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Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…
In this paper, we consider an integrated MSP-MDP framework which captures features of Markov decision process (MDP) and multistage stochastic programming (MSP). The integrated framework allows one to study a dynamic decision-making process…
We consider large-scale Markov decision processes (MDPs) with a risk measure of variability in cost, under the risk-aware MDPs paradigm. Previous studies showed that risk-aware MDPs, based on a minimax approach to handling risk, can be…
We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…
A Markov decision process can be parameterized by a transition kernel and a reward function. Both play essential roles in the study of reinforcement learning as evidenced by their presence in the Bellman equations. In our inquiry of various…
State of the art methods for target tracking with sensor management (or controlled sensing) are model-based and are obtained through solutions to Partially Observable Markov Decision Process (POMDP) formulations. In this paper a…
Robust Markov Decision Processes (RMDPs) have recently been recognized as a valuable and promising approach to discovering a policy with creditable performance, particularly in the presence of a dynamic environment and estimation errors in…
We study a Q learning algorithm for continuous time stochastic control problems. The proposed algorithm uses the sampled state process by discretizing the state and control action spaces under piece-wise constant control processes. We show…
In this paper, we investigate the concentration properties of cumulative reward in Markov Decision Processes (MDPs), focusing on both asymptotic and non-asymptotic settings. We introduce a unified approach to characterize reward…
We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the optimal policy and…
We study reinforcement learning (RL) with linear function approximation where the underlying transition probability kernel of the Markov decision process (MDP) is a linear mixture model (Jia et al., 2020; Ayoub et al., 2020; Zhou et al.,…
Value-at-risk (VaR), also known as quantile, is a crucial risk measure in finance and other fields. However, optimizing VaR metrics in Markov decision processes (MDPs) is challenging because VaR is non-additive and the traditional dynamic…
We consider the problem of constrained Markov Decision Process (CMDP) where an agent interacts with a unichain Markov Decision Process. At every interaction, the agent obtains a reward. Further, there are $K$ cost functions. The agent aims…
A central task in control theory, artificial intelligence, and formal methods is to synthesize reward-maximizing strategies for agents that operate in partially unknown environments. In environments modeled by gray-box Markov decision…
This work addresses the general problem of control synthesis for continuous-space, discrete-time stochastic systems with probabilistic guarantees via finite abstractions. While established methods exist, they often trade off accuracy for…
This work tackles the problem of robust zero-shot planning in non-stationary stochastic environments. We study Markov Decision Processes (MDPs) evolving over time and consider Model-Based Reinforcement Learning algorithms in this setting.…
We study infinite-horizon robust Markov decision processes (MDPs) on continuous state spaces with structured rectangular ambiguity set. The proposed ambiguity set falls within the convex hull of unknown generating kernels. We utilize the…
Designing sample-efficient and computationally feasible reinforcement learning (RL) algorithms is particularly challenging in environments with large or infinite state and action spaces. In this paper, we advance this effort by presenting…
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the…
Multi-period mean-variance optimization is a long-standing problem, caused by the failure of dynamic programming principle. This paper studies the mean-variance optimization in a setting of finite-horizon discrete-time Markov decision…