相关论文: Maturity randomization for stochastic control prob…
Many problems in Reinforcement Learning (RL) seek an optimal policy with large discrete multidimensional yet unordered action spaces; these include problems in randomized allocation of resources such as placements of multiple security…
We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of…
In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial…
This paper analyzes a discretization of a stochastic parabolic optimal control problem, where the diffusion term contains the control variable. With rough data, the convergence of the discretization is derived. In addition, a Monte-Carlo…
We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This…
We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…
This article presents a dynamic regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…
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…
Policy optimization is among the most popular and successful reinforcement learning algorithms, and there is increasing interest in understanding its theoretical guarantees. In this work, we initiate the study of policy optimization for the…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
We employ optimal control theory to study the problem of estimating the probability density function from a data set originating from an unknown probability distribution. The original variational problem is reformulated as a multi-stage…
This paper studies the optimization of observation channels (stochastic kernels) in partially observed stochastic control problems. In particular, existence and continuity properties are investigated mostly (but not exclusively)…
In this paper, the problem of load uncertainty in compliance problems is addressed where the uncertainty is described in the form of a set of finitely many loading scenarios. Computationally more efficient methods are proposed to exactly…
In this paper the connection between stochastic optimal control and reinforcement learning is investigated. Our main motivation is to apply importance sampling to sampling rare events which can be reformulated as an optimal control problem.…
Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…
We examine a multi-stage stochastic optimization problem characterized by stagewise-independent, decision-dependent noises with strict constraints. The problem assumes convexity in that, following a specific relaxation, it transforms into a…