Session: Models and Algorithms for Optimization with Rare Events
Chair: Anirudh Subramanyam
Cluster: Optimization Under Uncertainty and Data-driven Optimization
Talk 1: Decision-Making under Extreme Risks: Configuring Optimization Algorithms for Rare-Event Optimization
Speaker: Henry Lam
Abstract: We consider stochastic optimization where the goal is not only to optimize an average-case objective, but also mitigate the occurrence of rare but catastrophic events. This problem, which is motivated from emerging applications such as safe AI, requires an integration of variance reduction methods into sampling-based optimization algorithms in order to attain sufficient solution accuracy. However, we explain how natural variance-reduction-optimization integration, even executed in an adaptive fashion studied by recent works, encounters fundamental challenges. On a high level, the challenge arises from the extreme sensitivity of tail-based objectives with respect to the decision variables, which renders the failure of traditional Lipschitz-based analyses. We offer some potential remedies and supporting numerical results.
Talk 2: Risk-Aware Path Integral Diffusion to Sample Rare Events
Speaker: Michael Chertkov
Abstract: TBD
Talk 3: Scaling Scenario-Based Chance-Constrained Optimization under Rare Events
Speaker: Jaeseok Choi
Abstract: Chance-constrained optimization is a suitable modeling framework for mitigating extreme event risk in many practical settings. The scenario approach is a popular solution method for chance-constrained problems, due to its straightforward implementation and ability to preserve problem structure. However, for safety-critical applications where violating constraints is nearly unacceptable, the scenario approach becomes computationally infeasible due to the excessively large sample sizes it demands. We address this limitation with a new yet straightforward decision-scaling technique. Our method leverages large deviation principles and relies on only mild nonparametric assumptions about the underlying uncertainty distributions. The method achieves an exponential reduction in sample size requirements compared to the classical scenario approach for a wide variety of constraint structures, while also guaranteeing feasibility with respect to the uncertain constraints. Numerical experiments spanning engineering and management applications show that our decision-scaling technique significantly expands the scope of problems that can be solved both efficiently and reliably.
