Related papers: From Optimization to Control: Quasi Policy Iterati…
Many applications -- including power systems, robotics, and economics -- involve a dynamical system interacting with a stochastic and hard-to-model environment. We adopt a reinforcement learning approach to control such systems.…
Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…
In this paper, we provide a novel algorithm for solving planning and learning problems of Markov decision processes. The proposed algorithm follows a policy iteration-type update by using a rank-one approximation of the transition…
In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
Advances in the experimental demonstration of quantum processors have provoked a surge of interest to the idea of practical implementation of quantum computing over last years. It is expected that the use of quantum algorithms will…
In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…
Novel advanced policy gradient (APG) methods, such as Trust Region policy optimization and Proximal policy optimization (PPO), have become the dominant reinforcement learning algorithms because of their ease of implementation and good…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
This paper considers a cross-layer adaptive modulation system that is modeled as a Markov decision process (MDP). We study how to utilize the monotonicity of the optimal transmission policy to relieve the computational complexity of dynamic…
We study an approximation method for partially observed Markov decision processes (POMDPs) with continuous spaces. Belief MDP reduction, which has been the standard approach to study POMDPs requires rigorous approximation methods for…
Policy Iteration (PI) is a classical family of algorithms to compute an optimal policy for any given Markov Decision Problem (MDP). The basic idea in PI is to begin with some initial policy and to repeatedly update the policy to one from an…
This note re-visits the rolling-horizon control approach to the problem of a Markov decision process (MDP) with infinite-horizon discounted expected reward criterion. Distinguished from the classical value-iteration approach, we develop an…
In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one,…
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 (or minimize…
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…
In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true…
Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…
Policy iteration enjoys a local quadratic rate of contraction, but its iterations are computationally expensive for Markov decision processes (MDPs) with a large number of states. In light of the connection between policy iteration and the…
We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…