Scientific discovery relies on large-scale hypothesis testing. However, the capacity to identify true discoveries while controlling false discovery faces major challenges: obtaining relevant reference data (the null distribution) is resource-intensive, leaving finite-data uncertainty, and the procedure should account for the inherent structure in the hypothesis space, when such structure exists. Here, we present a framework for controlling the false discovery rate both when each hypothesis is evidenced only by a finite count of null draws, leaving its p-value uncertain, and when the hypothesis space carries arbitrary structure, requiring only that the structure be represented through a suitable reproducing kernel. We present two decision rules that are both robust to structural mis-specification, yet offer a distinct trade-off between exact FDR control and statistical power. The first rule guarantees exact FDR control; the second maximizes power by adapting mirror-statistic control into count space, utilizing an analytical framework to assess FDR control when exact mirror symmetry is relaxed. Furthermore, the tractability gained by the RKHS framework allows us to directly investigate finite-data uncertainties, which we leverage to suggest a policy for the efficient allocation of null distribution samples.

We study diffusion-based world models for reinforcement learning, which offer high generative fidelity but face critical efficiency challenges in control. Current methods either require heavyweight models at inference or rely on highly sequential imagination, both of which impose prohibitive computational costs. We propose Horizon Imagination (HI), an on-policy imagination process for discrete stochastic policies that denoises multiple future observations in parallel. HI incorporates a stabilization mechanism and a novel sampling schedule that decouples the denoising budget from the effective horizon over which denoising is applied while also supporting sub-frame budgets. Experiments on Atari 100K and Craftium show that our approach maintains control performance with a sub-frame budget of half the denoising steps and achieves superior generation quality under varied schedules. Code is released open-source https://anonymous.4open.science/r/horizon-3EA1.

Recent advancements in imitation learning have led to transformer-based behavior foundation models (BFMs) that enable multi-modal, human-like control for humanoid agents. While excelling at zero-shot generation of robust behaviors, BFMs often require meticulous prompt engineering for specific tasks, potentially yielding suboptimal results. We introduce "Task Tokens", a method to effectively tailor BFMs to specific tasks while preserving their flexibility. Our approach leverages the transformer architecture of BFMs to learn a new task-specific encoder through reinforcement learning, keeping the original BFM frozen. This allows incorporation of user-defined priors, balancing reward design and prompt engineering. By training a task encoder to map observations to tokens, used as additional BFM inputs, we guide performance improvement while maintaining the model's diverse control characteristics. We demonstrate Task Tokens' efficacy across various tasks, including out-of-distribution scenarios, and show their compatibility with other prompting modalities. Our results suggest that Task Tokens offer a promising approach for adapting BFMs to specific control tasks while retaining their generalization capabilities.

Representation learning is critical to the empirical and theoretical success of reinforcement learning. However, many existing methods are induced from model-learning aspects, misaligning them with the RL task in hand. This work introduces the Spectral Bellman Method, a novel framework derived from the Inherent Bellman Error (IBE) condition. It aligns representation learning with the fundamental structure of Bellman updates across a space of possible value functions, making it directly suited for value-based RL. Our key insight is a fundamental spectral relationship: under the zero-IBE condition, the transformation of a distribution of value functions by the Bellman operator is intrinsically linked to the feature covariance structure. This connection yields a new, theoretically-grounded objective for learning state-action features that capture this Bellman-aligned covariance, requiring only a simple modification to existing algorithms. We demonstrate that our learned representations enable structured exploration by aligning feature covariance with Bellman dynamics, improving performance in hard-exploration and long-horizon tasks. Our framework naturally extends to multi-step Bellman operators, offering a principled path toward learning more powerful and structurally sound representations for value-based RL.

Understanding how human health changes over time, and why responses to interventions vary between individuals, remains a central challenge in medicine. Here we present HealthFormer, a decoder-only transformer that models the human physiological trajectory generatively, by training on data from the Human Phenotype Project, a multi-visit cohort of over 15,000 deeply phenotyped individuals. We tokenise each participant's health trajectory across 667 measurements spanning seven domains: blood biomarkers, body composition, sleep physiology, continuous glucose monitoring, gut microbiome, wearable-derived physiology, and behaviour and medication exposure. We train HealthFormer to forecast individual physiological trajectories across these domains, and from this single generative objective a range of clinically relevant tasks can be expressed as queries on the model. We show that, without task-specific training, HealthFormer transfers to four independent cohorts and improves prediction for 27 of 30 incident-disease and mortality endpoints, exceeding established clinical risk scores in every comparison. We further show that the model can simulate interventions in silico: in a held-out personalised-nutrition trial, intervention-conditioned predictions recover individual six-month biomarker changes (e.g., Pearson r = 0.78 for diastolic blood pressure). Across 41 randomised intervention-outcome comparisons drawn from published trials, our results show that the predicted direction of effect agrees in every case, and the predicted mean falls within the reported 95

We study diffusion-based world models for reinforcement learning, which offer high generative fidelity but face critical efficiency challenges in control. Current methods either require heavyweight models at inference or rely on highly sequential imagination, both of which impose prohibitive computational costs. We propose Horizon Imagination (HI), an on-policy imagination process for discrete stochastic policies that denoises multiple future observations in parallel. HI incorporates a stabilization mechanism and a novel sampling schedule that decouples the denoising budget from the effective horizon over which denoising is applied while also supporting sub-frame budgets. Experiments on Atari 100K and Craftium show that our approach maintains control performance with a sub-frame budget of half the denoising steps and achieves superior generation quality under varied schedules. Code is available at https://github.com/leor-c/horizon-imagination.

Hybrid mechanistic models, physical priors with learned residuals, promise to reduce the data required for good decisions, but have no computable criterion to test this. We characterize the value of mechanistic priors in sequential decision-making within both asymptotic and burn-in regimes. To formalize this, we introduce the mechanistic information of a model – the mutual information between the model's recommended policy and the true optimal policy π^* – quantified via an occupancy-weighted bias B_μ. In the asymptotic regime (large N), matched bounds reveal that Bayesian regret scales with the residual entropy H_mech, delivering a theoretical sample complexity reduction of H(μ)/H_mech compared to an uninformed baseline. Furthermore, we provide a model certificate to determine empirical sample efficiency. Complementarily, in the clinically relevant burn-in regime (small N), we establish a lower bound on the penalty incurred by confidently wrong priors. We demonstrate both the asymptotic and burn-in bounds across 5-fluorouracil (5-FU) dosing simulations motivated by published FOLFOX pharmacokinetic data, where a hybrid prior yields large sample-efficiency gains in the burn-in regime. Finally, we contrast these grounded models with LLM priors, demonstrating that LLMs can suffer severe losses in mechanistic information, thereby motivating the exclusive use of physically-grounded priors for safety-critical applications.

Sequentially solving similar optimization problems under strict runtime constraints is essential for many applications, such as robot control, autonomous driving, and portfolio management. The performance of local optimization methods in these settings is sensitive to the initial solution: poor initialization can lead to slow convergence or suboptimal solutions. To address this challenge, we propose learning to predict multiple diverse initial solutions given parameters that define the problem instance. We introduce two strategies for utilizing multiple initial solutions: (i) a single-optimizer approach, where the most promising initial solution is chosen using a selection function, and (ii) a multiple-optimizers approach, where several optimizers, potentially run in parallel, are each initialized with a different solution, with the best solution chosen afterward. Notably, by including a default initialization among predicted ones, the cost of the final output is guaranteed to be equal or lower than with the default initialization. We validate our method on three optimal control benchmark tasks: cart-pole, reacher, and autonomous driving, using different optimizers: DDP, MPPI, and iLQR. We find significant and consistent improvement with our method across all evaluation settings and demonstrate that it efficiently scales with the number of initial solutions required.

Large-scale hypothesis testing is central to modern science, where controlling the False Discovery Rate (FDR) has become the standard approach to managing false positives across many simultaneous tests. Hypotheses rarely exist in isolation; they often exhibit structure through proximity, connectivity, or hierarchy. This structure represents both a challenge and an opportunity: while classical methods treat these dependencies as obstacles requiring conservative correction, leveraging them can substantially increase discovery power. Here, we reframe structured FDR control as a regularized learning problem. By optimizing within a suitable Reproducing Kernel Hilbert Space (RKHS), we introduce a framework that unifies continuous domains, graphs, and hierarchies under a single algorithm through kernel choice alone. This formulation enables smooth solutions in place of the piecewise-constant fits of prior methods, principled likelihood-based hyperparameter selection rather than heuristic tuning, and inference at unobserved locations which in turn supports sample-efficient experimental design. Building on this estimator, we provide two decision rules which we prove to control the FDR. We validate our method on two sources: spatial locations derived from high-dimensional real-world datasets, and a differential gene expression task utilizing protein-protein interaction graphs.

Recent advances in Large Language Models (LLMs) and Vision-Language Models (VLMs) have enabled powerful semantic and multimodal reasoning capabilities, creating new opportunities to enhance sample efficiency, high-level planning, and interpretability in reinforcement learning (RL). While prior work has integrated LLMs and VLMs into various components of RL, the replay buffer, a core component for storing and reusing experiences, remains unexplored. We propose addressing this gap by leveraging VLMs to guide the prioritization of experiences in the replay buffer. Our key idea is to use a frozen, pre-trained VLM (requiring no fine-tuning) as an automated evaluator to identify and prioritize promising sub-trajectories from the agent's experiences. Across scenarios, including game-playing and robotics, spanning both discrete and continuous domains, agents trained with our proposed prioritization method achieve 11-52

Dimension reduction for dynamical systems is standard practice, and the standard route is spectral: model the transfer (Koopman) operator by its leading modes. We show that on systems assembled from several weakly interacting components — a structure common in physical and biological settings — this may either require an exponential number of modes, or drop an entire component: the component is absent from the model rather than modeled coarsely, and no function of it can be predicted at any accuracy. We call this linear masking. The cause is that a rank-based model pays one coordinate per mode. We propose to score instead the σ-algebra the coordinates generate, so that products and powers come free and a component's cost is governed only by its generators rather than by all its interactions. The criterion is a χ^2-divergence between the embedded present and future, and it carries a budget guarantee: twice the intrinsic dimension of the dynamics is enough coordinates for an embedding whose algebra carries the operator's entire spectrum, with its full infinite rank. In variational form the criterion admits off-the-shelf estimators, and restricting its critic to the bilinear class returns the VAMP score on the span, so rank-based methods are one end of the same family. We demonstrate the proposed objective on a composite of published benchmark systems. We exhibit examples where the rank-based methods completely miss the masked components at all ranks k<100, while ten algebra coordinates recover all of them. In addition, the resulting algebra representation supports predicting the masked components from few labels, while direct regression from the high-dimensional observation or from the VAMP features fail.

Compositional priors describe the generic properties of layered functions in deep Bayesian models, where deep neural networks with random weights are a canonical example.In the wide-network limit, the prior is a Gaussian process with a depth-dependent kernel, and its behaviour as depth grows has been extensively studied through this kernel. Here, we study another case, where each layer itself is a vector valued Gaussian process, and our aim is similarly to understand the limiting behaviour of the prior as depth grows. Previous GP work has established that for the RBF kernel and a certain range of bandwidths r, the prior degenerates in the limit, converging to the set of constant functions – which is not useful as a probabilistic model. In this paper we establish several new results. First, we identify a sharp bandwidth threshold r_c(d) = Θ(√(d)) above which the limit is degenerate, strengthening the earlier bounds. Second, and more importantly, we show that for r below the threshold r_c(d) the prior converges to a limit distribution π_Z̅. We also prove that these distributions are non-degenerate and non-Gaussian, with non-vanishing dependence between coordinates. In contrast to the previously known degenerate regime, deep Gaussian process priors can therefore admit non-trivial limits. Empirically, we verify the threshold across a range of dimensions d, and demonstrate a complex multimodal behaviour of the limit distributions π_Z̅ – a regime that becomes increasingly narrow with d and would be hard to identify without knowing the threshold.

We establish an optimal sample complexity of O(ε^-2) for obtaining an ε-optimal global policy using a single-timescale actor-critic (AC) algorithm in infinite-horizon discounted Markov decision processes (MDPs) with finite state-action spaces, improving upon the prior state of the art of O(ε^-3). Our approach applies STORM (STOchastic Recursive Momentum) to reduce variance in the critic updates. However, because samples are drawn from a nonstationary occupancy measure induced by the evolving policy, variance reduction via STORM alone is insufficient. To address this challenge, we maintain a buffer of small fraction of recent samples and uniformly sample from it for each critic update. Importantly, these mechanisms are compatible with existing deep learning architectures and require only minor modifications, without compromising practical applicability.

Reinforcement learning (RL) struggles to scale to large, combinatorial action spaces common in many real-world problems. This paper introduces a novel framework for training discrete diffusion models as highly effective policies in these complex settings. Our key innovation is an efficient online training process that ensures stable and effective policy improvement. By leveraging policy mirror descent (PMD) to define an ideal, regularized target policy distribution, we frame the policy update as a distributional matching problem, training the expressive diffusion model to replicate this stable target. This decoupled approach stabilizes learning and significantly enhances training performance. Our method achieves state-of-the-art results and superior sample efficiency across a diverse set of challenging combinatorial benchmarks, including DNA sequence generation, RL with macro-actions, and multi-agent systems. Experiments demonstrate that our diffusion policies attain superior performance compared to other baselines. Crucially, our extensive empirical analysis reveals a key trade-off: FKL demonstrates superior sample efficiency and faster initial convergence, whereas RKL ensures greater training stability and higher asymptotic performance.

Active feature acquisition (AFA) sequentially selects which features to observe to reach a classification or ranking decision. Its central limitation is reliance on large amount of labeled data to fit probabilistic models guiding acquisition. Large language models (LLMs) supply unsupervised domain knowledge, but are poor sequential planners. Asking one to both know and decide conflates capabilities best kept separate. Here, we develop a framework for zero-shot AFA through disciplined elicitation: asking the LLM only for what it can be trusted to return, the unary deviations and pairwise co-variations that are the sufficient statistics of a Markov random field (MRF). We apply our framework to two settings: binary classification and top-k identification. In practice, the LLM reliably returns only discriminative statistics, what distinguishes the classes rather than each class in isolation, which precludes classical AFA. We apply a maximum-entropy closure that resolves this gauge ambiguity. We evaluate on a cohort of Inflammatory Bowel Disease (IBD) patients, an active clinical setting where diagnostic ambiguity and patient heterogeneity obstruct stable treatment strategies. Our framework outperforms the LLM both on real labels and on its own extracted beliefs. Where it matters most, on the hardest patients, our top-k acquisition policy markedly outperforms all existing methods.

Standard reinforcement learning (RL) assumes that an agent can observe a reward for each state-action pair. However, in practical applications, it is often difficult and costly to collect a reward for each state-action pair. While there have been several works considering RL with trajectory feedback, it is unclear if trajectory feedback is inefficient for learning when trajectories are long. In this work, we consider a model named RL with segment feedback, which offers a general paradigm filling the gap between per-state-action feedback and trajectory feedback. In this model, we consider an episodic Markov decision process (MDP), where each episode is divided into m segments, and the agent observes reward feedback only at the end of each segment. Under this model, we study two popular feedback settings: binary feedback and sum feedback, where the agent observes a binary outcome and a reward sum according to the underlying reward function, respectively. To investigate the impact of the number of segments m on learning performance, we design efficient algorithms and establish regret upper and lower bounds for both feedback settings. Our theoretical and experimental results show that: under binary feedback, increasing the number of segments m decreases the regret at an exponential rate; in contrast, surprisingly, under sum feedback, increasing m does not reduce the regret significantly.

In many sequential decision problems, an agent performs a repeated task. He then suffers regret and obtains information that he may use in the following rounds. However, sometimes the agent may also obtain information and avoid suffering regret by querying external sources. We study the trade-off between the information an agent accumulates and the regret it suffers. We invoke information-theoretic methods for obtaining regret lower bounds, that also allow us to easily re-derive several known lower bounds. We introduce the first Bayesian regret lower bounds that depend on the information an agent accumulates. We also prove regret upper bounds using the amount of information the agent accumulates. These bounds show that information measured in bits, can be traded off for regret, measured in reward. Finally, we demonstrate the utility of these bounds in improving the performance of a question-answering task with large language models, allowing us to obtain valuable insights.

We study the problem of selecting a subset from a large action space shared by a family of bandits, with the goal of achieving performance nearly matching that of using the full action space. Indeed, in many natural situations, while the nominal set of actions may be large, there also exist significant correlations between the rewards of different actions. In this paper we propose an algorithm that can significantly reduce the action space when such correlations are present, without the need to a-priori know the correlation structure. We provide theoretical guarantees on the performance of the algorithm and demonstrate its practical effectiveness through empirical comparisons with Thompson Sampling and Upper Confidence Bound methods.

We analyze the global convergence of the single-timescale actor-critic (AC) algorithm for the infinite-horizon discounted Markov Decision Processes (MDPs) with finite state spaces. To this end, we introduce an elegant analytical framework for handling complex, coupled recursions inherent in the algorithm. Leveraging this framework, we establish that the algorithm converges to an $\epsilon$-close \textbf{globally optimal} policy with a sample complexity of $ O(\epsilon^{-3}) $. This significantly improves upon the existing complexity of $O(\epsilon^{-2})$ to achieve $\epsilon$-close \textbf{stationary policy}, which is equivalent to the complexity of $O(\epsilon^{-4})$ to achieve $\epsilon$-close \textbf{globally optimal} policy using gradient domination lemma. Furthermore, we demonstrate that to achieve this improvement, the step sizes for both the actor and critic must decay as $ O(k^{-\frac{2}{3}}) $ with iteration $k$, diverging from the conventional $O(k^{-\frac{1}{2}}) $ rates commonly used in (non)convex optimization.

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous applications, from growing markets like last-mile delivery to emerging use-cases like interactive logistics planning. In many applications, one has to repeatedly solve VRP instances drawn from the same distribution, yet current state-of-the-art solvers treat each instance on its own without leveraging previous examples. We introduce an optimization framework where a reinforcement learning agent is trained on prior instances and quickly generates initial solutions, which are then further optimized by a genetic algorithm. This framework, Evolutionary Algorithm with Reinforcement Learning Initialization (EARLI), consistently outperforms current state-of-the-art solvers across various time budgets. For example, EARLI handles vehicle routing with 500 locations within one second, 10x faster than current solvers for the same solution quality, enabling real-time and interactive routing at scale. EARLI can generalize to new data, as we demonstrate on real e-commerce delivery data of a previously unseen city. By combining reinforcement learning and genetic algorithms, our hybrid framework takes a step forward to closer interdisciplinary collaboration between AI and optimization communities towards real-time optimization in diverse domains.