Related papers: An exact solution in Markov decision process with …
A time-discrete approach avoids the assumption of an 'integration sense'. New path increments (in a short time step) are complete in the order of that step, and not Gaussian distributed when the noise is multiplicative; this eliminates an…
Policy optimization algorithms are crucial in many fields but challenging to grasp and implement, often due to complex calculations related to Markov decision processes and varying use of discount and average reward setups. This paper…
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon. Such…
In this paper, we establish the well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations with generalized Lipschitz-type coefficients driven by general multiplicative noises. To ensure the…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
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…
In this paper, we prove the existence of a unique maximal local strong solutions to a stochastic system for both 2D and 3D penalised nematic liquid crystals driven by multiplicative Gaussian noise. In the 2D case, we show that this solution…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…
Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian…
We consider a dynamical system with finitely many equilibria and perturbed by small noise, in addition to being controlled by an `expensive' control. The controlled process is optimal for an ergodic criterion with a running cost that…
Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for…
It is well known that for any finite state Markov decision process (MDP) there is a memoryless deterministic policy that maximizes the expected reward. For partially observable Markov decision processes (POMDPs), optimal memoryless policies…
Stochastic optimization is a vital field in the realm of mathematical optimization, finding applications in diverse areas ranging from operations research to machine learning. In this paper, we introduce a novel first-order optimization…
We study computationally and statistically efficient Reinforcement Learning algorithms for the linear Bellman Complete setting. This setting uses linear function approximation to capture value functions and unifies existing models like…
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…
The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decision-making by economic agents. In the average-cost optimal control…
We resolve the open question regarding the sample complexity of policy learning for maximizing the long-run average reward associated with a uniformly ergodic Markov decision process (MDP), assuming a generative model. In this context, the…