI explanations and are surprisingly misaligned with widely accepted notions of faithfulness. Although faithful and PI explanations are informative, they are intractable to find and we show that they can be prohibitively large. Motivated by this, we propose Dual-Channel GNNs that integrate a white-box rule extractor and a standard SE-GNN, adaptively combining both channels when the task benefits. Our experiments show that even a simple instantiation of Dual-Channel GNNs can recover succinct rules and perform on par or better than widely used SE-GNNs. Our code can be found in the supplementary material.

In the estimation of causal effects, one common method for removing the influence of confounders is to adjust the variables that satisfy the back-door criterion. However, it is not always possible to uniquely determine sets of such variables. Moreover, real-world data is almost always limited, which means it may be insufficient for statistical estimation. Therefore, we propose criteria for selecting variables from a list of candidate adjustment variables along with an algorithm to prevent accuracy degradation in causal effect estimation. We initially focus on directed acyclic graphs (DAGs) and then outlines specific steps for applying this method to completed partially directed acyclic graphs (CPDAGs). We also present and prove a theorem on causal effect computation possibility in CPDAGs. Finally, we demonstrate the practical utility of our method using both existing and artificial data.

Partially Observable Markov Decision Processes (POMDPs) provide a robust framework for decision-making under uncertainty in applications such as autonomous driving and robotic exploration. Their extension, $\rho$POMDPs, introduces belief-dependent rewards, enabling explicit reasoning about uncertainty. Existing online $\rho$POMDP solvers for continuous spaces rely on fixed belief representations, limiting adaptability and refinement - critical for tasks such as information-gathering. We present $\rho$POMCPOW, an anytime solver that dynamically refines belief representations, with formal guarantees of improvement over time. To mitigate the high computational cost of updating belief-dependent rewards, we propose a novel incremental computation approach. We demonstrate its effectiveness for common entropy estimators, reducing computational cost by orders of magnitude. Experimental results show that $\rho$POMCPOW outperforms state-of-the-art solvers in both efficiency and solution quality.

Interactive digital agents (IDAs) leverage APIs of stateful digital environments to perform tasks in response to user requests. While IDAs powered by instruction-tuned large language models (LLMs) can react to feedback from interface invocations in multi-step exchanges, they have not been trained in their respective digital environments. Prior methods accomplish less than half of tasks in sophisticated benchmarks such as AppWorld. We present a reinforcement learning (RL) approach that trains IDAs directly in their target environments. We formalize this training as a partially observable Markov decision process and derive LOOP, a data- and memory-efficient variant of proximal policy optimization. LOOP uses no value network and maintains exactly one copy of the underlying LLM in memory, making its implementation straightforward and as memory-efficient as fine-tuning a single LLM. A 32-billion-parameter agent trained with LOOP in the AppWorld environment outperforms the much larger OpenAI o1 agent by 9 percentage points (15% relative). To our knowledge, this is the first reported application of RL to IDAs that interact with a stateful, multi-domain, multi-app environment via direct API calls. Our analysis sheds light on the effectiveness of RL in this area, showing that the agent learns to consult the API documentation, avoid unwarranted assumptions, minimize confabulation, and recover from setbacks.

We introduce OmniRL, a highly generalizable in-context reinforcement learning (ICRL) model that is meta-trained on hundreds of thousands of diverse tasks. These tasks are procedurally generated by randomizing state transitions and rewards within Markov Decision Processes. To facilitate this extensive meta-training, we propose two key innovations: 1. An efficient data synthesis pipeline for ICRL, which leverages the interaction histories of diverse behavior policies; and 2. A novel modeling framework that integrates both imitation learning and reinforcement learning (RL) within the context, by incorporating prior knowledge. For the first time, we demonstrate that in-context learning (ICL) alone, without any gradient-based fine-tuning, can successfully tackle unseen Gymnasium tasks through imitation learning, online RL, or offline RL. Additionally, we show that achieving generalized ICRL capabilities-unlike task identification-oriented few-shot learning-critically depends on long trajectories generated by variant tasks and diverse behavior policies. By emphasizing the potential of ICL and departing from pre-training focused on acquiring specific skills, we further underscore the significance of meta-training aimed at cultivating the ability of ICL itself.

We present the first gap-dependent analysis of regret and communication cost for on-policy federated $Q$-Learning in tabular episodic finite-horizon Markov decision processes (MDPs). Existing FRL methods focus on worst-case scenarios, leading to $\sqrt{T}$-type regret bounds and communication cost bounds with a $\log T$ term scaling with the number of agents $M$, states $S$, and actions $A$, where $T$ is the average total number of steps per agent. In contrast, our novel framework leverages the benign structures of MDPs, such as a strictly positive suboptimality gap, to achieve a $\log T$-type regret bound and a refined communication cost bound that disentangles exploration and exploitation. Our gap-dependent regret bound reveals a distinct multi-agent speedup pattern, and our gap-dependent communication cost bound removes the dependence on $MSA$ from the $\log T$ term. Notably, our gap-dependent communication cost bound also yields a better global switching cost when $M=1$, removing $SA$ from the $\log T$ term.

Stochastic approximation (SA) algorithms, first introduced by Robbins and Monro in the 1950's [24], has become one of the most important classes of stochastic numerical methods. Originally aimed at finding the the root of a continuous function given noisy observations, SA is now a fundamental tool in a range of areas such as statistics, optimization, electrical engineering, and machine learning, to mention but a few. Within the latter, the importance of SA algorithms is illustrated by the fact that a specific subclass of methods--stochastic gradient descent (SGD) methods--is central to the training of deep learning methods, and in reinforcement learning the standard methods (Q-learning and temporal-difference-learning) are variants of SA. The general class that is SA algorithms with state-dependent noise (see below for the definition) therefore constitute a rich and important family of stochastic recursive algorithms. In addition to the examples already mentioned (SGD, reinforcement learning), this class also includes persistent contrastive divergence, adaptive Markov chain Monte-Carlo (MCMC) and extended ensemble algorithms such as the Wang-Landau algorithm. The theory of SA stems from the pioneering work of Robbins and Monro [24] and Kiefer and Wolfowitz [20], and remains an active research area within probability theory. This is in part due to the many and diverse applications of SA algorithms where, due to the complex nature of the systems under considerations, different variants of the original Robbins-Monro algorithm are needed. In turn, developing the theoretical foundation for SA algorithms, such as, e.g., convergence results, central limit theorems, concentration results and results on deviations, is of fundamental importance; monographs covering many of the standard results of

This tutorial intends to introduce readers with a background in AI to quantum machine learning (QML) -- a rapidly evolving field that seeks to leverage the power of quantum computers to reshape the landscape of machine learning. For self-consistency, this tutorial covers foundational principles, representative QML algorithms, their potential applications, and critical aspects such as trainability, generalization, and computational complexity. In addition, practical code demonstrations are provided in https://qml-tutorial.github.io/ to illustrate real-world implementations and facilitate hands-on learning. Together, these elements offer readers a comprehensive overview of the latest advancements in QML. By bridging the gap between classical machine learning and quantum computing, this tutorial serves as a valuable resource for those looking to engage with QML and explore the forefront of AI in the quantum era.