Decision making under uncertainty often requires choosing packages , or bags of tuples, that collectively optimize expected outcomes while limiting risks. Processing Stochastic Package Queries (SPQs) involves solving very large optimization problems on uncertain data. Monte Carlo methods create numerous scenarios , or sample realizations of the stochastic attributes of all the tuples, and generate packages with optimal objective values across these scenarios. The number of scenarios needed for accurate approximation—and hence the size of the optimization problem when using prior methods—increases with variance in the data, and the search space of the optimization problem increases exponentially with the number of tuples in the relation. Existing solvers take hours to process SPQs on large relations containing stochastic attributes with high variance. Besides enriching the SPaQL language to capture a broader class of risk specifications, we make two fundamental contributions toward scalable SPQ processing. First, we propose risk-constraint linearization (RCL), which converts SPQs into Integer Linear Programs (ILPs) whose size is independent of the number of scenarios used. Solving these ILPs gives us feasible and near-optimal packages. Second, we propose Stochastic SketchRefine, a divide and conquer framework that breaks down a large stochastic optimization problem into subproblems involving smaller subsets of tuples. Our experiments show that, together, RCL and Stochastic SketchRefine produce high-quality packages in orders of magnitude lower runtime than the state of the art.

A package query returns a package---a multiset of tuples---that maximizes or minimizes a linear objective function subject to linear constraints, thereby enabling in-database decision support. Prior work has established the equivalence of package queries to Integer Linear Programs (ILPs) and developed the SketchRefine algorithm for package query processing. While this algorithm was an important first step toward supporting prescriptive analytics scalably inside a relational database, it struggles when the data size grows beyond a few hundred million tuples or when the constraints become very tight. In this paper, we present Progressive Shading, a novel algorithm for processing package queries that can scale efficiently to billions of tuples and gracefully handle tight constraints. Progressive Shading solves a sequence of optimization problems over a hierarchy of relations, each resulting from an ever-finer partitioning of the original tuples into homogeneous groups until the original relation is obtained. This strategy avoids the premature discarding of high-quality tuples that can occur with SketchRefine. Our novel partitioning scheme, Dynamic Low Variance, can handle very large relations with multiple attributes and can dynamically adapt to both concentrated and spread-out sets of attribute values, provably outperforming traditional partitioning schemes such as kd-tree. We further optimize our system by replacing our off-the-shelf optimization software with customized ILP and LP solvers, called Dual Reducer and Parallel Dual Simplex respectively, that are highly accurate and orders of magnitude faster.

Combating an epidemic entails finding a plan that describes when and how to apply different interventions, such as mask-wearing mandates, vaccinations, school or workplace closures. An optimal plan will curb an epidemic with minimal loss of life, disease burden, and economic cost. Finding an optimal plan is an intractable computational problem in realistic settings. Policy-makers, however, would greatly benefit from tools that can efficiently search for plans that minimize disease and economic costs especially when considering multiple possible interventions over a continuous and complex action space given a continuous and equally complex state space. We formulate this problem as a Markov decision process. Our formulation is unique in its ability to represent multiple continuous interventions over any disease model defined by ordinary differential equations. We illustrate how to effectively apply state-of-the-art actor-critic reinforcement learning algorithms (PPO and SAC) to search for plans that minimize overall costs. We empirically evaluate the learning performance of these algorithms and compare their performance to hand-crafted baselines that mimic plans constructed by policy-makers. Our method outperforms baselines. Our work confirms the viability of a computational approach to support policy-makers.