A Novel Multi-Timescale Stability-Preserving Hierarchical Reinforcement Learning Controller Framework for Adaptive Control in High-Dimensional Dynamical Systems

Controlling high-dimensional stochastic systems, critical in robotics, autonomous vehicles, and hyperchaotic systems, faces the curse of dimensionality, lacks temporal abstraction, and often fails to ensure stochastic stability. To overcome these limitations, this study introduces the Multi-Timescale Lyapunov-Constrained Hierarchical Reinforcement Learning (MTLHRL) framework. MTLHRL integrates a hierarchical policy within a semi-Markov Decision Process (SMDP), featuring a high-level policy for strategic planning and a low-level policy for reactive control, which effectively manages complex, multi-timescale decision-making and reduces dimensionality overhead. Stability is rigorously enforced using a neural Lyapunov function optimized via Lagrangian relaxation and multi-timescale actor-critic updates, ensuring mean-square boundedness or asymptotic stability in the face of stochastic dynamics. The framework promotes efficient and reliable learning through trust-region constraints and decoupled optimization. Extensive simulations on an 8D hyperchaotic system and a 5-DOF robotic manipulator demonstrate MTLHRL's empirical superiority. It significantly outperforms baseline methods in both stability and performance, recording the lowest error indices (e.g., Integral Absolute Error (IAE): 3.912 in hyperchaotic control and IAE: 1.623 in robotics), achieving faster convergence, and exhibiting superior disturbance rejection. MTLHRL offers a theoretically grounded and practically viable solution for robust control of complex stochastic systems.

HRM-Agent: Training a recurrent reasoning model in dynamic environments using reinforcement learning

The Hierarchical Reasoning Model (HRM) has impressive reasoning abilities given its small size, but has only been applied to supervised, static, fully-observable problems. One of HRM's strengths is its ability to adapt its computational effort to the difficulty of the problem. However, in its current form it cannot integrate and reuse computation from previous time-steps if the problem is dynamic, uncertain or partially observable, or be applied where the correct action is undefined, characteristics of many real-world problems. This paper presents HRM-Agent, a variant of HRM trained using only reinforcement learning. We show that HRM can learn to navigate to goals in dynamic and uncertain maze environments. Recent work suggests that HRM's reasoning abilities stem from its recurrent inference process. We explore the dynamics of the recurrent inference process and find evidence that it is successfully reusing computation from earlier environment time-steps.

Hybrid DQN-TD3 Reinforcement Learning for Autonomous Navigation in Dynamic Environments

This paper presents a hierarchical path-planning and control framework that combines a high-level Deep Q-Network (DQN) for discrete sub-goal selection with a low-level Twin Delayed Deep Deterministic Policy Gradient (TD3) controller for continuous actuation. The high-level module selects behaviors and sub-goals; the low-level module executes smooth velocity commands. We design a practical reward shaping scheme (direction, distance, obstacle avoidance, action smoothness, collision penalty, time penalty, and progress), together with a LiDAR-based safety gate that prevents unsafe motions. The system is implemented in ROS + Gazebo (TurtleBot3) and evaluated with PathBench metrics, including success rate, collision rate, path efficiency, and re-planning efficiency, in dynamic and partially observable environments. Experiments show improved success rate and sample efficiency over single-algorithm baselines (DQN or TD3 alone) and rule-based planners, with better generalization to unseen obstacle configurations and reduced abrupt control changes. Code and evaluation scripts are available at the project repository.

Multi-Agent Reinforcement Learning for Market Making: Competition without Collusion

Algorithmic collusion has emerged as a central question in AI: Will the interaction between different AI agents deployed in markets lead to collusion? More generally, understanding how emergent behavior, be it a cartel or market dominance from more advanced bots, affects the market overall is an important research question. We propose a hierarchical multi-agent reinforcement learning framework to study algorithmic collusion in market making. The framework includes a self-interested market maker (Agent~A), which is trained in an uncertain environment shaped by an adversary, and three bottom-layer competitors: the self-interested Agent~B1 (whose objective is to maximize its own PnL), the competitive Agent~B2 (whose objective is to minimize the PnL of its opponent), and the hybrid Agent~B$^\star$, which can modulate between the behavior of the other two. To analyze how these agents shape the behavior of each other and affect market outcomes, we propose interaction-level metrics that quantify behavioral asymmetry and system-level dynamics, while providing signals potentially indicative of emergent interaction patterns. Experimental results show that Agent~B2 secures dominant performance in a zero-sum setting against B1, aggressively capturing order flow while tightening average spreads, thus improving market execution efficiency. In contrast, Agent~B$^\star$ exhibits a self-interested inclination when co-existing with other profit-seeking agents, securing dominant market share through adaptive quoting, yet exerting a milder adverse impact on the rewards of Agents~A and B1 compared to B2. These findings suggest that adaptive incentive control supports more sustainable strategic co-existence in heterogeneous agent environments and offers a structured lens for evaluating behavioral design in algorithmic trading systems.

Reinforcement Learning for Pollution Detection in a Randomized, Sparse and Nonstationary Environment with an Autonomous Underwater Vehicle

Reinforcement learning (RL) algorithms are designed to optimize problem-solving by learning actions that maximize rewards, a task that becomes particularly challenging in random and nonstationary environments. Even advanced RL algorithms are often limited in their ability to solve problems in these conditions. In applications such as searching for underwater pollution clouds with autonomous underwater vehicles (AUVs), RL algorithms must navigate reward-sparse environments, where actions frequently result in a zero reward. This paper aims to address these challenges by revisiting and modifying classical RL approaches to efficiently operate in sparse, randomized, and nonstationary environments. We systematically study a large number of modifications, including hierarchical algorithm changes, multigoal learning, and the integration of a location memory as an external output filter to prevent state revisits. Our results demonstrate that a modified Monte Carlo-based approach significantly outperforms traditional Q-learning and two exhaustive search patterns, illustrating its potential in adapting RL to complex environments. These findings suggest that reinforcement learning approaches can be effectively adapted for use in random, nonstationary, and reward-sparse environments.

Hierarchical DLO Routing with Reinforcement Learning and In-Context Vision-language Models

Long-horizon routing tasks of deformable linear objects (DLOs), such as cables and ropes, are common in industrial assembly lines and everyday life. These tasks are particularly challenging because they require robots to manipulate DLO with long-horizon planning and reliable skill execution. Successfully completing such tasks demands adapting to their nonlinear dynamics, decomposing abstract routing goals, and generating multi-step plans composed of multiple skills, all of which require accurate high-level reasoning during execution. In this paper, we propose a fully autonomous hierarchical framework for solving challenging DLO routing tasks. Given an implicit or explicit routing goal expressed in language, our framework leverages vision-language models~(VLMs) for in-context high-level reasoning to synthesize feasible plans, which are then executed by low-level skills trained via reinforcement learning. To improve robustness in long horizons, we further introduce a failure recovery mechanism that reorients the DLO into insertion-feasible states. Our approach generalizes to diverse scenes involving object attributes, spatial descriptions, as well as implicit language commands. It outperforms the next best baseline method by nearly 50% and achieves an overall success rate of 92.5% across long-horizon routing scenarios.

Network-Constrained Policy Optimization for Adaptive Multi-agent Vehicle Routing

Traffic congestion in urban road networks leads to longer trip times and higher emissions, especially during peak periods. While the Shortest Path First (SPF) algorithm is optimal for a single vehicle in a static network, it performs poorly in dynamic, multi-vehicle settings, often worsening congestion by routing all vehicles along identical paths. We address dynamic vehicle routing through a multi-agent reinforcement learning (MARL) framework for coordinated, network-aware fleet navigation. We first propose Adaptive Navigation (AN), a decentralized MARL model where each intersection agent provides routing guidance based on (i) local traffic and (ii) neighborhood state modeled using Graph Attention Networks (GAT). To improve scalability in large networks, we further propose Hierarchical Hub-based Adaptive Navigation (HHAN), an extension of AN that assigns agents only to key intersections (hubs). Vehicles are routed hub-to-hub under agent control, while SPF handles micro-routing within each hub region. For hub coordination, HHAN adopts centralized training with decentralized execution (CTDE) under the Attentive Q-Mixing (A-QMIX) framework, which aggregates asynchronous vehicle decisions via attention. Hub agents use flow-aware state features that combine local congestion and predictive dynamics for proactive routing. Experiments on synthetic grids and real urban maps (Toronto, Manhattan) show that AN reduces average travel time versus SPF and learning baselines, maintaining 100% routing success. HHAN scales to networks with hundreds of intersections, achieving up to 15.9% improvement under heavy traffic. These findings highlight the potential of network-constrained MARL for scalable, coordinated, and congestion-aware routing in intelligent transportation systems.

Optimistic Reinforcement Learning-Based Skill Insertions for Task and Motion Planning

Task and motion planning (TAMP) for robotics manipulation necessitates long-horizon reasoning involving versatile actions and skills. While deterministic actions can be crafted by sampling or optimizing with certain constraints, planning actions with uncertainty, i.e., probabilistic actions, remains a challenge for TAMP. On the contrary, Reinforcement Learning (RL) excels in acquiring versatile, yet short-horizon, manipulation skills that are robust with uncertainties. In this letter, we design a method that integrates RL skills into TAMP pipelines. Besides the policy, a RL skill is defined with data-driven logical components that enable the skill to be deployed by symbolic planning. A plan refinement sub-routine is designed to further tackle the inevitable effect uncertainties. In the experiments, we compare our method with baseline hierarchical planning from both TAMP and RL fields and illustrate the strength of the method. The results show that by embedding RL skills, we extend the capability of TAMP to domains with probabilistic skills, and improve the planning efficiency compared to the previous methods.

Hi-Agent: Hierarchical Vision-Language Agents for Mobile Device Control

Building agents that autonomously operate mobile devices has attracted increasing attention. While Vision-Language Models (VLMs) show promise, most existing approaches rely on direct state-to-action mappings, which lack structured reasoning and planning, and thus generalize poorly to novel tasks or unseen UI layouts. We introduce Hi-Agent, a trainable hierarchical vision-language agent for mobile control, featuring a high-level reasoning model and a low-level action model that are jointly optimized. For efficient training, we reformulate multi-step decision-making as a sequence of single-step subgoals and propose a foresight advantage function, which leverages execution feedback from the low-level model to guide high-level optimization. This design alleviates the path explosion issue encountered by Group Relative Policy Optimization (GRPO) in long-horizon tasks and enables stable, critic-free joint training. Hi-Agent achieves a new State-Of-The-Art (SOTA) 87.9% task success rate on the Android-in-the-Wild (AitW) benchmark, significantly outperforming prior methods across three paradigms: prompt-based (AppAgent: 17.7%), supervised (Filtered BC: 54.5%), and reinforcement learning-based (DigiRL: 71.9%). It also demonstrates competitive zero-shot generalization on the ScreenSpot-v2 benchmark. On the more challenging AndroidWorld benchmark, Hi-Agent also scales effectively with larger backbones, showing strong adaptability in high-complexity mobile control scenarios.

ReLAM: Learning Anticipation Model for Rewarding Visual Robotic Manipulation

Reward design remains a critical bottleneck in visual reinforcement learning (RL) for robotic manipulation. In simulated environments, rewards are conventionally designed based on the distance to a target position. However, such precise positional information is often unavailable in real-world visual settings due to sensory and perceptual limitations. In this study, we propose a method that implicitly infers spatial distances through keypoints extracted from images. Building on this, we introduce Reward Learning with Anticipation Model (ReLAM), a novel framework that automatically generates dense, structured rewards from action-free video demonstrations. ReLAM first learns an anticipation model that serves as a planner and proposes intermediate keypoint-based subgoals on the optimal path to the final goal, creating a structured learning curriculum directly aligned with the task's geometric objectives. Based on the anticipated subgoals, a continuous reward signal is provided to train a low-level, goal-conditioned policy under the hierarchical reinforcement learning (HRL) framework with provable sub-optimality bound. Extensive experiments on complex, long-horizon manipulation tasks show that ReLAM significantly accelerates learning and achieves superior performance compared to state-of-the-art methods.