Robust Optimization

General chemical reaction conditions that achieve consistently high performance across multiple substrates are important for practical applications such as library synthesis and high-throughput experimentation. However, identifying such conditions efficiently has been a longstanding challenge, as it requires decision making under uncertainty with respect to both conditions and substrates, while minimizing the number of required experiments. Here, we introduce CurryBO, a high-level framework for generality-oriented optimization. By formalizing the problem as Bayesian optimization over curried functions, CurryBO provides a unified framework that accommodates different generality definitions (e.g., mean yield across substrates), and supports a range of substrate and condition selection strategies. We evaluate this framework on four benchmark tasks in experimental reaction optimization, and systematically analyze key algorithmic components. Our results show that efficient experiment planning can be achieved by emphasizing exploration when selecting reaction conditions, followed by the uncertainty-guided prioritization of substrates in a sequential decison-making scheme. Based on these insights, we design and validate an optimization policy that substantially improves sample efficiency relative to previously reported approaches across all benchmarks. Overall, the flexibility and modularity of CurryBO facilitate the integration of generality-oriented optimization into experimental settings, enabling more efficient identification of solutions that perform robustly across diverse tasks.

We study a class of stochastic nonsmooth optimization problems in which an outer variable minimizes the expectation of a pointwise maximum. This minimization--expectation--maximization (minEmax) problem arises in Wasserstein distributionally robust optimization and adversarially robust training, and it cannot in general be reformulated as a finite-dimensional minimax problem when the underlying distribution is not empirical. We propose a stochastic smoothing proximal gradient method based on log-mean-exp smoothing of the value function. Under compactness and Lipschitz-type assumptions, we present nonasymptotic analysis in terms of Goldstein stationarity and show that every almost-sure cluster point generated by our method is a Clarke stationary point; by Clarke regularity, such a point is also directional stationary for the original problem. Numerical experiments on newsvendor, robust regression, and adversarially robust learning problems show that the proposed method is competitive with existing baselines.

Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ sample complexity to find an $\varepsilon$-stationary point. Some works indicate that this complexity can be improved to $\mathcal{O}(\varepsilon^{-3})$ when the stochastic loss gradient is Lipschitz continuous. The question of achieving enhanced convergence rates under distinct conditions, remains open. In this work, we address this question for optimization problems that are nonconvex in the minimization variable and strongly concave or Polyak-Lojasiewicz (PL) in the maximization variable. We introduce novel bias-corrected momentum algorithms utilizing efficient Hessian-vector products. We establish convergence conditions and demonstrate a lower iteration complexity of $\mathcal{O}(\varepsilon^{-3})$ for the proposed algorithms. The effectiveness of the proposed method is validated through applications to robust logistic regression and robust adaptive cruise control.

We present an optimization-based framework for robust permissive synthesis for Interval Markov Decision Processes (IMDPs). While robust IMDP controller synthesis typically yields a single policy and most permissive-synthesis methods assume exact transition models, we synthesize multi-strategies that retain multiple actions while guaranteeing satisfaction of probabilistic reachability or expected-reward specifications under all admissible transition probabilities. We formulate the problem as a mixed-integer linear program (MILP) that maximizes the number of enabled state--action pairs subject to robust Bellman constraints. We develop two encodings: a direct vertex-enumeration formulation and a dualization-based formulation that avoids explicit enumeration of uncertainty-polytope vertices and has size linear in the number of successor transitions. Experiments on four benchmark domains show that both encodings achieve the same optimal permissiveness and scale to IMDPs with hundreds of thousands of states. Compared with standard robust single-policy synthesis, the resulting multi-strategies retain substantially more action choices.