Statistical Properties of Robust Learning under Distributional Shifts

Distributional shifts arise when the target deployment environment differs from the source environment that generated the training data. Robust learning frameworks such as Distributionally Robust Optimization (DRO) and Robust Satisficing (RS) aim to address this challenge, yet their finite-sample guarantees under such shifts, and their systematic comparison, remain underexplored: existing analyses typically establish guarantees either in the source environment or for adversarial worst-case performance over an ambiguity set. This paper instead studies generalization error in the target environment---the excess loss under the shifted target distribution. Our contributions are threefold. First, we derive finite-sample generalization error bounds in the shifted target environment for both DRO and RS. These bounds explicitly characterize the trade-off between reduced sensitivity to shift and the regularization penalty induced by each method's robustness hyperparameter, and they avoid the curse of dimensionality associated with Wasserstein empirical concentration. Second, when partial shift information such as shift magnitude or direction is available, we propose information-directed hyperparameter calibrations and compare the two methods given the same information. Under these calibrations, and in the partial-information regimes we study, DRO and RS exhibit complementary theoretical and empirical behavior. Finally, we apply the framework to a network lot-sizing problem, using it to interpret how robust policies respond to positive shifts in the demand distribution. Together, these results fill a gap in understanding the statistical properties of robust learning methods under distributional shifts and provide a principled basis for comparing DRO and RS.

Adversarially Robust Abductive Fusion of Pre-trained Transformer-based Perception Models

Deploying pre-trained perception models in novel environments degrades their accuracy under distributional shift, and assembling them alone does not recover it: combiners such as majority voting trade recall for precision and are brittle to coordinated failures. Prior metacognitive methods learn logical rules that flag a model's errors, but rely on hand-authored domain-knowledge cues (object-size priors, segmentation masks) that do not transfer to genuinely novel scenes. We show that this metacognitive layer can be learned without any domain knowledge by exploiting vector-space geometry: per-model Label Vector Pools (LVP), built from each model's own training embeddings, yield error-detection rules from the geometry of detections relative to training-determined prototypes, reaching parity with domain-knowledge rules to within $0.002$ every F1 on test set. Because the approach remains neurosymbolic, these geometric rules share a single logical framework and can still be complemented by domain knowledge when available. We frame the fusion of multiple imperfect ViT-based detectors as a consistency-based abduction problem solved at test time by an exact Integer Program (IP) and a polynomial-time heuristic. On an aerial-imagery benchmark of 15 weather-shifted test sets and six ViT detectors, our domain-knowledge-free layer matches the strongest majority-vote variant on clean data (within $0.005$ F1) and, unlike every majority-vote baseline, retains its performance under a coordinated label-flipping attack: at a $90\%$ flip rate it averages $0.42$ F1 versus $0.35$ for MV-Plurality (a $22\%$ relative gain) and attains the highest F1 on \emph{every} test set once the flip rate exceeds $0.4$

Evaluating Time Series Foundation Models for Electricity Price Forecasting: Contamination Risk, Distributional Shifts, and Covariate Dependence

Time series foundation models (TSFMs) have shown strong zero-shot forecasting performance, but their generalization in covariate-driven, non-stationary settings is underexplored. Electricity price forecasting (EPF) presents a challenging testbed due to complex temporal dependencies, distributional shifts, and strong reliance on structural and contextual information. We propose a two-dataset-benchmarking framework for EPF to mitigate contamination risk and enable fair evaluation of TSFMs. We examine key aspects of EPF including point and probabilistic forecasting performance, tail behavior, price spikes, and comparisons against domain-specific methods. We find that TSFMs are highly competitive and often outperform general-purpose baselines. Yet, their performance depends critically on covariate support, and they do not consistently surpass domain-specific methods tailored to EPF. Interestingly, simple ensembles of TSFMs and domain-specific methods appear to have significant potential, suggesting that the two approaches capture complementary predictive information.

A Unified Causal-Origin Taxonomy of Distributional Shifts in Reinforcement Learning

Reinforcement learning (RL) systems often degrade when operating conditions differ from those previously encountered, reflecting distributional shifts in the underlying data-generating process. Such shifts may occur between training and evaluation, as in In-Distribution (ID) and Out-of-Distribution (OOD) generalization, or within non-stationary settings where environment dynamics evolve over time. However, the formal relationship between these views remains unclear, and existing work mainly focuses on mitigation rather than the causal origin of shift within the agent-environment interaction. This work develops a unified causal-origin taxonomy that characterizes sources of distributional shift in RL and relates ID/OOD generalization to non-stationary settings. We transfer the classical dataset-shift principle from supervised learning to RL by reformulating distributional shift in terms of the generative interaction process. Using a Partially Observable Markov Decision Process (POMDP), we decompose the interaction into structural components, including the state distribution, observation process, policy, reward, and transition dynamics, together with the shifted-time boundary. The proposed taxonomy distinguishes internal, agent-driven, and external, environment-driven, distributional shifts. The shifted-time boundary perspective further characterizes explicit, implicit, and hybrid shifts. This formulation unifies ID/OOD generalization and non-stationarity as structured changes in the underlying process. We also introduce an evaluation framework for measuring shift impact and adaptation through performance degradation and recovery metrics. By grounding distributional shift in the causal-origin structure of RL, this work supports systematic analysis of robustness under distributional shift.

Generalized Conformal Predictive Systems Under Distributional Shifts

Conformal predictive systems (CPS) output calibrated bands of CDFs under exchangeability. We extend generalized CPS to non-exchangeable settings by encoding distributional shifts through observation-specific permutation weights. This yields shift-aware predictive systems that remain valid whenever the test point is, conditionally on the unordered sample, a weighted draw from the observed atoms. Since such weights are typically estimated, we introduce weight-uncertainty boxes and construct robust CPS envelopes with finite-sample or asymptotic confidence guarantees. We derive efficient computation for conformity-measure CPS, conformal binning, and conformal isotonic distributional regression. Experiments under covariate shift and feedback-driven biomolecular design show calibrated predictive bands that widen under stronger shifts and tighten as sample size increases.

RCEM: Embedder Equipped with Query Rewriting Skill for Robust Conversational Search in Distributional Shift

Conversational search has become increasingly important in retrieval-augmented generation (RAG) systems, where users interact with AI assistants through multi-turn conversations containing context-dependent queries. We propose RCEM, a conversational dense retrieval model that distills the query reformulation capability of LLMs into the embedding model, enabling context-aware retrieval without explicit query rewriting during inference. Unlike prior conversational dense retrieval approaches that learn direct conversation-to-document matching, RCEM aligns conversational-query embeddings with rewritten-query embeddings, improving robustness under distributional shift. RCEM does not require conversational query-to-document relevance mappings for training, which are often expensive and difficult to obtain with high quality. Extensive experiments on QReCC, TopiOCQA, and TREC CAsT demonstrate that RCEM consistently outperforms strong conversational retrieval baselines, achieving particularly large gains under distributional shift, including up to 20% improvement in Recall@10. RCEM further extends the base embedding model with conversational query rewriting capability while preserving its original retrieval functionality, allowing both standalone and conversational queries to be encoded by a single model and searched against existing document indexes without rebuilding the retrieval database.