Related papers: Fully lifted random duality theory
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…
The robustness of fault detection algorithms against uncertainty is crucial in the real-world industrial environment. Recently, a new probabilistic design scheme called distributionally robust fault detection (DRFD) has emerged and received…
In this letter, the optimality of the likelihood ratio test (LRT) is investigated for binary hypothesis testing problems in the presence of a behavioral decision-maker. By utilizing prospect theory, a behavioral decision-maker is modeled to…
Self-reflection capabilities emerge in Large Language Models after RL post-training, with multi-turn RL achieving substantial gains over SFT counterparts. Yet the mechanism of how a unified optimization objective gives rise to functionally…
There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true…
The Doob transform technique enables the study of a killed random walk (KRW) via a random walk (RW) with transition probabilities tilted by a discrete massive harmonic function. The main contribution of this paper is to transfer this…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We find large deviations rates for consensus-based distributed inference for directed networks. When the topology is deterministic, we establish the large deviations principle and find exactly the corresponding rate function, equal at all…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any…
Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows…
Inductive reasoning, a cornerstone of human cognition, enables generalization from limited data but hasn't yet been fully achieved by large language models (LLMs). While modern LLMs excel at reasoning tasks, their ability to maintain stable…
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…
Reinforcement Learning (RL) serves as a versatile framework for sequential decision-making, finding applications across diverse domains such as robotics, autonomous driving, recommendation systems, supply chain optimization, biology,…
Distributionally robust optimization (DRO) is a worst-case framework for stochastic optimization under uncertainty that has drawn fast-growing studies in recent years. When the underlying probability distribution is unknown and observed…
One key challenge for multi-task Reinforcement learning (RL) in practice is the absence of task indicators. Robust RL has been applied to deal with task ambiguity, but may result in over-conservative policies. To balance the worst-case…
Researchers have demonstrated that Deep Reinforcement Learning (DRL) is a powerful tool for finding policies that perform well on complex robotic systems. However, these policies are often unpredictable and can induce highly variable…
While traditional Deep Learning (DL) optimization methods treat all training samples equally, Distributionally Robust Optimization (DRO) adaptively assigns importance weights to different samples. However, a significant gap exists between…
We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed…
The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph…