Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this paper, we investigate a class of nonconvex min-max optimization problems with nonconvex infinite constraints, motivated by applications such as adversarial robustness and safety-constrained learning. We propose a novel inexact dynamic barrier primal-dual algorithm and establish its convergence properties.

We study the problem of sequential decision-making in environments governed by evolving causal mechanisms. Prior work on structural causal bandits--formulations that integrate causal graphs into multi-armed bandit problems to guide intervention selection--has shown that leveraging the causal structure can reduce unnecessary interventions by identifying possibly-optimal minimal intervention sets (POMISs). However, such formulations fall short in dynamic settings where reward distributions may vary over time, due to their static--and thus myopic--nature focuses on immediate rewards and overlooks the long-term effects of interventions. In this work, we propose a non-stationary structural causal bandit framework that leverages temporal structural causal models to capture evolving dynamics over time. We characterize how interventions propagate over time by developing graphical tools and assumptions, which form the basis for identifying non-myopic intervention strategies. Within this framework, we devise POMIS+, which captures the existence of variables that contribute to maximizing both immediate and long-term rewards. Our framework provides a principled way to reason about temporally-aware interventions by explicitly modeling information propagation across time. Empirical results validate the effectiveness of our approach, demonstrating improved performance over myopic baselines.

Time series foundation models (TSFMs) are widely used as generic feature extractors, yet the notion of non-stationarity in their embedding spaces remains poorly understood. Recent work often conflates non-stationarity with distribution shift, blurring distinctions fundamental to classical time-series analysis and long-standing methodologies such as statistical process control (SPC). In SPC, non-stationarity signals a process leaving a stable regime - via shifts in mean, variance, or emerging trends - and detecting such departures is central to quality monitoring and change-point analysis. Motivated by this diagnostic tradition, we study how different forms of distributional non-stationarity - mean shifts, variance changes, and linear trends - become linearly accessible in TSFM embedding spaces under controlled conditions. We further examine temporal non-stationarity arising from persistence, which reflects violations of weak stationarity due to long-memory or near-unit-root behavior rather than explicit distributional shifts. By sweeping shift strength and probing multiple TSFMs, we find that embedding-space detectability of non-stationarity degrades smoothly and that different models exhibit distinct, model-specific failure modes.

Neural Information Processing Systems http://nips.cc/

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels.

Accurately differentiating between what are truly unpredictably random and systematic changes that occur at random can have profound effect on affect and cognition. To examine the underlying computational principles that guide different learning behavior in an uncertain environment, we compared an R-W model and a Bayesian approach in a visual search task with different volatility levels. Both R-W model and the Bayesian approach reflected an individual's estimation of the environmental volatility, and there is a strong correlation between the learning rate in R-W model and the belief of stationarity in the Bayesian approach in different volatility conditions. In a low volatility condition, R-W model indicates that learning rate positively correlates with lose-shift rate, but not choice optimality (inverted U shape). The Bayesian approach indicates that the belief of environmental stationarity positively correlates with choice optimality, but not lose-shift rate (inverted U shape). In addition, we showed that comparing to Expert learners, individuals with high lose-shift rate (sub-optimal learners) had significantly higher learning rate estimated from R-W model and lower belief of stationarity from the Bayesian model.

Neural Information Processing Systems http://nips.cc/

It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither allow connections that are not dyadic nor permit relationships between sets of nodes. We thus turn to simplicial complexes for connecting more than two nodes as well as modeling relationships between simplices, such as edges and triangles. Our data then consist of signals lying on topological spaces, represented by simplicial complexes. Much recent work explores these topological signals, albeit primarily through deterministic formulations. We propose a probabilistic framework for random signals defined on simplicial complexes. Specifically, we generalize the classical notion of stationarity. By spectral dualities of Hodge and Dirac theory, we define stationary topological signals as the outputs of topological filters given white noise. This definition naturally extends desirable properties of stationarity that hold for both time-series and graph signals. Crucially, we properly define topological power spectral density (PSD) through a clear spectral characterization. We then discuss the advantages of topological stationarity due to spectral properties via the PSD. In addition, we empirically demonstrate the practicality of these benefits through multiple synthetic and real-world simulations.