Solving Markov Decision Processes (MDPs) remains a central challenge in sequential decision-making, especially when dealing with large state spaces and long-term optimization criteria. A key step in Bellman dynamic programming algorithms is the policy evaluation, which becomes computationally demanding in infinite-horizon settings such as average-reward or discounted-reward formulations. In the context of Markov chains, aggregation and disaggregation techniques have for a long time been used to reduce complexity by exploiting structural decompositions. In this work, we extend these principles to a structured class of MDPs. We define the Single-Input Superstate Decomposable Markov Decision Process (SISDMDP), which combines Chiu's single-input decomposition with Robertazzi's single-cycle recurrence property. When a policy induces this structure, the resulting transition graph can be decomposed into interacting components with centralized recurrence. We develop an exact and efficient policy evaluation method based on this structure. This yields a scalable solution applicable to both average and discounted reward MDPs.

Bayesian neural networks and deep ensemble methods have been proposed for uncertainty quantification; however, they are computationally intensive and require large storage. By utilizing a single deterministic model, we can solve the above issue. We propose an effective method based on feature space density to quantify uncertainty for distributional shifts and out-of-distribution (OOD) detection. Specifically, we leverage the information potential field derived from kernel density estimation to approximate the feature space density of the training set. By comparing this density with the feature space representation of test samples, we can effectively determine whether a distributional shift has occurred. Experiments were conducted on a 2D synthetic dataset (Two Moons and Three Spirals) as well as an OOD detection task (CIFAR-10 vs. SVHN). The results demonstrate that our method outperforms baseline models.

Hyperproperties for Time Window Temporal Logic (HyperTWTL) is a domain-specific formal specification language known for its effectiveness in compactly representing security, opacity, and concurrency properties for robotics applications. This paper focuses on HyperTWTL-constrained secure reinforcement learning (SecRL). Although temporal logic-constrained safe reinforcement learning (SRL) is an evolving research problem with several existing literature, there is a significant research gap in exploring security-aware reinforcement learning (RL) using hyperproperties. Given the dynamics of an agent as a Markov Decision Process (MDP) and opacity/security constraints formalized as HyperTWTL, we propose an approach for learning security-aware optimal policies using dynamic Boltzmann softmax RL while satisfying the HyperTWTL constraints. The effectiveness and scalability of our proposed approach are demonstrated using a pick-up and delivery robotic mission case study. We also compare our results with two other baseline RL algorithms, showing that our proposed method outperforms them.

Spectrum resources are often underutilized across time and space, motivating dynamic spectrum access strategies that allow secondary users to exploit unused frequencies. A key challenge is predicting when and where spectrum will be available (i.e., unused by primary licensed users) in order to enable proactive and interference-free access. This paper proposes a scalable framework for spectrum availability prediction that combines a two-state Markov chain model of primary user activity with high-fidelity propagation models from the ITU-R (specifically Recommendations P.528 and P.2108). The Markov chain captures temporal occupancy patterns, while the propagation models incorporate path loss and clutter effects to determine if primary signals exceed interference thresholds at secondary user locations. By integrating these components, the proposed method can predict spectrum opportunities both in time and space with improved accuracy. We develop the system model and algorithm for the approach, analyze its scalability and computational efficiency, and discuss assumptions, limitations, and potential applications. The framework is flexible and can be adapted to various frequency bands and scenarios. The results and analysis show that the proposed approach can effectively identify available spectrum with low computational cost, making it suitable for real-time spectrum management in cognitive radio networks and other dynamic spectrum sharing systems.

We develop information theory for the temporal behavior of memoryful agents moving through complex -- structured, stochastic -- environments. We introduce and explore information processes -- stochastic processes produced by cognitive agents in real-time as they interact with and interpret incoming stimuli. We provide basic results on the ergodicity and semantics of the resulting time series of Shannon information measures that monitor an agent's adapting view of uncertainty and structural correlation in its environment.

--Modern cyber attacks unfold through multiple stages, requiring defenders to dynamically prioritize mitigations under uncertainty. While game-theoretic models capture attacker-defender interactions, existing approaches often rely on static assumptions and lack integration with real-time threat intelligence, limiting their adaptability. This paper presents Cy-GATE, a game-theoretic framework modeling attacker-defender interactions, using large language models (LLMs) with retrieval-augmented generation (RAG) to enhance tactic selection and patch prioritization. Applied to a two-agent scenario, CyGATE frames cyber conflicts as a partially observable stochastic game (POSG) across Cyber Kill Chain stages. Both agents use belief states to navigate uncertainty, with the attacker adapting tactics and the defender re-prioritizing patches based on evolving risks and observed adversary behavior . The framework's flexible architecture enables extension to multi-agent scenarios involving coordinated attackers, collaborative defenders, or complex enterprise environments with multiple stakeholders. The evolving cybersecurity landscape presents increasingly sophisticated threats that necessitate adaptive, proactive defense strategies. Patch management, a cornerstone of cyber defense, requires intelligent prioritization of vulnerabilities under resource constraints such as maintenance windows and operational cost [1] [2] . However, traditional scoring systems like common vulnerability scoring system (CVSS) [3] fail to capture the evolving nature of cyber threats, where attackers adapt their strategies based on defender actions. Game theory provides a structured framework for modeling attacker-defender interactions [4], with chained or multistage games particularly suited to representing complex attack progressions along the Cyber Kill Chain (CKC) [5][6][7]. These models allow defenders to reason about long-term risks and preempt cascading compromises. Despite these advancements, existing models remain constrained by fixed strategies, static payoff structures, and minimal integration of threat intelligence, failing to dynamically prioritize vulnerabilities based on evolving exploitation trends [8]. Traditional game-theoretical approaches typically use predefined rules to analyze strategies, hence are limited in dynamic cyber environments where adversaries continuously adapt, operate under uncertainty, and employ unpredictable tactics [9].

Mitigating partial observability is a necessary but challenging task for general reinforcement learning algorithms. To improve an algorithm's ability to mitigate partial observability, researchers need comprehensive benchmarks to gauge progress. Most algorithms tackling partial observability are only evaluated on benchmarks with simple forms of state aliasing, such as feature masking and Gaussian noise. Such benchmarks do not represent the many forms of partial observability seen in real domains, like visual occlusion or unknown opponent intent. We argue that a partially observable benchmark should have two key properties. The first is coverage in its forms of partial observability, to ensure an algorithm's generalizability. The second is a large gap between the performance of a agents with more or less state information, all other factors roughly equal. This gap implies that an environment is memory improvable: where performance gains in a domain are from an algorithm's ability to cope with partial observability as opposed to other factors. We introduce best-practice guidelines for empirically benchmarking reinforcement learning under partial observability, as well as the open-source library POBAX: Partially Observable Benchmarks in JAX. We characterize the types of partial observability present in various environments and select representative environments for our benchmark. These environments include localization and mapping, visual control, games, and more. Additionally, we show that these tasks are all memory improvable and require hard-to-learn memory functions, providing a concrete signal for partial observability research. This framework includes recommended hyperparameters as well as algorithm implementations for fast, out-of-the-box evaluation, as well as highly performant environments implemented in JAX for GPU-scalable experimentation.

In analyses with severe data-limitations, augmenting the target dataset with information from ancillary datasets in the application domain, called source datasets, can lead to significantly improved statistical procedures. However, existing methods for this transfer learning struggle to deal with situations where the source datasets are also limited and not guaranteed to be well-aligned with the target dataset. A typical strategy is to use the empirical loss minimizer on the source data as a prior mean for the target parameters, which places the estimation of source parameters outside of the Bayesian formalism. Our key conceptual contribution is to use a risk minimizer conditional on source parameters instead. This allows us to construct a single joint prior distribution for all parameters from the source datasets as well as the target dataset. As a consequence, we benefit from full Bayesian uncertainty quantification and can perform model averaging via Gibbs sampling over indicator variables governing the inclusion of each source dataset. We show how a particular instantiation of our prior leads to a Bayesian Lasso in a transformed coordinate system and discuss computational techniques to scale our approach to moderately sized datasets. We also demonstrate that recently proposed minimax-frequentist transfer learning techniques may be viewed as an approximate Maximum a Posteriori approach to our model. Finally, we demonstrate superior predictive performance relative to the frequentist baseline on a genetics application, especially when the source data are limited.

Despite the recent proliferation of machine learning methods like SINDy that promise automatic discovery of governing equations from time-series data, there remain significant challenges to discovering models from noisy datasets. One reason is that the linear regression underlying these methods assumes that all noise resides in the training target (the regressand), which is the time derivative, whereas the measurement noise is in the states (the regressors). Recent methods like modified-SINDy and DySMHO address this error-in-variable problem by leveraging information from the model's temporal evolution, but they are also imposing the equation as a hard constraint, which effectively assumes no error in the regressand. Without relaxation, this hard constraint prevents assimilation of data longer than Lyapunov time. Instead, the fulfilment of the model equation should be treated as a soft constraint to account for the small yet critical error introduced by numerical truncation. The uncertainties in both the regressor and the regressand invite the use of orthogonal distance regression (ODR). By incorporating ODR with the Bayesian framework for model selection, we introduce a novel method for model discovery, termed ODR-BINDy, and assess its performance against current SINDy variants using the Lorenz63, Rossler, and Van Der Pol systems as case studies. Our findings indicate that ODR-BINDy consistently outperforms all existing methods in recovering the correct model from sparse and noisy datasets. For instance, our ODR-BINDy method reliably recovers the Lorenz63 equation from data with noise contamination levels of up to 30%.

Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through summary statistics, which sacrifice complexity and interdependent structure intrinsic to these data in favor of parameter identifiability. This imposes a fundamental constraint on reliably extracting mechanistic insights from spatiotemporal data, highlighting the need for analytical frameworks that preserve the full richness of these dynamical systems. To address this, we developed a simulation-based inference framework that employs vision transformer-driven variational encoding to generate compact representations of the data, exploiting the inherent contextual dependencies. These representations are subsequently integrated into a likelihood-free Bayesian approach for parameter inference. The central idea is to construct a fine-grained, structured mesh of latent representations from simulated dynamics through systematic exploration of the parameter space. This encoded mesh of latent embeddings then serves as a reference map for retrieving parameter values that correspond to observed data. By integrating generative modeling with Bayesian principles, our approach provides a unified inference framework to identify both spatial and temporal patterns that manifest in multivariate dynamical systems.