LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems

Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce \textit{LieStoNet}, an end-to-end, \emph{template-free} framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or canonical coordinates. Building on the seminal SDE Lie-symmetry theory of Gaeta and Quintero (1999), which formalizes Lie-point SDE symmetries and their relation to Fokker-Planck symmetries, LieStoNet learns neural surrogates for drift and diffusion from increments, then learns projectable generators by enforcing the SDE determining equations, separately regularizing for closure under Lie brackets, adherence to the Lie algebra axioms (bilinearity, antisymmetry, Jacobi), and a non-redundant independent basis. The surrogate also defines an associated Fokker-Planck equation, enabling optional discovery of its Lie-point symmetries in parallel. Across multiple canonical SDEs with known analytic symmetries, LieStoNet recovers generators consistent with the ground-truth symmetry algebra, providing interpretable symmetry discovery for noisy dynamics. Code is available at \href{https://github.com/sumit-sinha-seas/LieStoNet_Final.git}{this link}.

Latent Memory Palace: Reasoning for Control as Autoregressive Variational Inference

Human decision-making is highly flexible -- some actions are taken immediately; others require longer deliberation. Language models have exhibited a similar capacity for adaptive "reasoning." However, transferring this capability to continuous control policies has been challenging, as directly reasoning in language space may lack the granularity for spatial understanding and precise motions. In this work, we show that reasoning for control policies can emerge by organizing information in an autoregressive latent space reminiscent of a memory palace, where retrieval is iterative and adaptive. Our method, Latent Memory Palace (LMP), formulates reasoning as variational inference with an autoregressive latent distribution. We derive a latent-space reinforcement learning technique to tractably optimize its variational lower bound. The resulting policy, LMP-$π$, achieves strong empirical performance in simulation and real-world domains while exhibiting interpretable, adaptive allocation of test-time compute. We further show that the same framework yields a variable-length action tokenizer, LMP-$\texttt{tok}$, which significantly improves the performance of downstream autoregressive policies. Together, these results present a new perspective on latent reasoning for control through the lens of variational inference.

From Consistency to Collaborative Discovery: MFEA-CoD for Multitask Novelty Search

Evolutionary multitasking (EMT) has shown strong capability in solving multiple optimization problems simultaneously by exploiting latent inter-task consistency, such as similarities in promising solutions or search directions. However, most existing EMT studies remain focused on objective-driven optimization, where such consistency is mainly used to accelerate convergence toward predefined optima. In this paper, we move EMT from consistency to collaborative discovery and propose a multifactorial evolutionary algorithm with collaborative discovery (MFEA-CoD) for multitask novelty search. Unlike conventional EMT, MFEA-CoD coordinates multiple novelty search tasks to collaboratively discover behaviorally novel solutions rather than merely transferring consistent search information for faster convergence. Specifically, a multitask repulsion operator encourages different tasks to explore distinct regions of the unified search space, thereby reducing redundant behavioral discoveries. Meanwhile, an adaptive inter-task transfer mechanism exploits shared discovery opportunities in overlapping novelty-improving regions by adjusting the transfer probability according to the online contribution of transferred information. Furthermore, MFEA-CoD is extended to multitask novelty-augmented optimization, where behavioral novelty is jointly considered with objective information to alleviate premature convergence caused by deceptive objectives. Experiments on synthetic basin-type problems, deceptive maze navigation problems, MuJoCo policy optimization problems, and generative novelty search problems demonstrate that MFEA-CoD improves the efficiency of discovering diverse novel solutions and shows clear advantages in deceptive objective landscapes.

Support-Constrained RL Enables Real-World Policy Improvement without Real-World Experience

Robots trained on real world data tend to be imprecise, slow, and brittle to perturbations. Improving these policies with reinforcement learning (RL) is an appealing alternative, but this process often requires expensive training in the real world. Performing policy improvement in simulation instead provides a far cheaper alternative, but unconstrained RL in simulation can exploit contact and dynamics mismatches, resulting in unsafe behaviors that do not transfer to hardware. Common forms of regularization can furthermore limit improvement by overconstraining to an imperfect behavior prior. In this work, we propose Support-Constrained Off-Domain REinforcement (SCORE), a real-to-sim-to-real framework that constrains RL in simulation to the support of a generative policy pretrained on real data. We instantiate this constraint through flow steering, restricting SCORE to actions the base policy can already produce, which ensures transferable behaviors while maximizing policy improvement. Improving a policy with SCORE requires minimal effort: it learns from sparse rewards, avoids distillation, and leaves the base policy untouched. Across eight real-world dexterous multi-fingered robotic manipulation tasks, SCORE improves average success rate from 37.8% to 89.9%, compared to 59.5% for the best baseline, and reaches success in 36.8% fewer steps than the base policy. Ultimately, through extensive experiments and ablations, we show that simulation can substantially improve real-world manipulation policies when policy optimization is appropriately constrained, introducing a new paradigm for real-to-sim-to-real policy improvement. Videos and code are available at https://weirdlabuw.github.io/score/.

Difference-Aware Retrieval Policies for Imitation Learning

Parametric imitation learning via behavior cloning can suffer from poor generalization to out-of-distribution states due to compounding errors during deployment. We show that reusing the training data during inference via a semi-parametric retrieval-based imitation learning approach can alleviate this challenge. We present Difference-Aware Retrieval Policies for Imitation Learning (DARP), a semi-parametric retrieval-based imitation learning approach that addresses this limitation by reparameterizing the imitation learning problem in terms of local neighborhood structure rather than direct state-to-action mappings. Instead of learning a global policy, DARP trains a model to predict actions based on $k$-nearest neighbors from expert demonstrations, their corresponding actions, and the relative distance vectors between neighbor states and query states. DARP requires no additional assumptions beyond those made for standard behavior cloning -- it does not require additional data collection, online expert feedback, or task-specific knowledge. We demonstrate consistent performance improvements of 15-46% over standard behavior cloning across diverse domains, including continuous control and robotic manipulation, and across different representations, including high-dimensional visual features. Code and demos are available at https://weirdlabuw.github.io/darp-site/.

TMRL: Diffusion Timestep-Modulated Pretraining Enables Exploration for Efficient Policy Finetuning

Fine-tuning pre-trained robot policies with reinforcement learning (RL) often inherits the bottlenecks introduced by pre-training with behavioral cloning (BC), which produces narrow action distributions that lack the coverage necessary for downstream exploration. We present a unified framework that enables the exploration necessary to enable efficient robot policy finetuning by bridging BC pre-training and RL fine-tuning. Our pre-training method, Context-Smoothed Pre-training (CSP), injects forward-diffusion noise into policy inputs, creating a continuum between precise imitation and broad action coverage. We then fine-tune pre-trained policies via Timestep-Modulated Reinforcement Learning (TMRL), which trains the agent to dynamically adjust this conditioning during fine-tuning by modulating the diffusion timestep, granting explicit control over exploration. Integrating seamlessly with arbitrary policy inputs, e.g., states, 3D point clouds, or image-based VLA policies, we show that TMRL improves RL fine-tuning sample efficiency. Notably, TMRL enables successful real-world fine-tuning on complex manipulation tasks in under one hour. Videos and code available at https://weirdlabuw.github.io/tmrl/.

Learning to Compress Time-to-Control: A Reinforcement Learning Framework for Chronic Disease Management

Reinforcement learning (RL) in healthcare has had mixed results, with reward sparsity, unreliable off-policy evaluation, and deployment-simulation gap as recurring failure modes. We argue that chronic disease management is structurally a more tractable RL setting than the acute-care problems the field has primarily studied, but only if the problem is formalized to exploit chronic care's properties. We propose such a formalization. The agent's objective is to compress time-to-control (TTC) under a tiered reward calibrated to the CMS ACCESS Model. Two quantities from our companion preference-learning paper [Singh et al. 2026] enter as load-bearing structural elements: the execution intensity εbounds action availability under a constrained Markov Decision Process, and the clinician capability κweights offline-data transitions during RL training. Together they couple preference learning and RL into a two-loop architecture. We present simulation results on synthetic state machines for hypertension and type 2 diabetes. Capability-weighted offline RL outperforms uniform-weighted offline RL and the behavior policy by 15 percentage points on T2D TTC; the uniform-weighted formulation (the standard in existing healthcare RL) underperforms even the heterogeneous behavior policy. \Epsilon-aware policies generalize across deployment regimes while ε-naive policies do not.

OGPO: Sample Efficient Full-Finetuning of Generative Control Policies

Generative control policies (GCPs), such as diffusion- and flow-based control policies, have emerged as effective parameterizations for robot learning. This work introduces Off-policy Generative Policy Optimization (OGPO), a sample-efficient algorithm for finetuning GCPs that maintains off-policy critic networks to maximize data reuse and propagate policy gradients through the full generative process of the policy via a modified PPO objective, using critics as the terminal reward. OGPO achieves state-of-the-art performance on manipulation tasks spanning multi-task settings, high-precision insertion, and dexterous control. To our knowledge, it is also the only method that can fine-tune poorly-initialized behavior cloning policies to near full task-success with no expert data in the online replay buffer, and does so with few task-specific hyperparameter tuning. Through extensive empirical investigations, we demonstrate the OGPO drastically outperforms methods alternatives on policy steering and learning residual corrections, and identify the key mechanisms behind its performance. We further introduce practical stabilizers, including success-buffer regularization, conservative advantages, $χ^2$ regularization, and Q-variance reduction, to mitigate critic over-exploitation across state- and pixel-based settings. Beyond proposing OGPO, we conduct a systematic empirical study of GCP finetuning, identifying the stabilizing mechanisms and failure modes that govern successful off-policy full-policy improvement.

Transferable Physics-Informed Representations via Closed-Form Head Adaptation

Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the learning process, PINN models have demonstrated the ability to learn physical outcomes reasonably well. However, current PINN approaches struggle to predict or solve new PDEs effectively when there is a lack of training examples, indicating they do not generalize well to unseen problem instances. In this paper, we present a transferable learning approach for PINNs premised on a fast Pseudoinverse PINN framework (Pi-PINN). Pi-PINN learns a transferable physics-informed representation in a shared embedding space and enables rapid solving of both known and unknown PDE instances via closed-form head adaptation using a least-squares-optimal pseudoinverse under PDE constraints. We further investigate the synergies between data-driven multi-task learning loss and physics-informed loss, providing insights into the design of more performant PINNs. We demonstrate the effectiveness of Pi-PINN on various PDE problems, including Poisson's equation, Helmholtz equation, and Burgers' equation, achieving fast and accurate physics-informed solutions without requiring any data for unseen instances. Pi-PINN can produce predictions 100-1000 times faster than a typical PINN, while producing predictions with 10-100 times lower relative error than a typical data-driven model even with only two training samples. Overall, our findings highlight the potential of transferable representations with closed-form head adaptation to enhance the efficiency and generalization of PINNs across PDE families and scientific and engineering applications.

Operator-Theoretic Foundations and Policy Gradient Methods for General MDPs with Unbounded Costs

Markov decision processes (MDPs) is viewed as an optimization of an objective function over certain linear operators over general function spaces. Using the well-established perturbation theory of linear operators, this viewpoint allows one to identify derivatives of the objective function as a function of the linear operators. This leads to generalization of many well-known results in reinforcement learning to cases with generate state and action spaces. Prior results of this type were only established in the finite-state finite-action MDP settings and in settings with certain linear function approximations. The framework also leads to new low-complexity PPO-type reinforcement learning algorithms for general state and action space MDPs.