Dynamic Regret for Non-Stationary Linear Bandits via Misspecification Reductions

Many online decision-making problems involve both round-specific feasible actions and drifting reward models: eligible ad impressions, feasible prices, and available treatments can change over time, while user preferences, demand curves, and patient responses may evolve. Motivated by these applications, we study non-stationary linear bandits with round-specific feasible decision sets. Existing methods that obtain the optimal \(\widetilde O(T^{2/3}P_T^{1/3})\) dependence, where \(P_T\) is the path length of the reward-parameter sequence, impose an orthogonal-structure assumption on round-specific decision sets, which can be restrictive in contextual applications. We address this gap through a unified misspecification-reduction viewpoint: after partitioning the horizon into blocks, we relate each block's dynamic regret to regret against a fixed-parameter linear bandit benchmark, with the within-block parameter drift entering as bounded misspecification. Restarting algorithms with misspecification-dependent regret guarantees then yields the optimal \(T^{2/3}P_T^{1/3}\) dynamic-regret dependence for both linear bandits with general compact decision sets and \(K\)-armed contextual linear bandits.

MA-SBI: Misspecification-Aware Simulation-Based Inference via Side-Channel Guidance

Simulation-based inference (SBI) of latent parameters is often hindered by simulator misspecification, the mismatch between simulated and real-world observations caused by inherent modeling simplifications. RoPE, the recent state-of-the-art for robust SBI, addresses this through optimal transport between learned representations of real and simulated observations, but requires ground-truth parameter calibration pairs that are typically unavailable in the very settings where SBI is needed. What practitioners do have is unstructured side-information such as regime labels, instruction text, and policy bulletins. We propose Misspecification-Aware Simulation-Based Inference (MA-SBI), a calibration-free framework that turns this side-channel into a posterior correction. A learned corrector maps side-channel text to an observation-space shift applied before any pre-trained amortized posterior, requiring no retraining and no parameter ground-truth. Our main theorem bounds achievable bias reduction by the mutual information between misspecification and side-channel, with a non-vacuous constant that extends to all sub-Gaussian noise via Donsker-Varadhan. On hide-the-calibration benchmarks, MA-SBI with text alone matches the oracle posterior across 10 seeds and two backbones (TOST equivalence), while RoPE given more data does not. The two approaches are complementary: where misspecification is structural and recoverable from parameter pairs, RoPE dominates, as the theory predicts. A stochastic variant improves posterior-predictive log-likelihood on real COVID and OxCGRT epidemiological data, and correctly leaves the posterior unchanged on a well-specified cognitive-science corpus.

Transfer Learning Across Policy Regimes in Adaptive Multi-Agent Systems

Policy models often assume that the relationship between a policy instrument and its outcome remains stable across institutional conditions. In adaptive socio-technical systems this assumption may fail: regulatory change can alter incentives, agents can respond strategically, and the mapping from policy variables to aggregate outcomes can change. This paper studies such regime change as a transfer-learning problem in adaptive multi-agent systems. A policy regime is represented as a learning problem induced by an observable input distribution and a target function mapping policy variables to outcomes. We compare a blank-slate learner that searches a flexible hypothesis class in the new regime with a transfer learner whose effective hypothesis class is restricted by structural knowledge from the previous regime. Transfer is beneficial when this restriction preserves the new target function while reducing effective complexity; it is harmful when the restriction excludes the new target and creates misspecification. A stylized emissions-regulation experimental environment and a dynamic ABM robustness experiment support the claim. When the target regime preserves an affine monotone tax-emissions relation, transfer improves empirical small-sample performance. When the target regime introduces a threshold break, the same transferred structure produces negative transfer: held-out error remains high, online prediction generates more mistakes, and repeated online streams show larger cumulative and final-window error under misspecification. The contribution is methodological: previous regulatory experience should be reused when it captures stable structural invariants, but treated cautiously when policy change alters the policy-outcome relationship.