Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift

Conditional conformal test martingales provide sequential tests for detecting distribution shifts, using a fixed reference dataset to avoid contamination from test-time samples. Prior work used a penalized betting function via online optimization with smoothing, clipping, and other hyperparameters, which can adapt slowly when a shift occurs after a long stationary period. In this work, we introduce an approach that requires no hyperparameters and provably adapts quickly to shifts occurring at unknown times. Our key idea is to frame the penalized betting problem as portfolio selection in a three-asset market. Then, we use a restarting universal portfolio, with a heavy-tailed wealth allocation over time. We establish anytime false-alarm control and derive optimal finite-sample bounds on detection delay under detectable alternatives. We also develop an FFT-based implementation that computes the portfolio sequence over $T$ rounds in $\mathcal{O}(T^2\ln T)$ time, instead of $\mathcal{O}(T^3)$ of the naive implementation. Synthetic and real-world experiments suggest that the proposed approach adapts rapidly after long periods of null samples, with detection delays depending substantially less on shift time than prior baselines.

A rapidly growing range of sequential data tasks, such as identifying trend reversals in financial markets, auto-segmenting video and audio recordings, detecting changes in movement direction from motion sensors cannot be fully addressed without detection of distributional shifts in time-ordered data. We consider a sequential change-point detection problem where the conditional density switches at an unknown time, yet neither the pre- nor post-change distribution admits a closed-form. Classical likelihood-ratio statistics are inapplicable in this settings. A conditional diffusion model, trained on pre-change-point data with a frozen context encoder, defines a deterministic bijection via the probability flow ODE. Pre-change observations are mapped onto standard Gaussian latent variables. Post-change observations, processed through the same frozen map, deviate from this reference. We employ the Maximum Mean Discrepancy as the test statistic, derive closed-form expressions for its components under the Gaussian null, and establish its asymptotic distribution as a degenerate U-statistic. Afterwards we apply an online detection procedure of Shiryaev--Roberts to the resulting statistic with exact threshold calibration. The method detects arbitrary distributional shifts, including covariance rotations and higher-order structural breaks, without parametric assumptions on either regime.

Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and leverage them to solve downstream problems, for example risk-averse formulations. We focus on human choice settings that can be formulated as (integer) linear programs. In such settings, existing inverse optimization and choice modelling methods infer preferences from observed choices but typically produce point estimates or fail to capture contextual shifts, making them unsuitable for risk-averse decision-making. Using a bounded-variance score function gradient estimator, we train a predictive model mapping contextual features to a rich class of parameterizable distributions. This approach yields a maximum likelihood estimate. The model generates scenarios for unseen contexts in the subsequent optimization phase. In a synthetic ridesharing environment, our approach reduces average post-decision surprise by up to 114$\times$ compared to a risk-neutral approach with perfect predictions and up to 25$\times$ compared to leading risk-averse baselines.