Recent advances in hierarchical policy learning highlight the advantages of decomposing systems into high-level and low-level agents, enabling efficient long-horizon reasoning and precise fine-grained control. However, the interface between these hierarchy levels remains underexplored, and existing hierarchical methods often ignore domain symmetry, resulting in the need for extensive demonstrations to achieve robust performance. To address these issues, we propose Hierarchical Equivariant Policy (HEP), a novel hierarchical policy framework. We propose a frame transfer interface for hierarchical policy learning, which uses the high-level agent's output as a coordinate frame for the low-level agent, providing a strong inductive bias while retaining flexibility. Additionally, we integrate domain symmetries into both levels and theoretically demonstrate the system's overall equivariance. HEP achieves state-of-the-art performance in complex robotic manipulation tasks, demonstrating significant improvements in both simulation and real-world settings.

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in three dimensions to make predictions about novel images. However, imposing $SO(3)$-equivariance on two-dimensional inputs is difficult because the group of three-dimensional rotations does not have a natural action on the two-dimensional plane. Specifically, it is possible that an element of $SO(3)$ will rotate an image out of plane. We show that an algorithm that learns a three-dimensional representation of the world from two dimensional images must satisfy certain consistency properties which we formulate as $SO(2)$-equivariance constraints. We use the induced representation of $SO(2)$ on $SO(3)$ to construct and classify architectures that have two-dimensional inputs and which satisfy these consistency constraints. We prove that any architecture which respects said consistency constraints can be realized as an instance of our construction. We show that three previously proposed neural architectures for 3D pose prediction are special cases of our construction. We propose a new algorithm that is a learnable generalization of previously considered methods. We test our architecture on three pose predictions task and achieve SOTA results on both the PASCAL3D+ and SYMSOL pose estimation tasks.

Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often difficult, limiting the applicability of equivariant models. We propose learning symmetric embedding networks (SENs) that encode an input space (e.g. images), where we do not know the effect of transformations (e.g. rotations), to a feature space that transforms in a known manner under these operations. This network can be trained end-to-end with an equivariant task network to learn an explicitly symmetric representation. We validate this approach in the context of equivariant transition models with 3 distinct forms of symmetry. Our experiments demonstrate that SENs facilitate the application of equivariant networks to data with complex symmetry representations. Moreover, doing so can yield improvements in accuracy and generalization relative to both fully-equivariant and non-equivariant baselines.

Compositional generalization is a critical ability in learning and decision-making. We focus on the setting of reinforcement learning in object-oriented environments to study compositional generalization in world modeling. We (1) formalize the compositional generalization problem with an algebraic approach and (2) study how a world model can achieve that. We introduce a conceptual environment, Object Library, and two instances, and deploy a principled pipeline to measure the generalization ability. Motivated by the formulation, we analyze several methods with exact or no compositional generalization ability using our framework, and design a differentiable approach, Homomorphic Object-oriented World Model (HOWM), that achieves soft but more efficient compositional generalization.

To achieve good result quality and short query response time, search engines use specific match plans on Inverted Index to help retrieve a small set of relevant documents from billions of web pages. A match plan is composed of a sequence of match rules, which contain discrete match rule types and continuous stopping quotas. Currently, match plans are manually designed by experts according to their several years’ experience, which encounters difficulty in dealing with heterogeneous queries and varying data distribution. In this work, we formulate the match plan generation as a Partially Observable Markov Decision Process (POMDP) with a parameterized action space, and propose a novel reinforcement learning algorithm Parameterized Action Soft Actor-Critic (PASAC) to effectively enhance the exploration in both spaces. In our scene, we also discover a skew prioritizing issue of the original Prioritized Experience Replay (PER) and introduce Stratified Prioritized Experience Replay (SPER) to address it. We are the first group to generalize this task for all queries as a learning problem with zero prior knowledge and successfully apply deep reinforcement learning in the real web search environment. Our approach greatly outperforms the well-designed production match plans by over 70% reduction of index block accesses with the quality of documents almost unchanged, and 9% reduction of query response time even with model inference cost. Our method also beats the baselines on some open-source benchmarks1.

We present a deep imitation learning framework for robotic bimanual manipulation in a continuous state-action space. A core challenge is to generalize the manipulation skills to objects in different locations. We hypothesize that modeling the relational information in the environment can significantly improve generalization. To achieve this, we propose to (i) decompose the multi-modal dynamics into elemental movement primitives, (ii) parameterize each primitive using a recurrent graph neural network to capture interactions, and (iii) integrate a high-level planner that composes primitives sequentially and a low-level controller to combine primitive dynamics and inverse kinematics control. Our model is a deep, hierarchical, modular architecture. Compared to baselines, our model generalizes better and achieves higher success rates on several simulated bimanual robotic manipulation tasks. We open source the code for simulation, data, and models at: https://github.com/Rose-STL-Lab/HDR-IL.

This paper addresses the prognosis problem for hybrid systems with intermittent faults and uncertain parameters. First, a diagnostic hybrid bond graph in linear fractional form is used to model the uncertain hybrid system to generate the mode-dependent adaptive thresholds for fault detection purpose. Then, a global combinative fault signature matrix integrating independent and dependent augmented global analytical redundancy relations is proposed to improve the system fault isolability under the multiple-fault condition. After the possible fault set is isolated, an adaptive reinforcement unscented Kalman filter is introduced to identify the intermittent fault magnitude, where an auxiliary indicator is used to capture the fault appearing and disappearing time steps. To describe the degradation trend of the intermittent fault, a dynamic model with a mode-dependent degradation coefficient is used. Taking the variation of the degradation coefficient into account, an event-based sequential prognosis method is proposed, where the prognoser is only reactivated if the discrete event representing mode change is observed and its associated conditions are satisfied. Finally, the key concept of the proposed method is verified by experimental studies.