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 Markov Models


Bayesian Risk-Sensitive Policy Optimization For MDPs With General Loss Functions

arXiv.org Artificial Intelligence

Motivated by many application problems, we consider Markov decision processes (MDPs) with a general loss function and unknown parameters. To mitigate the epistemic uncertainty associated with unknown parameters, we take a Bayesian approach to estimate the parameters from data and impose a coherent risk functional (with respect to the Bayesian posterior distribution) on the loss. Since this formulation usually does not satisfy the interchangeability principle, it does not admit Bellman equations and cannot be solved by approaches based on dynamic programming. Therefore, We propose a policy gradient optimization method, leveraging the dual representation of coherent risk measures and extending the envelope theorem to continuous cases. We then show the stationary analysis of the algorithm with a convergence rate of $\mathcal{O}(T^{-1/2}+r^{-1/2})$, where $T$ is the number of policy gradient iterations and $r$ is the sample size of the gradient estimator. We further extend our algorithm to an episodic setting, and establish the global convergence of the extended algorithm and provide bounds on the number of iterations needed to achieve an error bound $\mathcal{O}(ฮต)$ in each episode.


Vision-driven River Following of UAV via Safe Reinforcement Learning using Semantic Dynamics Model

arXiv.org Artificial Intelligence

Vision-driven autonomous river following by Unmanned Aerial Vehicles is critical for applications such as rescue, surveillance, and environmental monitoring, particularly in dense riverine environments where GPS signals are unreliable. These safety-critical navigation tasks must satisfy hard safety constraints while optimizing performance. Moreover, the reward in river following is inherently history-dependent (non-Markovian) by which river segment has already been visited, making it challenging for standard safe Reinforcement Learning (SafeRL). To address these gaps, we propose three contributions. First, we introduce Marginal Gain Advantage Estimation, which refines the reward advantage function by using a sliding window baseline computed from historical episodic returns, aligning the advantage estimate with non-Markovian dynamics. Second, we develop a Semantic Dynamics Model based on patchified water semantic masks offering more interpretable and data-efficient short-term prediction of future observations compared to latent vision dynamics models. Third, we present the Constrained Actor Dynamics Estimator architecture, which integrates the actor, cost estimator, and SDM for cost advantage estimation to form a model-based SafeRL framework. Simulation results demonstrate that MGAE achieves faster convergence and superior performance over traditional critic-based methods like Generalized Advantage Estimation. SDM provides more accurate short-term state predictions that enable the cost estimator to better predict potential violations. Overall, CADE effectively integrates safety regulation into model-based RL, with the Lagrangian approach providing a "soft" balance between reward and safety during training, while the safety layer enhances inference by imposing a "hard" action overlay.


The challenge of hidden gifts in multi-agent reinforcement learning

arXiv.org Artificial Intelligence

Sometimes we benefit from actions that others have taken even when we are unaware that they took those actions. For example, if your neighbor chooses not to take a parking spot in front of your house when you are not there, you can benefit, even without being aware that they took this action. These ``hidden gifts'' represent an interesting challenge for multi-agent reinforcement learning (MARL), since assigning credit when the beneficial actions of others are hidden is non-trivial. Here, we study the impact of hidden gifts with a very simple MARL task. In this task, agents in a grid-world environment have individual doors to unlock in order to obtain individual rewards. As well, if all the agents unlock their door the group receives a larger collective reward. However, there is only one key for all of the doors, such that the collective reward can only be obtained when the agents drop the key for others after they use it. Notably, there is nothing to indicate to an agent that the other agents have dropped the key, thus this act for others is a ``hidden gift''. We show that several different state-of-the-art MARL algorithms, including MARL specific architectures, fail to learn how to obtain the collective reward in this simple task. Interestingly, we find that decentralized actor-critic policy gradient agents can succeed when we provide them with information about their own action history, but MARL agents still cannot solve the task with action history. Finally, we derive a correction term for policy gradient agents, inspired by learning aware approaches, which reduces the variance in learning and helps them to converge to collective success more reliably. These results show that credit assignment in multi-agent settings can be particularly challenging in the presence of ``hidden gifts'', and demonstrate that self learning-awareness in decentralized agents can benefit these settings.


Optimizing Fairness in Production Planning: A Human-Centric Approach to Machine and Workforce Allocation

arXiv.org Artificial Intelligence

This work presents a two-layer, human-centric production planning framework designed to optimize both operational efficiency and workforce fairness in industrial manufacturing. The first layer formulates the Order-Line allocation as a Constraint Programming (CP) problem, generating high-utilization production schedules that respect machine capacities, processing times, and due dates. The second layer models Worker-Line allocation as a Markov Decision Process (MDP), integrating human factors such as worker preference, experience, resilience, and medical constraints into the assignment process. Three solution strategies, greedy allocation, MCTS, and RL, are implemented and compared across multiple evaluation scenarios. The proposed system is validated through 16 test sessions with domain experts from the automotive industry, combining quantitative key performance indicators (KPIs) with expert ratings. Results indicate that the CP-based scheduling approach produces compact, feasible production plans with low tardiness, while the MDP-based worker allocation significantly improves fairness and preference alignment compared to baseline approaches. Domain experts rated both the Order-Line and Worker-Line components as effective and highlighted opportunities to further refine the objective function to penalize excessive earliness and improve continuity in worker assignments. Overall, the findings demonstrate that combining CP with learning-based decision-making provides a robust approach for human-centric production planning. The approach enables simultaneous optimization of throughput and workforce well-being, offering a practical foundation for fair and efficient manufacturing scheduling in industrial settings.


Replicable Reinforcement Learning with Linear Function Approximation

arXiv.org Artificial Intelligence

Replication of experimental results has been a challenge faced by many scientific disciplines, including the field of machine learning. Recent work on the theory of machine learning has formalized replicability as the demand that an algorithm produce identical outcomes when executed twice on different samples from the same distribution. Provably replicable algorithms are especially interesting for reinforcement learning (RL), where algorithms are known to be unstable in practice. While replicable algorithms exist for tabular RL settings, extending these guarantees to more practical function approximation settings has remained an open problem. In this work, we make progress by developing replicable methods for linear function approximation in RL. We first introduce two efficient algorithms for replicable random design regression and uncentered covariance estimation, each of independent interest. We then leverage these tools to provide the first provably efficient replicable RL algorithms for linear Markov decision processes in both the generative model and episodic settings. Finally, we evaluate our algorithms experimentally and show how they can inspire more consistent neural policies.


GUI-KV: Efficient GUI Agents via KV Cache with Spatio-Temporal Awareness

arXiv.org Artificial Intelligence

Graphical user interface (GUI) agents built on vision-language models have emerged as a promising approach to automate human-computer workflows. However, they also face the inefficiency challenge as they process long sequences of high-resolution screenshots and solving long-horizon tasks, making inference slow, costly and memory-bound. While key-value (KV) caching can mitigate this, storing the full cache is prohibitive for image-heavy contexts. Existing cache-compression methods are sub-optimal as they do not account for the spatial and temporal redundancy of GUIs. In this work, we first analyze attention patterns in GUI agent workloads and find that, unlike in natural images, attention sparsity is uniformly high across all transformer layers. This insight motivates a simple uniform budget allocation strategy, which we show empirically outperforms more complex layer-varying schemes. Building on this, we introduce GUI-KV, a plug-and-play KV cache compression method for GUI agents that requires no retraining. GUI-KV combines two novel techniques: (i) spatial saliency guidance, which augments attention scores with the L2 norm of hidden states to better preserve semantically important visual tokens, and (ii) temporal redundancy scoring, which projects previous frames' keys onto the current frame's key subspace to preferentially prune redundant history. Across standard GUI agent benchmarks and models, GUI-KV outperforms competitive KV compression baselines, closely matching full-cache accuracy at modest budgets. Notably, in a 5-screenshot setting on the AgentNetBench benchmark, GUI-KV reduces decoding FLOPs by 38.9% while increasing step accuracy by 4.1% over the full-cache baseline. These results demonstrate that exploiting GUI-specific redundancies enables efficient and reliable agent performance.


VLA-RFT: Vision-Language-Action Reinforcement Fine-tuning with Verified Rewards in World Simulators

arXiv.org Artificial Intelligence

Vision-Language-Action (VLA) models enable embodied decision-making but rely heavily on imitation learning, leading to compounding errors and poor robustness under distribution shift. Reinforcement learning (RL) can mitigate these issues yet typically demands costly real-world interactions or suffers from sim-to-real gaps. We introduce VLA-RFT, a reinforcement fine-tuning framework that leverages a data-driven world model as a controllable simulator. Trained from real interaction data, the simulator predicts future visual observations conditioned on actions, allowing policy rollouts with dense, trajectory-level rewards derived from goal-achieving references. This design delivers an efficient and action-aligned learning signal, drastically lowering sample requirements. With fewer than 400 fine-tuning steps, VLA-RFT surpasses strong supervised baselines and achieves greater efficiency than simulator-based RL. Moreover, it exhibits strong robustness under perturbed conditions, sustaining stable task execution. Our results establish world-model-based RFT as a practical post-training paradigm to enhance the generalization and robustness of VLA models. For more details, please refer to https://vla-rft.github.io/.


Initial Distribution Sensitivity of Constrained Markov Decision Processes

arXiv.org Artificial Intelligence

Constrained Markov Decision Processes (CMDPs) are notably more complex to solve than standard MDPs due to the absence of universally optimal policies across all initial state distributions. This necessitates re-solving the CMDP whenever the initial distribution changes. In this work, we analyze how the optimal value of CMDPs varies with different initial distributions, deriving bounds on these variations using duality analysis of CMDPs and perturbation analysis in linear programming. Moreover, we show how such bounds can be used to analyze the regret of a given policy due to unknown variations of the initial distribution.


Dependent Multinomial Models Made Easy: Stick-Breaking with the Polya-gamma Augmentation

Neural Information Processing Systems

Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children's names in a given state and year, and text documents are all commonly modeled with multinomial distributions. In all of these cases, we expect some form of dependency between the draws: the nucleotide at one position in the DNA strand may depend on the preceding nucleotides, children's names are highly correlated from year to year, and topics in text may be correlated and dynamic. These dependencies are not naturally captured by the typical Dirichlet-multinomial formulation. Here, we leverage a logistic stick-breaking representation and recent innovations in P olya-gamma augmentation to reformulate the multinomial distribution in terms of latent variables with jointly Gaussian likelihoods, enabling us to take advantage of a host of Bayesian inference techniques for Gaussian models with minimal overhead.


Infinite Factorial Dynamical Model

Neural Information Processing Systems

We propose the infinite factorial dynamic model (iFDM), a general Bayesian nonparametric model for source separation. Our model builds on the Markov Indian buffet process to consider a potentially unbounded number of hidden Markov chains (sources) that evolve independently according to some dynamics, in which the state space can be either discrete or continuous. For posterior inference, we develop an algorithm based on particle Gibbs with ancestor sampling that can be efficiently applied to a wide range of source separation problems. We evaluate the performance of our iFDM on four well-known applications: multitarget tracking, cocktail party, power disaggregation, and multiuser detection. Our experimental results show that our approach for source separation does not only outperform previous approaches, but it can also handle problems that were computationally intractable for existing approaches.