A Measure-Theoretic Finite-Sample Theory for Adaptive-Data Fitted Q-Iteration

While reinforcement learning (RL) promises to revolutionize the control of complex nonlinear robotic systems, a profound gap persists between the heuristic success of model-free off-policy deep RL and the underlying theory, which remains largely confined to tabular or linearizable settings. We identify the cause of this gap as an emergent isolation of three traditions: (i) measure-theoretic MDP foundations on general spaces limit their analysis to exact dynamic programming and ignore all error sources of a learning process; (ii) deterministic error propagation analysis addresses the approximation error via concentrability coefficients without a finite-sample analysis of the estimation error; and (iii) PAC generalization bounds characterize the estimation errors of simplified topologies. We bridge these traditions with a unified theoretical framework for fitted Q-iteration (FQI) on general measurable Borel spaces. Our main result provides a finite-sample, adaptive-data performance bound by chaining measure-theoretic probability with Bellman-operator contraction in Banach spaces. We prove that sequential Rademacher complexity controls Bellman-regression generalization under policy-dependent data collection. We further extend this analysis to provide the first cumulative, pathwise online regret guarantee for FQI in continuous spaces. These results lay the necessary foundations for the formal analysis of many modern deep RL algorithms.

Hitting Time Isomorphism for Multi-Stage Planning with Foundation Policies

We present a new operator-theoretic representation learning framework for offline reinforcement learning that recovers the directed temporal geometry of a controlled Markov process from hitting time observations. While prior art often produces symmetric distances or fails to satisfy the triangle inequality, our framework learns a Hilbert-space displacement geometry where expected hitting times are realized as linear functionals of latent displacements. We prove that this representation exists under latent linear closure and is uniquely identifiable up to a bounded linear isomorphism. For finite-dimensional implementations, we show that global hitting-time error is bounded by one-step transition error amplified by the environment's transient spectral radius. Furthermore, we provide finite-sample guarantees accounting for approximation, statistical complexity, and trajectory-label mismatch. Derived from this theory, we curate Isomorphic Embedding Learning (IEL) as a new goal-agnostic foundation policy learning algorithm that anchors a HILP-style consistency objective with explicit hitting-time regression to ensure that the learned geometry reflects actual decision-time progress. This asymmetric and compositional structure enables robust graph-based multi-stage planning for long-horizon navigation. Our experiments demonstrate that IEL improves the state of the art of learning foundation policy policies from offline maze locomotion data. Our code can be found on https://github.com/MagnusBoock/IEL

Policy-based Tuning of Autoregressive Image Models with Instance- and Distribution-Level Rewards

Autoregressive (AR) models are highly effective for image generation, yet their standard maximum-likelihood estimation training lacks direct optimization for sample quality and diversity. While reinforcement learning (RL) has been used to align diffusion models, these methods typically suffer from output diversity collapse. Similarly, concurrent RL methods for AR models rely strictly on instance-level rewards, often trading off distributional coverage for quality. To address these limitations, we propose a lightweight RL framework that casts token-based AR synthesis as a Markov Decision Process, optimized via Group Relative Policy Optimization (GRPO). Our core contribution is the introduction of a novel distribution-level Leave-One-Out FID (LOO-FID) reward; by leveraging an exponential moving average of feature moments, it explicitly encourages sample diversity and prevents mode collapse during policy updates. We integrate this with composite instance-level rewards (CLIP and HPSv2) for strict semantic and perceptual fidelity, and stabilize the multi-objective learning with an adaptive entropy regularization term. Extensive experiments on LlamaGen and VQGAN architectures demonstrate clear improvements across standard quality and diversity metrics within only a few hundred tuning iterations. The results also show that the model can be updated to produce competitive samples even without Classifier-Free Guidance, and bypass its 2x inference cost.

Distributional Active Inference

Optimal control of complex environments with robotic systems faces two complementary and intertwined challenges: efficient organization of sensory state information and far-sighted action planning. Because the reinforcement learning framework addresses only the latter, it tends to deliver sample-inefficient solutions. Active inference is the state-of-the-art process theory that explains how biological brains handle this dual problem. However, its applications to artificial intelligence have thus far been limited to extensions of existing model-based approaches. We present a formal abstraction of reinforcement learning algorithms that spans model-based, distributional, and model-free approaches. This abstraction seamlessly integrates active inference into the distributional reinforcement learning framework, making its performance advantages accessible without transition dynamics modeling.

Deep Actor-Critics with Tight Risk Certificates

After a period of research, deep actor-critic algorithms have reached a level where they influence our everyday lives. They serve as the driving force behind the continual improvement of large language models through user-collected feedback. However, their deployment in physical systems is not yet widely adopted, mainly because no validation scheme that quantifies their risk of malfunction. We demonstrate that it is possible to develop tight risk certificates for deep actor-critic algorithms that predict generalization performance from validation-time observations. Our key insight centers on the effectiveness of minimal evaluation data. Surprisingly, a small feasible of evaluation roll-outs collected from a pretrained policy suffices to produce accurate risk certificates when combined with a simple adaptation of PAC-Bayes theory. Specifically, we adopt a recently introduced recursive PAC-Bayes approach, which splits validation data into portions and recursively builds PAC-Bayes bounds on the excess loss of each portion's predictor, using the predictor from the previous portion as a data-informed prior. Our empirical results across multiple locomotion tasks and policy expertise levels demonstrate risk certificates that are tight enough to be considered for practical use.

Improving Plasticity in Non-stationary Reinforcement Learning with Evidential Proximal Policy Optimization

On-policy reinforcement learning algorithms use the most recently learned policy to interact with the environment and update it using the latest gathered trajectories, making them well-suited for adapting to non-stationary environments where dynamics change over time. However, previous studies show that they struggle to maintain plasticity$\unicode{x2013}$the ability of neural networks to adjust their synaptic connections$\unicode{x2013}$with overfitting identified as the primary cause. To address this, we present the first application of evidential learning in an on-policy reinforcement learning setting: $\textit{Evidential Proximal Policy Optimization (EPPO)}$. EPPO incorporates all sources of error in the critic network's approximation$\unicode{x2013}$i.e., the baseline function in advantage calculation$\unicode{x2013}$by modeling the epistemic and aleatoric uncertainty contributions to the approximation's total variance. We achieve this by using an evidential neural network, which serves as a regularizer to prevent overfitting. The resulting probabilistic interpretation of the advantage function enables optimistic exploration, thus maintaining the plasticity. Through experiments on non-stationary continuous control tasks, where the environment dynamics change at regular intervals, we demonstrate that EPPO outperforms state-of-the-art on-policy reinforcement learning variants in both task-specific and overall return.

In the Picture: Medical Imaging Datasets, Artifacts, and their Living Review

Datasets play a critical role in medical imaging research, yet issues such as label quality, shortcuts, and metadata are often overlooked. This lack of attention may harm the generalizability of algorithms and, consequently, negatively impact patient outcomes. While existing medical imaging literature reviews mostly focus on machine learning (ML) methods, with only a few focusing on datasets for specific applications, these reviews remain static -- they are published once and not updated thereafter. This fails to account for emerging evidence, such as biases, shortcuts, and additional annotations that other researchers may contribute after the dataset is published. We refer to these newly discovered findings of datasets as research artifacts. To address this gap, we propose a living review that continuously tracks public datasets and their associated research artifacts across multiple medical imaging applications. Our approach includes a framework for the living review to monitor data documentation artifacts, and an SQL database to visualize the citation relationships between research artifact and dataset. Lastly, we discuss key considerations for creating medical imaging datasets, review best practices for data annotation, discuss the significance of shortcuts and demographic diversity, and emphasize the importance of managing datasets throughout their entire lifecycle. Our demo is publicly available at http://130.226.140.142.

Deterministic Uncertainty Propagation for Improved Model-Based Offline Reinforcement Learning

Current approaches to model-based offline Reinforcement Learning (RL) often incorporate uncertainty-based reward penalization to address the distributional shift problem. While these approaches have achieved some success, we argue that this penalization introduces excessive conservatism, potentially resulting in suboptimal policies through underestimation. We identify as an important cause of over-penalization the lack of a reliable uncertainty estimator capable of propagating uncertainties in the Bellman operator. The common approach to calculating the penalty term relies on sampling-based uncertainty estimation, resulting in high variance. To address this challenge, we propose a novel method termed Moment Matching Offline Model-Based Policy Optimization (MOMBO). MOMBO learns a Q-function using moment matching, which allows us to deterministically propagate uncertainties through the Q-function. We evaluate MOMBO's performance across various environments and demonstrate empirically that MOMBO is a more stable and sample-efficient approach.

Exploring Pessimism and Optimism Dynamics in Deep Reinforcement Learning

Off-policy actor-critic algorithms have shown promise in deep reinforcement learning for continuous control tasks. Their success largely stems from leveraging pessimistic state-action value function updates, which effectively address function approximation errors and improve performance. However, such pessimism can lead to under-exploration, constraining the agent's ability to explore/refine its policies. Conversely, optimism can counteract under-exploration, but it also carries the risk of excessive risk-taking and poor convergence if not properly balanced. Based on these insights, we introduce Utility Soft Actor-Critic (USAC), a novel framework within the actor-critic paradigm that enables independent control over the degree of pessimism/optimism for both the actor and the critic via interpretable parameters. USAC adapts its exploration strategy based on the uncertainty of critics through a utility function that allows us to balance between pessimism and optimism separately. By going beyond binary choices of optimism and pessimism, USAC represents a significant step towards achieving balance within off-policy actor-critic algorithms. Our experiments across various continuous control problems show that the degree of pessimism or optimism depends on the nature of the task. Furthermore, we demonstrate that USAC can outperform state-of-the-art algorithms for appropriately configured pessimism/optimism parameters.

Calibrating Bayesian UNet++ for Sub-Seasonal Forecasting

Seasonal forecasting is a crucial task when it comes to detecting the extreme heat and colds that occur due to climate change. Confidence in the predictions should be reliable since a small increase in the temperatures in a year has a big impact on the world. Calibration of the neural networks provides a way to ensure our confidence in the predictions. However, calibrating regression models is an under-researched topic, especially in forecasters. We calibrate a UNet++ based architecture, which was shown to outperform physics-based models in temperature anomalies. We show that with a slight trade-off between prediction error and calibration error, it is possible to get more reliable and sharper forecasts. We believe that calibration should be an important part of safety-critical machine learning applications such as weather forecasters.