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 Markov Models


Sample Complexity Bounds for Linear Constrained MDPs with a Generative Model

arXiv.org Machine Learning

We consider infinite-horizon $γ$-discounted (linear) constrained Markov decision processes (CMDPs) where the objective is to find a policy that maximizes the expected cumulative reward subject to expected cumulative constraints. Given access to a generative model, we propose to solve CMDPs with a primal-dual framework that can leverage any black-box unconstrained MDP solver. For linear CMDPs with feature dimension $d$, we instantiate the framework by using mirror descent value iteration (\texttt{MDVI})~\citep{kitamura2023regularization} an example MDP solver. We provide sample complexity bounds for the resulting CMDP algorithm in two cases: (i) relaxed feasibility, where small constraint violations are allowed, and (ii) strict feasibility, where the output policy is required to exactly satisfy the constraint. For (i), we prove that the algorithm can return an $ε$-optimal policy with high probability by using $\tilde{O}\left(\frac{d^2}{(1-γ)^4ε^2}\right)$ samples. We note that these results exhibit a near-optimal dependence on both $d$ and $ε$. For (ii), we show that the algorithm requires $\tilde{O}\left(\frac{d^2}{(1-γ)^6ε^2ζ^2}\right)$ samples, where $ζ$ is the problem-dependent Slater constant that characterizes the size of the feasible region. Finally, we instantiate our framework for tabular CMDPs and show that it can be used to recover near-optimal sample complexities in this setting.


MISC: Minimal Intervention Shared Control with Guaranteed Safety under Non-Convex Constraints

arXiv.org Artificial Intelligence

Shared control combines human intention with autonomous decision-making, from low-level safety overrides to high-level task guidance, enabling systems that adapt to users while ensuring safety and performance. This enhances task effectiveness and user experience across domains such as assistive robotics, teleoperation, and autonomous driving. However, existing shared control methods, based on e.g. Model Predictive Control, Control Barrier Functions, or learning-based control, struggle with feasibility, scalability, or safety guarantees, particularly since the user input is unpredictable. To address these challenges, we propose an assistive controller framework based on Constrained Optimal Control Problem that incorporates an offline-computed Control Invariant Set, enabling online computation of control actions that ensure feasibility, strict constraint satisfaction, and minimal override of user intent. Moreover, the framework can accommodate structured class of non-convex constraints, which are common in real-world scenarios. We validate the approach through a large-scale user study with 66 participants--one of the most extensive in shared control research--using a computer game environment to assess task load, trust, and perceived control, in addition to performance. The results show consistent improvements across all these aspects without compromising safety and user intent.


Emotionally Intelligent Task-oriented Dialogue Systems: Architecture, Representation, and Optimisation

arXiv.org Artificial Intelligence

Task-oriented dialogue (ToD) systems are designed to help users achieve specific goals through natural language interaction. While recent advances in large language models (LLMs) have significantly improved linguistic fluency and contextual understanding, building effective and emotionally intelligent ToD systems remains a complex challenge. Effective ToD systems must optimise for task success, emotional understanding and responsiveness, and precise information conveyance, all within inherently noisy and ambiguous conversational environments. In this work, we investigate architectural, representational, optimisational as well as emotional considerations of ToD systems. We set up systems covering these design considerations with a challenging evaluation environment composed of a natural-language user simulator coupled with an imperfect natural language understanding module. We propose \textbf{LUSTER}, an \textbf{L}LM-based \textbf{U}nified \textbf{S}ystem for \textbf{T}ask-oriented dialogue with \textbf{E}nd-to-end \textbf{R}einforcement learning with both short-term (user sentiment) and long-term (task success) rewards. Our findings demonstrate that combining LLM capability with structured reward modelling leads to more resilient and emotionally responsive ToD systems, offering a practical path forward for next-generation conversational agents.


Gym4ReaL: A Suite for Benchmarking Real-World Reinforcement Learning

arXiv.org Artificial Intelligence

In recent years, \emph{Reinforcement Learning} (RL) has made remarkable progress, achieving superhuman performance in a wide range of simulated environments. As research moves toward deploying RL in real-world applications, the field faces a new set of challenges inherent to real-world settings, such as large state-action spaces, non-stationarity, and partial observability. Despite their importance, these challenges are often underexplored in current benchmarks, which tend to focus on idealized, fully observable, and stationary environments, often neglecting to incorporate real-world complexities explicitly. In this paper, we introduce \texttt{Gym4ReaL}, a comprehensive suite of realistic environments designed to support the development and evaluation of RL algorithms that can operate in real-world scenarios. The suite includes a diverse set of tasks that expose algorithms to a variety of practical challenges. Our experimental results show that, in these settings, standard RL algorithms confirm their competitiveness against rule-based benchmarks, motivating the development of new methods to fully exploit the potential of RL to tackle the complexities of real-world tasks.


Conceptual Framework Toward Embodied Collective Adaptive Intelligence

arXiv.org Artificial Intelligence

Collective Adaptive Intelligence (CAI) represent a transformative approach in embodied AI, wherein numerous autonomous agents collaborate, adapt, and self-organize to navigate complex, dynamic environments. By enabling systems to reconfigure themselves in response to unforeseen challenges, CAI facilitate robust performance in real-world scenarios. This article introduces a conceptual framework for designing and analyzing CAI. It delineates key attributes including task generalization, resilience, scalability, and self-assembly, aiming to bridge theoretical foundations with practical methodologies for engineering adaptive, emergent intelligence. By providing a structured foundation for understanding and implementing CAI, this work seeks to guide researchers and practitioners in developing more resilient, scalable, and adaptable AI systems across various domains.


Harnessing the Power of Reinforcement Learning for Adaptive MCMC

arXiv.org Machine Learning

Sampling algorithms drive probabilistic machine learning, and recent years have seen an explosion in the diversity of tools for this task. However, the increasing sophistication of sampling algorithms is correlated with an increase in the tuning burden. There is now a greater need than ever to treat the tuning of samplers as a learning task in its own right. In a conceptual breakthrough, Wang et al (2025) formulated Metropolis-Hastings as a Markov decision process, opening up the possibility for adaptive tuning using Reinforcement Learning (RL). Their emphasis was on theoretical foundations; realising the practical benefit of Reinforcement Learning Metropolis-Hastings (RLMH) was left for subsequent work. The purpose of this paper is twofold: First, we observe the surprising result that natural choices of reward, such as the acceptance rate, or the expected squared jump distance, provide insufficient signal for training RLMH. Instead, we propose a novel reward based on the contrastive divergence, whose superior performance in the context of RLMH is demonstrated. Second, we explore the potential of RLMH and present adaptive gradient-based samplers that balance flexibility of the Markov transition kernel with learnability of the associated RL task. A comprehensive simulation study using the posteriordb benchmark supports the practical effectiveness of RLMH.


Learning Attentive Neural Processes for Planning with Pushing Actions

arXiv.org Artificial Intelligence

Our goal is to enable robots to plan sequences of tabletop actions to push a block with unknown physical properties to a desired goal pose. We approach this problem by learning the constituent models of a Partially-Observable Markov Decision Process (POMDP), where the robot can observe the outcome of a push, but the physical properties of the block that govern the dynamics remain unknown. A common solution approach is to train an observation model in a supervised fashion, and do inference with a general inference technique such as particle filters. However, supervised training requires knowledge of the relevant physical properties that determine the problem dynamics, which we do not assume to be known. Planning also requires simulating many belief updates, which becomes expensive when using particle filters to represent the belief. We propose to learn an Attentive Neural Process that computes the belief over a learned latent representation of the relevant physical properties given a history of actions. To address the pushing planning problem, we integrate a trained Neural Process with a double-progressive widening sampling strategy. Simulation results indicate that Neural Process Tree with Double Progressive Widening (NPT-DPW) generates better-performing plans faster than traditional particle-filter methods that use a supervised-trained observation model, even in complex pushing scenarios.


Beat and Downbeat Tracking in Performance MIDI Using an End-to-End Transformer Architecture

arXiv.org Artificial Intelligence

Beat tracking in musical performance MIDI is a challenging and important task for notation-level music transcription and rhythmical analysis, yet existing methods primarily focus on audio-based approaches. This paper proposes an end-to-end transformer-based model for beat and downbeat tracking in performance MIDI, leveraging an encoder-decoder architecture for sequence-to-sequence translation of MIDI input to beat annotations. Our approach introduces novel data preprocessing techniques, including dynamic augmentation and optimized tokenization strategies, to improve accuracy and generalizability across different datasets. We conduct extensive experiments using the A-MAPS, ASAP, GuitarSet, and Leduc datasets, comparing our model against state-of-the-art hidden Markov models (HMMs) and deep learning-based beat tracking methods. The results demonstrate that our model outperforms existing symbolic music beat tracking approaches, achieving competitive F1-scores across various musical styles and instruments. Our findings highlight the potential of transformer architectures for symbolic beat tracking and suggest future integration with automatic music transcription systems for enhanced music analysis and score generation.


Minimizing Acoustic Noise: Enhancing Quiet Locomotion for Quadruped Robots in Indoor Applications

arXiv.org Artificial Intelligence

-- Recent advancements in quadruped robot research have significantly improved their ability to traverse complex and unstructured outdoor environments. However, the issue of noise generated during locomotion is generally overlooked, which is critically important in noise-sensitive indoor environments, such as service and healthcare settings, where maintaining low noise levels is essential. This study aims to optimize the acoustic noise generated by quadruped robots during locomotion through the development of advanced motion control algorithms. T o achieve this, we propose a novel approach that minimizes noise emissions by integrating optimized gait design with tailored control strategies. This method achieves an average noise reduction of approximately 8 dBA during movement, thereby enhancing the suitability of quadruped robots for deployment in noise-sensitive indoor environments. Experimental results demonstrate the effectiveness of this approach across various indoor settings, highlighting the potential of quadruped robots for quiet operation in noise-sensitive environments. I. INTRODUCTION Quadruped robots have garnered significant attention in recent years, particularly due to their versatility and capability to navigate complex terrains using Reinforcement Learning-based motion control [1]-[7].


Constructing Non-Markovian Decision Process via History Aggregator

arXiv.org Artificial Intelligence

In the domain of algorithmic decision-making, non-Markovian dynamics manifest as a significant impediment, especially for paradigms such as Reinforcement Learning (RL), thereby exerting far-reaching consequences on the advancement and effectiveness of the associated systems. Nevertheless, the existing benchmarks are deficient in comprehensively assessing the capacity of decision algorithms to handle non-Markovian dynamics. To address this deficiency, we have devised a generalized methodology grounded in category theory. Notably, we established the category of Markov Decision Processes (MDP) and the category of non-Markovian Decision Processes (NMDP), and proved the equivalence relationship between them. This theoretical foundation provides a novel perspective for understanding and addressing non-Markovian dynamics. We further introduced non-Markovianity into decision-making problem settings via the History Aggregator for State (HAS). With HAS, we can precisely control the state dependency structure of decision-making problems in the time series. Our analysis demonstrates the effectiveness of our method in representing a broad range of non-Markovian dynamics. This approach facilitates a more rigorous and flexible evaluation of decision algorithms by testing them in problem settings where non-Markovian dynamics are explicitly constructed.