Abstract When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with missing data as a two-stage adaptive optimization problem and propose a new class of models, adaptive linear regression models, where the regression coefficients adapt to the set of observed features. We show that some adaptive linear regression models are equivalent to learning an imputation rule and a downstream linear regression model simultaneously instead of sequentially. We leverage this joint-impute-then-regress interpretation to generalize our framework to non-linear models. In settings where data is strongly not missing at random, our methods achieve a 2–10% improvement in out-of-sample accuracy.

In collaboration with the San Francisco Unified School District (SFUSD), this paper introduces an interactive optimization framework to tackle complex school scheduling challenges. The choice of school start and end times is an optimization challenge, as schedules influence the district's transportation system, and limiting the associated costs is a computationally difficult combinatorial problem. However, it is also a policy challenge, as transportation costs are far from the only consequence of school schedule changes. Policymakers need time and knowledge to balance these considerations and reach a consensus carefully; past implementations have failed because of policy issues despite state-of-the-art optimization approaches.

Marketplace companies rely heavily on experimentation when making changes to the design or operation of their platforms. A fundamental challenge in marketplace experimentation is dealing with interference. For instance, consider a ride-hailing platform experimenting with a demand-side price discount. The platform performs a randomized control trial (RCT), or A/B test, where some demand units are offered the discounted price while others are offered the undiscounted price. Because the treated units are more likely to book rides as a result of the discount, they reduce the total supply available to all demand-side units, including the control units. This interference between treatment and control units causes the Stable Unit Treatment Value Assumption (SUTVA) to fail, and consequently induces bias in the standard estimator used to evaluate the value generated by the treatment.

Value-function-based methods have long played an important role in reinforcement learning. However, finding the best next action given a value function of arbitrary complexity is nontrivial when the action space is too large for enumeration. We develop a framework for value-function-based deep reinforcement learning with a combinatorial action space, in which the action selection problem is explicitly formulated as a mixed-integer optimization problem. As a motivating example, we present an application of this framework to the capacitated vehicle routing problem (CVRP), a combinatorial optimization problem in which a set of locations must be covered by a single vehicle with limited capacity. On each instance, we model an action as the construction of a single route, and consider a deterministic policy which is improved through a simple policy iteration algorithm. Our approach is competitive with other reinforcement learning methods and achieves an average gap of 1.7% with state-of-the-art OR methods on standard library instances of medium size.