Related papers: A Dual Approximate Dynamic Programming Approach to…
Several attempts to dampen the curse of dimensionnality problem of the Dynamic Programming approach for solving multistage optimization problems have been investigated. One popular way to address this issue is the Stochastic Dual Dynamic…
This paper presents a new column-and-constraint generation method for two-stage robust mixed-integer programs with finite uncertainty sets. Our method combines and extends speed-up techniques used in previous column-and-constraint…
We investigate the dual of a Multistage Stochastic Linear Program (MSLP) to study two questions for this class of problems. The first of these questions is the study of the optimal value of the problem as a function of the involved…
The maximization of reach-avoid probabilities for stochastic systems is a central topic in the control literature. Yet, the available methods are either restricted to low-dimensional systems or suffer from conservative approximations. To…
The paper addresses two variants of the stochastic shortest path problem ('optimize the accumulated weight until reaching a goal state') in Markov decision processes (MDPs) with integer weights. The first variant optimizes partial expected…
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…
Nowadays, algorithms with fast convergence, small memory footprints, and low per-iteration complexity are particularly favorable for artificial intelligence applications. In this paper, we propose a doubly stochastic algorithm with a novel…
It was recently shown that dynamic programming (DP) methods for finding static CVaR-optimal policies in Markov Decision Processes (MDPs) can fail when based on the dual formulation, yet the root cause of this failure remains unclear. We…
Network resource allocation shows revived popularity in the era of data deluge and information explosion. Existing stochastic optimization approaches fall short in attaining a desirable cost-delay tradeoff. Recognizing the central role of…
We consider a two-stage robust facility location problem on a metric under an uncertain demand. The decision-maker needs to decide on the (integral) units of supply for each facility in the first stage to satisfy an uncertain second-stage…
Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
We consider a dynamic programming (DP) approach to approximately solving an infinite-horizon constrained Markov decision process (CMDP) problem with a fixed initial-state for the expected total discounted-reward criterion with a…
Stochastic gradient descent (SGD) is a powerful optimization technique that is particularly useful in online learning scenarios. Its convergence analysis is relatively well understood under the assumption that the data samples are…
Adaptive dynamic programming (ADP) for stochastic linear quadratic regulation (LQR) demands the precise computation of stochastic integrals during policy iteration (PI). In a fully model-free problem setting, this computation can only be…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…
We consider a two-stage stochastic optimization problem, in which a long-term optimization variable is coupled with a set of short-term optimization variables in both objective and constraint functions. Despite that two-stage stochastic…
The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…
The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the…