Sahana Rayan

Yash Patel, Sahana Rayan, Ambuj Tewari

Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative uncertainty regions, often resulting in suboptimal decisionmaking. To this end, we propose Conformal-Predict-Then-Optimize (CPO), a framework for leveraging highly informative, nonconvex conformal prediction regions over high-dimensional spaces based on conditional generative models, which have the desired distribution-free coverage guarantees. Despite guaranteeing robustness, such black-box optimization procedures alone inspire little confidence owing to the lack of explanation of why a particular decision was found to be optimal. We, therefore, augment CPO to additionally provide semantically meaningful visual summaries of the uncertainty regions to give qualitative intuition for the optimal decision. We highlight the CPO framework by demonstrating results on a suite of simulation-based inference benchmark tasks and a vehicle routing task based on probabilistic weather prediction.

Sahana Rayan, Ambuj Tewari

In the Learning to Defer (L2D) framework, a prediction model can either make a prediction or defer it to an expert, as determined by a rejector. Current L2D methods train the rejector to decide whether to reject the {\em entire prediction}, which is not desirable when the model predicts long sequences. We present an L2D setting for sequence outputs where the system can defer \textit{specific outputs} of the whole model prediction to an expert in an effort to interleave the expert and machine throughout the prediction. We propose two types of model-based post-hoc rejectors for pre-trained predictors: a token-level rejector, which defers specific token predictions to experts with next token prediction capabilities, and a one-time rejector for experts without such abilities, which defers the remaining sequence from a specific point onward. In the experiments, we also empirically demonstrate that such granular deferrals achieve better cost-accuracy tradeoffs than whole deferrals on Traveling salesman solvers, News summarization, and Weather prediction.

Sahana Rayan, Yash Patel, Ambuj Tewari

When solving PDEs, classical numerical solvers are often computationally expensive, while machine learning methods can suffer from spectral bias, failing to capture high-frequency components. Designing an optimal hybrid iterative solver--where, at each iteration, a solver is selected from an ensemble of solvers to leverage their complementary strengths--poses a challenging combinatorial problem. While the greedy selection strategy is desirable for its constant-factor approximation guarantee to the optimal solution, it requires knowledge of the true error at each step, which is generally unavailable in practice. We address this by proposing an approximate greedy router that efficiently mimics a greedy approach to solver selection. Empirical results on the Poisson and Helmholtz equations demonstrate that our method outperforms single-solver baselines and existing hybrid solver approaches, such as HINTS, achieving faster and more stable convergence.