Related papers: Neural Stochastic Dual Dynamic Programming
Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…
Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for…
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…
Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…
The Dynamic Pickup and Delivery Problem (DPDP) is aimed at dynamically scheduling vehicles among multiple sites in order to minimize the cost when delivery orders are not known a priori. Although DPDP plays an important role in modern…
This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as…
Approximate dynamic programming (ADP) has proven itself in a wide range of applications spanning large-scale transportation problems, health care, revenue management, and energy systems. The design of effective ADP algorithms has many…
Constrained Markov Decision Processes (CMDPs) are critical in many high-stakes applications, where decisions must optimize cumulative rewards while strictly adhering to complex nonlinear constraints. In domains such as power systems,…
We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the…
Economic forecasting is concerned with the estimation of some variable like gross domestic product (GDP) in the next period given a set of variables that describes the current situation or state of the economy, including industrial…
In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…
Large-scale deep learning models contribute to significant performance improvements on varieties of downstream tasks. Current data and model parallelism approaches utilize model replication and partition techniques to support the…
Though many compilation and runtime systems have been developed for DNNs in recent years, the focus has largely been on static DNNs. Dynamic DNNs, where tensor shapes and sizes and even the set of operators used are dependent upon the input…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
The presented work addresses two-stage stochastic programs (2SPs), a broadly applicable model to capture optimization problems subject to uncertain parameters with adjustable decision variables. In case the adjustable or second-stage…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…