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In many real-world applications, agents must make sequential decisions in environments where conditions are subject to change due to various exogenous factors. These non-stationary environments pose significant challenges to traditional decision-making models, which typically assume stationary dynamics. Non-stationary Markov decision processes (NS-MDPs) offer a framework to model and solve decision problems under such changing conditions. However, the lack of standardized benchmarks and simulation tools has hindered systematic evaluation and advance in this field. We present NS-Gym, the first simulation toolkit designed explicitly for NS-MDPs, integrated within the popular Gymnasium framework. In NS-Gym, we segregate the evolution of the environmental parameters that characterize non-stationarity from the agent’s decision-making module, allowing for modular and flexible adaptations to dynamic environments. We review prior work in this domain and present a toolkit encapsulating key problem characteristics and types in NS-MDPs. This toolkit is the first effort to develop a set of standardized interfaces and benchmark problems to enable consistent and reproducible evaluation of algorithms under non-stationary conditions. We also benchmark six algorithmic approaches from prior work on NS-MDPs using NS-Gym. Our vision is that NS-Gym will enable researchers to assess the adaptability and robustness of their decision-making algorithms to non-stationary conditions. 

Partially observable Markov decision processes (POMDPs) are a general mathematical model for sequential decision-making in stochastic environments under state uncertainty. POMDPs are often solved online, which enables the algorithm to adapt to new information in real time. Online solvers typically use bootstrap particle filters based on importance resampling for updating the belief distribution. Since directly sampling from the ideal state distribution given the latest observation and previous state is infeasible, particle filters approximate the posterior belief distribution by propagating states and adjusting weights through prediction and resampling steps. However, in practice, the importance resampling technique often leads to particle degeneracy and sample impoverishment when the state transition model poorly aligns with the posterior belief distribution, especially when the received observation is noisy. We propose an approach that constructs a sequence of bridge distributions between the state-transition and optimal distributions through iterative Monte Carlo steps, better accommodating noisy observations in online POMDP solvers. Our algorithm demonstrates significantly superior performance compared to state-of-the-art methods when evaluated across multiple challenging POMDP domains. 

In Partially Observable Markov Decision Processes (POMDPs), maintaining and updating belief distributions over possible underlying states provides a principled way to summarize action-observation history for effective decision-making under uncertainty. As environments grow more realistic, belief distributions develop complexity that standard mathematical models cannot accurately capture, creating a fundamental challenge in maintaining representational accuracy. Despite advances in deep learning and probabilistic modeling, existing POMDP belief approximation methods fail to accurately represent complex uncertainty structures such as high-dimensional, multi-modal belief distributions, resulting in estimation errors that lead to suboptimal agent behaviors. To address this challenge, we present ESCORT (Efficient Stein-variational and sliced Consistency-Optimized Representation for Temporal beliefs), a particle-based framework for capturing complex, multi-modal distributions in high-dimensional belief spaces. ESCORT extends SVGD with two key innovations: correlation-aware projections that model dependencies between state dimensions, and temporal consistency constraints that stabilize updates while preserving correlation structures. This approach retains SVGD's attractive-repulsive particle dynamics while enabling accurate modeling of intricate correlation patterns. Unlike particle filters prone to degeneracy or parametric methods with fixed representational capacity, ESCORT dynamically adapts to belief landscape complexity without resampling or restrictive distributional assumptions. We demonstrate ESCORT's effectiveness through extensive evaluations on both POMDP domains and synthetic multi-modal distributions of varying dimensionality, where it consistently outperforms state-of-the-art methods in terms of belief approximation accuracy and downstream decision quality. 

A fundamental (and largely open) challenge in sequential decision-making is dealing with non-stationary environments, where exogenous environmental conditions change over time. Such problems are traditionally modeled as non-stationary Markov decision processes (NSMDP). However, existing approaches for decision-making in NSMDPs have two major shortcomings: first, they assume that the updated environmental dynamics at the current time are known (although future dynamics can change); and second, planning is largely pessimistic, i.e., the agent acts ``safely'' to account for the non-stationary evolution of the environment. We argue that both these assumptions are invalid in practice -- updated environmental conditions are rarely known, and as the agent interacts with the environment, it can learn about the updated dynamics and avoid being pessimistic, at least in states whose dynamics it is confident about. We present a heuristic search algorithm called \textit{Adaptive Monte Carlo Tree Search (ADA-MCTS)} that addresses these challenges. We show that the agent can learn the updated dynamics of the environment over time and then act as it learns, i.e., if the agent is in a region of the state space about which it has updated knowledge, it can avoid being pessimistic. To quantify ``updated knowledge,'' we disintegrate the aleatoric and epistemic uncertainty in the agent's updated belief and show how the agent can use these estimates for decision-making. We compare the proposed approach with the multiple state-of-the-art approaches in decision-making across multiple well-established open-source problems and empirically show that our approach is faster and highly adaptive without sacrificing safety. 

Sequential decision-making under uncertainty is present in many important problems. Two popular approaches for tackling such problems are reinforcement learning and online search (e.g., Monte Carlo tree search). While the former learns a policy by interacting with the environment (typically done before execution), the latter uses a generative model of the environment to sample promising action trajectories at decision time. Decision-making is particularly challenging in non-stationary environments, where the environment in which an agent operates can change over time. Both approaches have shortcomings in such settings -- on the one hand, policies learned before execution become stale when the environment changes and relearning takes both time and computational effort. Online search, on the other hand, can return sub-optimal actions when there are limitations on allowed runtime. In this paper, we introduce \textit{Policy-Augmented Monte Carlo tree search} (PA-MCTS), which combines action-value estimates from an out-of-date policy with an online search using an up-to-date model of the environment. We prove theoretical results showing conditions under which PA-MCTS selects the one-step optimal action and also bound the error accrued while following PA-MCTS as a policy. We compare and contrast our approach with AlphaZero, another hybrid planning approach, and Deep Q Learning on several OpenAI Gym environments. Through extensive experiments, we show that under non-stationary settings with limited time constraints, PA-MCTS outperforms these baselines. 

Route Planning Systems (RPS) are a core component of autonomous personal transport systems essential for safe and efficient navigation of dynamic urban environments with the support of edge-based smart city infrastructure, but they also raise concerns about user route privacy in the context of both privately-owned and commercial vehicles. Numerous high profile data breaches in recent years have fortunately motivated research on privacy-preserving RPS, but most of them are rendered impractical by greatly increased communication and processing overhead. We address this by proposing an approach called Hierarchical Privacy-Preserving Route Planning (HPRoP) which divides and distributes the route planning task across multiple levels, and protects locations along the entire route. This is done by combining Inertial Flow partitioning, Private Information Retrieval (PIR), and Edge Computing techniques with our novel route planning heuristic algorithm. Normalized metrics were also formulated to quantify the privacy of the source/destination points (endpoint location privacy) and the route itself (route privacy). Evaluation on a simulated road network showed that HPRoP reliably produces routes differing only by ≤20% in length from optimal shortest paths, with completion times within ∼ 25 seconds which is reasonable for a PIR-based approach. On top of this, more than half of the produced routes achieved near-optimal endpoint location privacy (∼ 1.0) and good route privacy (≥ 0.8). 

Modern smart cities need smart transportation solutions to quickly detect various traffic emergencies and incidents in the city to avoid cascading traffic disruptions. To materialize this, roadside units and ambient transportation sensors are being deployed to collect speed data that enables the monitoring of traffic conditions on each road segment. In this paper, we first propose a scalable data-driven anomaly-based traffic incident detection framework for a city-scale smart transportation system. Specifically, we propose an incremental region growing approximation algorithm for optimal Spatio-temporal clustering of road segments and their data; such that road segments are strategically divided into highly correlated clusters. The highly correlated clusters enable identifying a Pythagorean Mean-based invariant as an anomaly detection metric that is highly stable under no incidents but shows a deviation in the presence of incidents. We learn the bounds of the invariants in a robust manner such that anomaly detection can generalize to unseen events, even when learning from real noisy data. Second, using cluster-level detection, we propose a folded Gaussian classifier to pinpoint the particular segment in a cluster where the incident happened in an automated manner. We perform extensive experimental validation using mobility data collected from four cities in Tennessee, compare with the state-of-the-art ML methods, to prove that our method can detect incidents within each cluster in real-time and outperforms known ML methods.