Related papers: Algorithmic random duality theory -- large scale C…

Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces…

We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…

Reinforcement Learning (RL) algorithms are known to suffer from the curse of dimensionality, which refers to the fact that large-scale problems often lead to exponentially high sample complexity. A common solution is to use deep neural…

Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust…

Several well-known algorithms in the field of combinatorial optimization can be interpreted in terms of the primal-dual method for solving linear programs. For example, Dijkstra's algorithm, the Ford-Fulkerson algorithm, and the Hungarian…

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

This paper demonstrates a mathematically correct and computationally powerful method for solving 3D topology optimization problems. This method is based on canonical duality theory (CDT) developed by Gao in nonconvex mechanics and global…

Bias is a common problem inherent in recommender systems, which is entangled with users' preferences and poses a great challenge to unbiased learning. For debiasing tasks, the doubly robust (DR) method and its variants show superior…

We consider the capacity of \emph{treelike committee machines} (TCM) neural networks. Relying on Random Duality Theory (RDT), \cite{Stojnictcmspnncaprdt23} recently introduced a generic framework for their capacity analysis. An upgrade…

In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with non-Lipschitzian value…

We consider primal-dual-based reinforcement learning (RL) in episodic constrained Markov decision processes (CMDPs) with non-stationary objectives and constraints, which plays a central role in ensuring the safety of RL in time-varying…

A basic model in sequential decision making is the Markov decision process (MDP), which is extended to Robust MDPs (RMDPs) by allowing uncertainty in transition probabilities and optimizing against the worst-case transition probabilities…

We establish a collection of closed-loop guarantees and propose a scalable optimization algorithm for distributionally robust model predictive control (DRMPC) applied to linear systems, convex constraints, and quadratic costs. Via standard…

There hardly exists a general solver that is efficient for scheduling problems due to their diversity and complexity. In this study, we develop a two-stage framework, in which reinforcement learning (RL) and traditional operations research…

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…

In this study, we present a deep learning-optimization framework to tackle dynamic mixed-integer programs. Specifically, we develop a bidirectional Long Short Term Memory (LSTM) framework that can process information forward and backward in…

We study robust Markov decision processes (RMDPs) with non-rectangular uncertainty sets, which capture interdependencies across states unlike traditional rectangular models. While non-rectangular robust policy evaluation is generally…

We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…

We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex…

Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that…