Distributionally robust optimization hedges a decision against an ambiguity set of candidate distributions. In a cold-start setting the target distribution is unobserved and no sample from it is available, so only related source distributions provide evidence for constructing that set. We propose an inclusive-exclusive Wasserstein ball model that jointly learns a center and radius from … Read more
Stochastic dual dynamic programming (SDDP) and its variants are run in practice with forward passes that sample the noise at random. Recent iteration-complexity results favour another choice: when the trial points are selected deterministically, for instance along the scenario with the largest gap, the number of iterations is polynomial in the horizon $T$, whereas every … Read more
Deep hedging learns trading policies from historical or simulated market trajectories, yet under nonstationarity these training paths may not represent future market conditions. We propose WRAP (Wasserstein-Reweighting Adversarial Perturbation), a drift-aware adversarial training framework derived from a two-budget distributionally robust optimization (DRO) formulation. The formulation is anchored to a weighted empirical reference distribution whose fixed … Read more
We study stochastic optimization with a completely unobserved target distribution and samples from related source distributions. Treating the sources and the target as independent draws from a common meta-distribution, we propose Wasserstein-metric meta-distribution support learning (MDSL). The model jointly learns the center and radius of a Wasserstein ball, with an exclusion parameter controlling the fraction … Read more
Many optimization problems solved repeatedly in practice, such as in power systems or logistics, share a fixed structure but with different parameter values. Re-optimizing each instance from scratch can be computationally prohibitive, while adopting a single solution for all realizations is overly conservative. The K-adaptability paradigm offers a flexible compromise by precomputing a small set … Read more
Stochastic Gradient Descent (\(\textsf{SGD}\)) is one of the most classical optimization algorithms with favorable theoretical guarantees, yet its practical implementation differs subtly from its well-known form and is often referred to as Shuffling Stochastic Gradient Descent (\(\textsf{Shuffling SGD}\)). A particularly popular strategy in \(\textsf{Shuffling SGD}\) is Random Reshuffling (\(\textsf{RR}\)), which has achieved great empirical success. … Read more
We propose an algorithmic framework for solving adaptive robust optimization with provable guarantees on both tractability and solution accuracy. The framework introduces soft separation, a probabilistic mechanism for identifying worst-case uncertainty realizations via a time-inhomogeneous Markov chain. Rather than solving an exact separation problem in each iteration, which is intractable in general, the chain carries … Read more
Multistage stochastic programs model decisions under uncertainty where earlier decisions change later feasible sets. We propose a feasible pathwise gradient method (FeasPG) that can update the policy as new sample paths arrive. The policy proposes a decision and projects it onto the current feasible set, so every decision is feasible. We derive the full trajectory … Read more
In this paper, we propose and analyze an augmented Lagrangian framework for solving stochastic nonconvex optimization problems with expectation-based equality constraints over a closed and convex constraint set. The framework generates a sequence of nonconvex primal subproblems, which are solved inexactly using stochastic second-order methods. We establish iteration complexity results for obtaining approximate second-order stationary … Read more
We revisit the framework of generalized Benders decomposition over a compact but non-finite master domain. We show by counterexample that strong general dual functions alone may fail to guarantee convergence. We then define a condition of uniform local strongness and prove that strong general dual functions satisfying this condition guarantee finite \(\epsilon\)-termination. Finally, we show … Read more