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We propose a new stochastic primal-dual optimization algorithm for planning in a large discounted Markov decision process with a generative model and linear function approximation. Assuming that the feature map approximately satisfies…
We propose a new method for optimistic planning in infinite-horizon discounted Markov decision processes based on the idea of adding regularization to the updates of an otherwise standard approximate value iteration procedure. This…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (minimize…
Continuous-time Markov decision processes are an important class of models in a wide range of applications, ranging from cyber-physical systems to synthetic biology. A central problem is how to devise a policy to control the system in order…
We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
We study the $(\varepsilon, \delta)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
Calculating optimal policies is known to be computationally difficult for Markov decision processes (MDPs) with Borel state and action spaces. This paper studies finite-state approximations of discrete time Markov decision processes with…
This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation…
For parameterized mixed-binary optimization problems, we construct local decision rules that prescribe near-optimal courses of action across a set of parameter values. The decision rules stem from solving risk-adaptive training problems…
We propose an algorithm for deterministic continuous Markov Decision Processes with sparse rewards that computes the optimal policy exactly with no dependency on the size of the state space. The algorithm has time complexity of $O( |R|^3…
Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address…
In this paper we propose several novel distributed gradient-based temporal difference algorithms for multi-agent off-policy learning of linear approximation of the value function in Markov decision processes with strict information…
We study the computational complexity of the infinite-horizon discounted-reward Markov Decision Problem (MDP) with a finite state space $|\mathcal{S}|$ and a finite action space $|\mathcal{A}|$. We show that any randomized algorithm needs a…
Revision of the paper previously entitled "Learning a Machine for the Decision in a Partially Observable Markov Universe" In this paper, we are interested in optimal decisions in a partially observable universe. Our approach is to directly…
In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with non-negative real-valued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a…
In this paper, we consider the problem of optimization and learning for constrained and multi-objective Markov decision processes, for both discounted rewards and expected average rewards. We formulate the problems as zero-sum games where…
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that…
This paper considers the problem of finding near-optimal Markovian randomized (MR) policies for finite-state-action, infinite-horizon, constrained risk-sensitive Markov decision processes (CRSMDPs). Constraints are in the form of standard…