Session: Decision-Aware Optimization
Chair: Vishal Gupta
Cluster: Optimization Under Uncertainty and Data-driven Optimization
Talk 1: Contextual Linear Optimization with Bandit Feedback
Speaker: Yichun Hu
Abstract: Contextual linear optimization (CLO) uses predictive contextual features to reduce uncertainty in random cost coefficients and thereby improve average-cost performance. An example is stochastic shortest path with random edge costs (e.g., traffic) and contextual features (e.g., lagged traffic, weather). Existing work on CLO assumes the data has fully observed cost coefficient vectors, but in many applications we can only see the realized cost of a historical decision, that is, just one projection of the random cost coefficient vector, to which we refer as bandit feedback. We study a class of offline learning algorithms for CLO with bandit feedback, which we term induced empirical risk minimization (IERM), where we fit a predictive model to directly optimize downstream performance of the policy it induces. We show a fast-rate regret bound for IERM that allows for misspecified model classes and flexible choices of the optimization estimate, and we develop computationally tractable surrogate losses. A byproduct of our theory of independent interest is fast-rate regret bound for IERM with full feedback and misspecified policy class. We compare the performance of different modeling choices numerically using a stochastic shortest path example and provide practical insights from the empirical results.
Talk 2: Learning Uncertainty Sets in Dynamic Robust Optimization
Speaker: Irina Wang
Abstract: We present a data-driven technique to automatically learn uncertainty sets in dynamic decision making under uncertainty. We formulate the learning problem as a control design problem where the control policy involves solving a robust optimization problem parametrized by the past disturbances, as well as the parameters of the uncertainty set. We propose a learning procedure to dynamically predict the parameters of the uncertainty set to minimize a closed-loop performance metric while satisfying probabilistic guarantees of constraint satisfaction. Our approach allows for uncertain data that is correlated across time periods, and can learn a wide range of commonly used uncertainty sets. By modeling our training problem objective and constraints using coherent risk metrics, we derive finite sample probabilistic guarantees of constraint satisfaction in multi-stage settings.
Talk 3: Surrogates for Decision-Aware Learning: Beyond the Linear Setting
Speaker: Vishal Gupta
Abstract: Designing surrogates that exploit downstream optimization structures is one of the key approaches to decision-aware learning. However, most work to date is either restricted to the linear contextual optimization setting or is largely heuristic with few theoretical performance guarantees. By extending recent work on using directional gradients to approximate decision loss, we show how to design surrogates with provable performance guarantees for nonlinear settings. This approach provides a natural recipe for attacking non-parametric and high-dimensional settings.
