Related papers: Two-stage Linear Decision Rules for Multi-stage St…

Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the…

We consider a general class of two-stage distributionally robust optimization (DRO) problems where the ambiguity set is constrained by fixed marginal probability laws that are not necessarily discrete. We derive primal and dual formulations…

In this paper, we extend the adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse to the multistage stochastic programming setting. The proposed algorithms integrate the adaptive partition-based…

We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz assumptions on the coefficients, we show that the MLP algorithm…

We consider a multi-stage stochastic lot-sizing problem with service level constraints and supplier-driven product substitution. A firm has multiple products and it has the option to meet demand from substitutable products at a cost.…

We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…

One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…

In the literatur there exist approximation methods for McKean-Vlasov stochastic differential equations which have a computational effort of order $3$. In this article we introduce full-history recursive multilevel Picard (MLP)…

Solving large-scale multistage stochastic programming (MSP) problems poses a significant challenge as commonly used stagewise decomposition algorithms, including stochastic dual dynamic programming (SDDP), face growing time complexity as…

We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…

In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…

Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML…

We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the…

Large language models (LLMs) achieve strong performance in long-horizon decision-making tasks through multi-step interaction and reasoning at test time. While practitioners commonly believe a higher task success rate necessitates the use of…

Reinforcement learning with verifiers (RLVR) is a central paradigm for improving large language model (LLM) reasoning, yet existing methods often suffer from limited exploration. Policies tend to collapse onto a few reasoning patterns and…

Linear Temporal Logic (LTL) is a formal way of specifying complex objectives for planning problems modeled as Markov Decision Processes (MDPs). The planning problem aims to find the optimal policy that maximizes the satisfaction probability…

We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…

Based on the notion of supercodes, we propose a two-phase maximum-likelihood soft-decision decoding (tpMLSD) algorithm for binary linear block codes in this work. The first phase applies the Viterbi algorithm backwardly to a trellis derived…

The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but…

We consider the problem of finding a control policy for a Markov Decision Process (MDP) to maximize the probability of reaching some states while avoiding some other states. This problem is motivated by applications in robotics, where such…