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Repetitive Scenario Design (RSD) is a randomized approach to robust design based on iterating two phases: a standard scenario design phase that uses $N$ scenarios (design samples), followed by randomized feasibility phase that uses $N_o$…
In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which…
This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the…
Complete reliance on the fitted model in response surface experiments is risky and relaxing this assumption, whether out of necessity or intentionally, requires an experimenter to account for multiple conflicting objectives. This work…
In safe reinforcement learning (SRL) problems, an agent explores the environment to maximize an expected total reward and meanwhile avoids violation of certain constraints on a number of expected total costs. In general, such SRL problems…
This paper presents an algorithm for reliability-based topology optimization of linear elastic continua under random-field material model. The modelling random field is discretized into a small number of random variables, and then the…
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…
First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…
The goal of robust constrained reinforcement learning (RL) is to optimize an agent's performance under the worst-case model uncertainty while satisfying safety or resource constraints. In this paper, we demonstrate that strong duality does…
Time-distributed Optimization (TDO) is an approach for reducing the computational burden of Model Predictive Control (MPC). When using TDO, optimization iterations are distributed over time by maintaining a running solution estimate and…
LiDAR-based SLAM is recognized as one effective method to offer localization guidance in rough environments. However, off-the-shelf LiDAR-based SLAM methods suffer from significant pose estimation drifts, particularly components relevant to…
Single-trajectory reinforcement learning (RL) methods aim to optimize policies from datasets consisting of (prompt, response, reward) triplets, where scalar rewards are directly available. This supervision format is highly practical, as it…
Multimodal large language models (MLLMs) have shown promising capabilities in reasoning tasks, yet still struggle with complex problems requiring explicit self-reflection and self-correction, especially compared to their unimodal text-based…
Large Language Models (LLMs) have demonstrated remarkable in-context learning capabilities, enabling flexible utilization of limited historical information to play pivotal roles in reasoning, problem-solving, and complex pattern recognition…
Although multimodal large language models (MLLMs) excel in high-level vision-language reasoning, they lack inherent awareness of visual saliency, making it difficult to identify key visual elements. To bridge this gap, we propose…
Wasserstein distance-based distributionally robust optimization (DRO) has received much attention lately due to its ability to provide a robustness interpretation of various learning models. Moreover, many of the DRO problems that arise in…
Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively…
We consider the task of estimating a structural model of dynamic decisions by a human agent based upon the observable history of implemented actions and visited states. This problem has an inherent nested structure: in the inner problem, an…
Reliability-based optimization (RBO) is crucial for identifying optimal risk-informed decisions for designing and operating engineering systems. However, its computation remains challenging as it requires a concurrent task of optimization…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…