Non-Stationarity

We study finite-horizon budget allocation as a closed-loop economic control problem and evaluate receding-horizon Model Predictive Control (MPC) relative to reactive budgeting policies. Budgets are allocated periodically under execution noise and operational constraints, while return efficiency may evolve over time. Using a controlled simulation framework motivated by digital marketing, we compare reactive pacing to MPC across environments with increasing degrees of non-stationarity. Our results show that non-stationarity alone does not justify predictive control. When return dynamics are stationary or evolve through unpredictable stochastic drift, MPC offers no systematic advantage over reactive baselines. By contrast, when return efficiency exhibits predictable structure over the planning horizon, that is captured through an underlying model, MPC consistently outperforms reactive budgeting by exploiting intertemporal trade-offs.

The widespread availability of complex time series data in various domains such as environmental science, epidemiology, and economics demands robust causal discovery methods that can identify intricate contemporaneous and lagged relationships in non-stationary, nonlinear, and noisy settings. Existing constraint-based methods often rely heavily on conditional independence tests that degrade for limited data samples and complex distributions, while score-based methods impose strong statistical assumptions. Recent methods address special cases such as change point detection or distribution shifts, but struggle to provide a unified solution. We propose the Transformer Integrated Temporal Causal Discovery (TTCD) Framework, a novel end-to-end approach that learns contemporaneous and lagged causal relations from non-stationary time series. TTCD introduces a Non-Stationary Feature Learner integrating temporal and frequency-domain attention with dynamic non-stationarity profiling, and a custom Causal Structure Learner. A key innovation is reconstruction-guided causal signal distillation, to distill essential causal signals through the reconstruction process of the transformer decoder, which mitigates noise and spurious correlations while preserving meaningful dependencies. The Causal Structure Learner operates on distilled reconstructed signals to infer the underlying causal graph without restrictive assumptions on noise distributions or data generation processes. Experiments on synthetic, benchmark, and real world datasets show that TTCD consistently outperforms state-of-the-art baselines in both accuracy and consistency with domain knowledge, demonstrating the approach's effectiveness for causal discovery in challenging real world contexts.

Real-world visual systems face time-varying perturbations, including weather, sensor noise, compression artifacts, and background distractions. Existing image restoration methods are typically designed for fixed corruption types and optimized for pixel-level fidelity, leaving open two questions: how restoration behaves under non-stationary corruption switching, and whether pixel-level fidelity preserves the task-relevant information needed by downstream models. To study this setting, we introduce the Visual Degraded Control Suite (VDCS), a benchmark that injects Markov-switching physical degradations into rendered scenes. We further identify a fundamental failure mode of reconstruction-based representations: faithfully reconstructing corrupted observations forces the latent state to encode corruption-specific nuisance information, thereby contaminating downstream models. From an information-bottleneck perspective, anchoring the representation to the clean foreground eliminates this contamination. Motivated by this analysis, we propose \emph{Agent-Centric Observations with Mixture-of-Experts} (ACO-MoE), a frozen, plug-and-play observation adapter that combines a routed bank of restoration experts with a foreground-mask branch. ACO-MoE is pretrained entirely offline on synthetic rendered data with automatically generated degradation pairs and simulation-derived foreground masks, requiring no manual annotation. At inference time, it takes only corrupted RGB as input without corruption labels, clean reference frames, or foreground masks. Across VDCS, DMC-GB, and RoboSuite, ACO-MoE consistently improves downstream control with both model-free and model-based backbones, recovering 95.3% of clean-input performance under challenging Markov-switching corruptions. It also generalizes zero-shot to unseen visual perturbations excluded from adapter pretraining.

Natural gas is undoubtedly an essential component of the global energy system. Accurate short-term forecasting of natural gas price is challenging due to pronounced volatility driven by seasonal demand patterns, geopolitical developments, and shifting macroeconomic conditions. The nonlinear dynamics and frequent regime changes can limit the effectiveness of traditional time-series models. In this study, we explore the use of Liquid Neural Networks (LNNs) for short-horizon forecasting of the Henry Hub spot price, a primary benchmark for pricing. LNNs are designed to adapt continuously to evolving temporal patterns through dynamic internal state updates, making them well suited for nonstationary price behavior. By improving forecast accuracy in volatile market conditions, this work aims to reduce uncertainty and enhance decision support across energy trading and power market applications.

In many application domains (e.g., recommender systems, intelligent tutoring systems), the rewards associated to the actions tend to decrease over time. This decay is either caused by the actions executed in the past (e.g., a user may get bored when songs of the same genre are recommended over and over) or by an external factor (e.g., content becomes outdated). These two situations can be modeled as specific instances of the rested and restless bandit settings, where arms are rotting (i.e., their value decrease over time). These problems were thought to be significantly different, since Levine et al. (2017) showed that state-of-the-art algorithms for restless bandit perform poorly in the rested rotting setting. In this paper, we introduce a novel algorithm, Rotting Adaptive Window UCB (RAW-UCB), that achieves near-optimal regret in both rotting rested and restless bandit, without any prior knowledge of the setting (rested or restless) and the type of non-stationarity (e.g., piece-wise constant, bounded variation). This is in striking contrast with previous negative results showing that no algorithm can achieve similar results as soon as rewards are allowed to increase. We confirm our theoretical findings on a number of synthetic and dataset-based experiments.

Policies for Partially Observable Markov Decision Processes (POMDPs) are often designed using a nominal system model. In practice, this model can deviate from the true system during deployment due to factors such as calibration drift or sensor degradation, leading to unexpected performance degradation. This work studies policy robustness against deviations in the POMDP observation model. We introduce the Policy Observation Robustness Problem: to determine the maximum tolerable deviation in a POMDP's observation model that guarantees the policy's value remains above a specified threshold. We analyze two variants: the sticky variant, where deviations are dependent on state and actions, and the non-sticky variant, where they can be history-dependent. We show that the Policy Observation Robustness Problem can be formulated as a bi-level optimization problem in which the inner optimization is monotonic in the size of the observation deviation. This enables efficient solutions using root-finding algorithms in the outer optimization. For the non-sticky variant, we show that when policies are represented with finite-state controllers (FSCs) it is sufficient to consider observations which depend on nodes in the FSC rather than full histories. We present Robust Interval Search, an algorithm with soundness and convergence guarantees, for both the sticky and non-sticky variants. We show this algorithm has polynomial time complexity in the non-sticky variant and at most exponential time complexity in the sticky variant. We provide experimental results validating and demonstrating the scalability of implementations of Robust Interval Search to POMDP problems with tens of thousands of states. We also provide case studies from robotics and operations research which demonstrate the practical utility of the problem and algorithms.

Reinforcement learning (RL) offers a compelling data-driven paradigm for synthesizing controllers for complex systems when accurate physical models are unavailable; however, most existing control-oriented RL methods assume stationarity and, therefore, struggle in real-world non-stationary deployments where system dynamics and operating conditions can change unexpectedly. Moreover, RL controllers acting in physical environments must satisfy safety constraints throughout their learning and execution phases, rendering transient violations during adaptation unacceptable. Although continual RL and safe RL have each addressed non-stationarity and safety, respectively, their intersection remains comparatively unexplored, motivating the study of safe continual RL algorithms that can adapt over the system's lifetime while preserving safety. In this work, we systematically investigate safe continual reinforcement learning by introducing three benchmark environments that capture safety-critical continual adaptation and by evaluating representative approaches from safe RL, continual RL, and their combinations. Our empirical results reveal a fundamental tension between maintaining safety constraints and preventing catastrophic forgetting under non-stationary dynamics, with existing methods generally failing to achieve both objectives simultaneously. To address this shortcoming, we examine regularization-based strategies that partially mitigate this trade-off and characterize their benefits and limitations. Finally, we outline key open challenges and research directions toward developing safe, resilient learning-based controllers capable of sustained autonomous operation in changing environments.

Many deployed systems expose black-box objectives whose minimizing configuration shifts with an externally observed context. When contexts revisit a small set of latent regimes, an optimizer that discards history pays repeated adaptation cost; when each step must remain inexpensive, full Gaussian-process (GP) refits at high observation counts are difficult to sustain. We cast online tuning as context-conditioned regret minimization and present RASP-Tuner, which instantiates a decomposition motivated by first principles: (i) identify a regime proxy by retrieving similar past contexts; (ii) predict short-horizon loss with a mixture-of-experts surrogate whose input concatenates parameters, context, and a retrieved soft prompt; (iii) adapt chiefly in a low-dimensional prompt subspace, invoking full surrogate updates only when scalarized error or disagreement spikes. A RealErrorComposer maps heterogeneous streaming metrics to [0,1] via EMA-stabilized logistic scores, supplying a single differentiable training target. On nine synthetic non-stationary benchmarks, an adversarial-context sanity check, and three tabular real-world streams (Section on real-world experiments), RASP-Tuner improves or matches cumulative regret relative to our GP-UCB and CMA-ES implementations on seven of nine synthetic tasks under paired tests at horizon T=100, while recording 8-12 times lower wall-clock per step than sliding-window GP-UCB on identical hardware. Idealized analysis in a cluster-separated, strongly convex regime model (RA-GD) supplies sufficient conditions for bounded dynamic regret; the deployed pipeline violates several of these premises, and we articulate which gaps remain open.

Non-stationary sequences arise naturally in control, forecasting, and decision-making. The data-generating process shifts at unknown times, and models must detect the change, discard or downweight obsolete evidence, and adapt to new dynamics on the fly. Transformer-based foundation models increasingly rely on in-context learning for time series forecasting, tabular prediction, and continuous control. As these models are deployed in non-stationary environments, understanding their ability to detect and adapt to regime shifts is important. We formalize this as an in-context change-point detection problem and formally establish the existence of transformer models that solve this problem. Our construction demonstrates that model complexity, in layers and parameters, depends on the level of information available about the change-point location, from no knowledge to knowing exact timing. We validate our results with experiments on synthetic linear regression and linear dynamical systems, where trained transformers match the performance of optimal baselines across information levels. We also show that encoding and incorporating changepoint knowledge indeed improves the real-world performance of a pretrained foundation models on infectious disease forecasting and on financial volatility forecasting around Federal Open Market Committee (FOMC) announcements without retraining, demonstrating practical applicability to real-world regime changes.

Sequential associative memories (SAMs) are difficult to build and maintain in real-world streaming environments, where observations arrive incrementally over time, have imbalanced sampling, and non-stationary temporal dynamics. Vector Symbolic Architectures (VSAs) provide a biologically-inspired framework for building SAMs. Entities and attributes are encoded as quasi-orthogonal hyperdimensional vectors and processed with well defined algebraic operations. Despite this rich framework, most VSA systems rely on simple additive updates, where repeated observations reinforce existing information even when no new information is introduced. In non-stationary environments, this leads to the persistence of stale information after the underlying system changes. In this work, we introduce the Sequential Relevance Memory Unit (SRMU), a domain- and cleanup-agnostic update rule for VSA-based SAMs. The SRMU combines temporal decay with a relevance gating mechanism. Unlike prior approaches that solely rely on cleanup, the SRMU regulates memory formation by filtering redundant, conflicting, and stale information before storage. We evaluate the SRMU on streaming state-tracking tasks that isolate non-uniform sampling and non-stationary temporal dynamics. Our results show that the SRMU increases memory similarity by $12.6\%$ and reduces cumulative memory magnitude by $53.5\%$. This shows that the SRMU produces more stable memory growth and stronger alignment with the ground-truth state.

Large Language Models (LLMs) generalize across tasks through reusable representations and flexible reasoning, yet remain brittle in real deployment when faced with evolving tasks and continual distribution shift. While test-time adaptation addresses this by updating models with unsupervised objectives on test data, prevailing methods are fundamentally limited by their neglect of source knowledge preservation and adaptation signal reliability. Inspired by how Drosophila orchestrates memory update by balancing retroactive and proactive interference via Rac1 and MAPK pathways, we design Synapse Consolidation (SyCo) with two core components: a Rac1-inspired plasticity confiner and a MAPK-inspired update controller. The former dynamically confines plasticity to a tail-gradient subspace that is less critical for source knowledge, enabling rapid specialization while preserving source representations. The latter uses a tiered controller to suppress noisy updates and consolidate useful adaptations under non-stationary streams. To further model real deployments with multiple sources and continually emerging tasks, we introduce Multi-source Open-set Adaptation (MOA) setting, where a model is trained on multiple labeled source tasks and then adapts on open, non-stationary unlabeled test streams mixing seen and unseen tasks with partial overlap in label and intent space. Across 18 NLP datasets under the MOA setting, SyCo consistently outperforms strong baselines, achieving 78.31% on unseen-task adaptation and 85.37% versus unseen-data shifts, setting a new state-of-the-art.

This study presents a controlled comparison of baseline Kolmogorov-Arnold Networks (KAN), implemented via PyKAN, and Long Short-Term Memory (LSTM) networks for the forecasting of stochastic, non-stationary financial time series. The two architectures are assessed in terms of predictive accuracy, computational efficiency, and interpretability, with accuracy measured by the Root Mean Square Error (RMSE) in normalised feature space. Under a direct multi-output forecasting protocol, LSTM attains clearly superior accuracy across all tested prediction horizons, consistent with its well-established effectiveness for sequential data modelling. Baseline KAN, although offering theoretical interpretability through the Kolmogorov-Arnold representation theorem, exhibits substantially higher error rates and limited practical applicability for time series forecasting in its standard form. Several specialised temporal variants -- including Temporal KAN and Time-Frequency KAN -- have since been proposed to address these sequential modelling limitations, but they lie outside the scope of the present study. KAN is observed to converge faster during training under the configurations tested, although direct runtime comparisons are constrained by methodological factors. These findings support the adoption of LSTM for accuracy-critical financial forecasting and establish an empirical baseline for standard KAN on stochastic sequential data, motivating further investigation of temporally-aware KAN architectures. The study benchmarks baseline KAN against baseline LSTM only; the results do not extend to specialised KAN variants designed for sequential data, nor to the broader family of temporal models.

Adaptive video streaming optimizes Quality of Experience (QoE) metrics by selecting appropriate bitrates according to varying network bandwidth and user demands. In practice, however, real-world network bandwidth often exhibits heterogeneity relative to training environments. Current methods predominantly tackle this problem through learning-based approaches designed to improve generalization performance. While our systematic investigation reveals a critical limitation: neural networks suffer from plasticity loss, significantly impeding their ability to adapt to heterogeneous network conditions. Through theoretical analysis of neural propagation mechanisms, we demonstrate that existing dormant neuron metrics inadequately characterize neural plasticity loss. To address this limitation, we have developed the Silent Neuron theory, which provides a more comprehensive framework for understanding plasticity degradation. Based on these theoretical insights, we propose the Reset Silent Neuron (ReSiN), which preserves neural plasticity through strategic neuron resets guided by both forward and backward propagation states. Moreover, we establish a tighter performance bound for ReSiN under non-stationary network conditions. In our implementation of an adaptive video streaming system, ReSiN has shown significant improvements over existing solutions, achieving up to 168% higher bitrate and 108% better quality of experience (QoE) while maintaining comparable smoothness. Furthermore, ReSiN consistently outperforms in stationary environments, demonstrating its robust adaptability across different network conditions.