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We study the Constrained Convex Markov Decision Process (MDP), where the goal is to minimize a convex functional of the visitation measure, subject to a convex constraint. Designing algorithms for a constrained convex MDP faces several…
The allocation of scarce spectral resources to support as many user applications as possible while maintaining reasonable quality of service is a fundamental problem in wireless communication. We argue that the problem is best formulated in…
Multi-model Markov decision process (MMDP) is a promising framework for computing policies that are robust to parameter uncertainty in MDPs. MMDPs aim to find a policy that maximizes the expected return over a distribution of MDP models.…
We build on a recently introduced geometric interpretation of Markov Decision Processes (MDPs) to analyze classical MDP-solving algorithms: Value Iteration (VI) and Policy Iteration (PI). First, we develop a geometry-based analytical…
Dynamic Programming (DP) provides standard algorithms to solve Markov Decision Processes. However, these algorithms generally do not optimize a scalar objective function. In this paper, we draw connections between DP and (constrained)…
Markov decision processes (MDPs) is viewed as an optimization of an objective function over certain linear operators over general function spaces. A new existence result is established for the existence of optimal policies in general MDPs,…
We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs). The primary goal of our techniques is to improve performance by avoiding an exhaustive…
Markov Chain Monte Carlo (MCMC) sampling methods are widely used but often encounter either slow convergence or biased sampling when applied to multimodal high dimensional distributions. In this paper, we present a general framework of…
We investigate the problem of best-policy identification in discounted Markov Decision Processes (MDPs) when the learner has access to a generative model. The objective is to devise a learning algorithm returning the best policy as early as…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not…
To overcome the curses of dimensionality and modeling of Dynamic Programming (DP) methods to solve Markov Decision Process (MDP) problems, Reinforcement Learning (RL) methods are adopted in practice. Contrary to traditional RL algorithms…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
The importance of hierarchically structured representations for tractable planning has long been acknowledged. However, the questions of how people discover such abstractions and how to define a set of optimal abstractions remain open. This…
Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a…
General purpose intelligent learning agents cycle through (complex,non-MDP) sequences of observations, actions, and rewards. On the other hand, reinforcement learning is well-developed for small finite state Markov Decision Processes…
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…
We consider the reinforcement learning problem for the constrained Markov decision process (CMDP), which plays a central role in satisfying safety or resource constraints in sequential learning and decision-making. In this problem, we are…
We present a new geometric interpretation of Markov Decision Processes (MDPs) with a natural normalization procedure that allows us to adjust the value function at each state without altering the advantage of any action with respect to any…
The main goal of this paper is to investigate continuous-time distributed dynamic programming (DP) algorithms for networked multi-agent Markov decision problems (MAMDPs). In our study, we adopt a distributed multi-agent framework where…