arXiv subjects

Julien Grand-Clement

Publications and source records attributed to Julien Grand-Clement.

2 recordsLinked to original sources

arXiv2021

A First-Order Approach To Accelerated Value Iteration

Markov decision processes (MDPs) are used to model stochastic systems in many applications. Several efficient algorithms to compute optimal policies have been studied in the literature, including value iteration (VI) and policy iteration. However, these do not scale well especially when the discount factor for the infinite horizon discounted reward, $λ$, gets close to $1$. In particular, the running time scales as $O \left( 1/(1-λ) \right)$ for these algorithms. In this paper, our goal is to design new algorithms that scale better than previous approaches when $λ$ approaches $1$. Our main contribution is to present a connection between VI and gradient descent and adapt the ideas of acceleration and momentum in convex optimization to design faster algorithms for MDPs. We prove theoretical guarantees of a faster convergence of our algorithms for the computation of the value function of a policy, where the running times of our algorithms scale as $O \left( 1/\sqrt{1-λ} \right)$ for reversible MDP instances. The improvement is quite analogous to Nesterov's acceleration and momentum in convex optimization. We also provide a lower bound on the convergence properties of any first-order algorithm for solving MDPs, presenting a family of MDPs instances for which no algorithm can converge faster than VI when the number of iterations is smaller than the number of states. We introduce a Safe Accelerated Value Iteration (S-AVI), which alternates between accelerated updates and value iteration updates. Our algorithm S-AVI is worst-case optimal and retains the theoretical convergence properties of VI while exhibiting strong empirical performances, providing significant speedups compared to classical approaches (up to one order of magnitude in many cases) for a large test bed of MDP instances.

math.OC↗

arXiv2021

Robust Policies For Proactive ICU Transfers

Patients whose transfer to the Intensive Care Unit (ICU) is unplanned are prone to higher mortality rates than those who were admitted directly to the ICU. Recent advances in machine learning to predict patient deterioration have introduced the possibility of \emph{proactive transfer} from the ward to the ICU. In this work, we study the problem of finding \emph{robust} patient transfer policies which account for uncertainty in statistical estimates due to data limitations when optimizing to improve overall patient care. We propose a Markov Decision Process model to capture the evolution of patient health, where the states represent a measure of patient severity. Under fairly general assumptions, we show that an optimal transfer policy has a threshold structure, i.e., that it transfers all patients above a certain severity level to the ICU (subject to available capacity). As model parameters are typically determined based on statistical estimations from real-world data, they are inherently subject to misspecification and estimation errors. We account for this parameter uncertainty by deriving a robust policy that optimizes the worst-case reward across all plausible values of the model parameters. We show that the robust policy also has a threshold structure under fairly general assumptions. Moreover, it is more aggressive in transferring patients than the optimal nominal policy, which does not take into account parameter uncertainty. We present computational experiments using a dataset of hospitalizations at 21 KNPC hospitals, and present empirical evidence of the sensitivity of various hospital metrics (mortality, length-of-stay, average ICU occupancy) to small changes in the parameters. Our work provides useful insights into the impact of parameter uncertainty on deriving simple policies for proactive ICU transfer that have strong empirical performance and theoretical guarantees.

cs.LG↗